Have you ever tried to fix something, maybe a toy or a small gadget, and found that a tiny screw just wouldn’t fit? That’s exactly what happened to Sonu one day!
He was watching his mother trying to fix his favourite toy car. She had a small screw, but it just wasn’t the right size to join two pieces together.
Sonu watched with wide eyes, full of curiosity. Why wouldn’t it work?
Sonu’s mother trying to fix his toy with small screw
His mother explained, “This screw isn’t quite the right size, Sonu.” She rummaged through her toolbox and found another screw.
This time, it worked perfectly, and the toy was fixed! To Sonu, both screws looked almost exactly the same. He picked them up and looked very, very closely.
Ah! He could see it now – one screw was just a tiny bit longer than the other.Yes, one screw was bit longer than the other
Sonu was amazed. How could such a small, almost invisible difference in length make such a big difference in fixing his toy?
He became really curious. How much longer was one screw than the other?
And how could he even measure such a tiny difference when they looked so similar?
This little adventure with the screws got Sonu thinking about measurement. Sometimes, just saying something is ‘long’ or ‘short’ isn’t enough. We need to know exactly how long or short it is.
Measuring with Greater PrecisionLook at the screws below placed on different rulers. Can you see how the bottom ruler, with more marks, helps us measure more accurately?Screws placed on different Ruler to measure the length
Look at the top ruler first. It only has markings for whole centimeters (cm). Using this ruler, we can only say that both screws are between 2 cm and 3 cm long. That’s not very helpful when we need to know which one is longer!
Now look at the middle ruler. This one has more markings – it divides each centimeter into 10 equal parts. With this ruler, we can be more precise. The first screw measures 2 7/10 cm (or 2.7 cm). That means it’s 2 whole centimeters plus 7 tenths of a centimeter.
The bottom ruler is even more detailed. It divides each centimeter into many tiny parts, allowing for even more precise measurements.
A Tenth Part
Have you ever wondered how we can measure things more precisely? Let’s explore this with a simple example.
Look at the pencil shown in the figure below:
Notice how the pencil’s length isn’t exactly 3 units or 4 units. It’s somewhere in between. When we look at the ruler with more detailed markings (the bottom one), we can see that the pencil measures 3 and 4 tenths of a unit, which we write as
But what does actually mean? Let’s break it down:
3 represents the whole units (3 × 1)
4/10 represents four one-tenths (4 × 1/10)
So the total length is (3 × 1) + (4 × 1/10) units.
This length is the same as 34 one-tenths units because 10 one-tenths units make one unit.
There are different ways to express measurements with tenths:
is read as “four and one-tenth”
4/10 is read as “four-tenths”
41/10 is read as “forty-one tenths”
is read as “forty-one and one-tenth”
Example 1:Sonu was measuring parts of his arm. The length of his lower arm was units, and his upper arm was units. What is the total length of his arm?
Sol: To find the total length, we need to add the measurements:
Method 1:
Lower arm: 2 units and 7 tenths
Upper arm: 3 units and 6 tenths
Total units: 2 + 3 = 5 units
Total tenths: 7 + 6 = 13 tenths
But 13 tenths equals 1 unit and 3 tenths (since 10 tenths = 1 unit).
So the total length is 5 + 1 + 3/10 = units.
Method 2:
We can convert both measurements to tenths and then add:
So Sonu’s complete arm measures units long.
A Hundredth Part
We learned about tenths, which help us measure more precisely than whole units. But what if we need to be even more precise? Let’s explore!
Imagine you have a sheet of paper that measures 8 whole 9/10 units long. That’s 8 whole units and 9 tenths of a unit.
Now, what happens if you fold this paper exactly in half along its length? What would the new length be?
If we try to measure the folded paper using a ruler marked only in tenths, we might find that the length falls between two tenth markings. For example, it might be between and units. We can estimate, but we can’t get an exact measurement with just tenths.
Try yourself:
What did Sonu’s mother find in her toolbox to fix the toy car?
A.A bigger screw
B.A longer screw
C.A smaller screw
D.A different tool
View Solution
Introducing Hundredths
To measure even smaller lengths, we can do something similar to what we did before: we can divide each tenth into 10 smaller, equal parts.
Think about it:
1 unit is divided into 10 tenths.
Each tenth is divided into 10 smaller parts.
So, how many of these tiny parts make up one whole unit? That’s right!
10 tenths × 10 parts per tenth = 100 parts.
Each of these tiny parts is called one-hundredth (1/100) of the unit.
Measuring with Hundredths
Now, let’s go back to our folded paper. Using a ruler with hundredth markings, we can measure its length much more accurately. Let’s say the folded edge lands exactly on the 5th small mark after .
We’ve seen how dividing units into tenths and then hundredths helps us measure more precisely. But why do we always divide by 10? Why not 4, or 5, or 8 equal parts?
Yes, we can.
Look at the pencils in the image:
One ruler is marked in tenths (0.1, 0.2, 0.3…)
The other is marked in quarters (¼, ½, ¾…)
If we split each quarter further into 4 smaller parts, we get sixteenths (1⁄16), which are even more accurate.
So, why do we usually split into 10 parts?
That’s because of our number system – the Indian place value system (and the international system too) is based on 10s.
Each place value is 10 times:
Bigger than the one to its right
Smaller than the one to its left
For example:
10 ones = 1 ten
10 tens = 1 hundred
10 hundreds = 1 thousand
That’s why decimal place values go like:
0.1 = 1⁄10 (one-tenth)
0.01 = 1⁄100 (one-hundredth)
0.001 = 1⁄1000 (one-thousandth)
Notice a pattern?
Each place value is 10 times bigger than the one immediately to its right. Or, looking the other way, each place value is 10 times smaller (or one-tenth) than the one immediately to its left.
To extend this system to numbers smaller than one, it makes perfect sense to continue this pattern: divide the Ones place by 10!
Dividing 1 by 10 gives one-tenth (1/10).
Dividing one-tenth (1/10) by 10 gives one-hundredth (1/100).
Dividing one-hundredth (1/100) by 10 gives one-thousandth (1/1000).
…and so on!
What will the fraction be when 1/ 100 is split into 10 equal parts?
It will be 1/ 1000 , i.e., a thousand such parts make up a unit.
This system, based on the number 10, is called the decimal system.
Try yourself:
What is each tiny part called when a unit is divided into 100 parts?
A.One-quarter
B.One-tenth
C.One-hundredth
D.One-thousandth
View Solution
Notation, Writing and Reading of Numbers
We need a way to clearly separate the whole number part from the fractional part (tenths, hundredths, etc.). If we just wrote 42, how would we know if it means “4 tens and 2 ones” (42) or “4 ones and 2 tenths” ()?
To solve this, we use a special symbol: the decimal point (.) .
It acts as a separator between the Ones place and the Tenths place.
Whole Numbers are to the left of the decimal point.
Fractional Parts (tenths, hundredths, etc.) are to the right of the decimal point.
Let’s look at some examples:
These numbers, when shown through place value, are as follows:
Reading Decimal Numbers
How do we read these numbers aloud?
705: “Seven hundred five” (No decimal part)
70.5: “Seventy point five” (or “Seventy and five tenths”)
7.05: “Seven point zero five” (or “Seven and five hundredths”)
Important:When reading the digits after the decimal point, we usually say each digit individually (like “point two seven four”, not “point two hundred seventy-four”). This helps avoid confusion about place value.
Example 5: How can we write 234 tenths in decimal form?
Sol: 234 tenths = 234/10
We can break this down:
234/10 = (200 + 30 + 4) / 10
= 200/10 + 30/10 + 4/10
= 20 + 3 + 4/10
= 23.4
In decimal notation, this is 23.4.
Units of Measurement
Now that we understand decimal numbers, let’s see how they help us work with different units of measurement, especially for length.
Length Conversion: Millimeters (mm) and Centimeters (cm)
You’ve probably used a ruler marked in centimeters (cm) and millimeters (mm). You might already know that:
⇒ 1 cm = 10 mm
This means that each centimeter is divided into 10 equal parts, and each part is a millimeter.
So, how much of a centimeter is one millimeter?
Since 10 mm make 1 cm, then:
⇒ 1 mm = 1/10 cm
Using our new decimal notation, we can write this as:
⇒ 1 mm = 0.1 cm (one-tenth of a centimeter)
Let’s practice converting between mm and cm using decimals:
Q: How many cm is 5 mm?
5 mm = 5/10 cm = 0.5 cm
Q: How many cm is 12 mm?
12 mm = 10 mm + 2 mm
= 1 cm + 2/10 cm
= 1.2 cm
Q: How many mm is 5.6 cm?
5.6 cm = 5 cm and 6/10 cm
= (5 × 10 mm) + (6/10 × 10 mm)
= 50 mm + 6 mm = 56 mm
Length Conversion: Centimeters (cm) and Meters (m)
We also know the relationship between centimeters and meters:
⇒ 1 m = 100 cm
This means one meter is divided into 100 equal parts, and each part is a centimeter. So, how much of a meter is one centimeter?
Since 100 cm make 1 m, then:
⇒ 1 cm = 1/100 m
Using decimal notation:
⇒ 1 cm = 0.01 m (one-hundredth of a meter)
These tiny measurements show how important tenths and hundredths (and even smaller units!) are in science and everyday life.
Weight ConversionIt shows how weights can be expressed in decimal form and why that’s useful in real life.
1 kilogram (kg) = 1000 grams (g)
So, 1 gram = 1/1000 kg = 0.001 kg
Q: How many kilograms is 5 g?
5 g = 5 ÷ 1000 = 0.005 kg
Q: How many kilograms is 10 g?
10 g = 10 ÷ 1000 = 0.010 kg
As each gram is one-thousandth of a kg, 254 g can be written as
This can be broken as: 200 g → 0.2 kg 50 g → 0.05 kg 4 g → 0.004 kg Total = 0.254 kg
Rupee ─ Paise conversion
In India, the currency system is based on rupees and paise.
Basic Conversion Rule:
1 rupee = 100 paise
So, 1 paise = 1/100 rupee = ₹ 0.01
That means if you divide 1 rupee into 100 equal parts, each part is called 1 paise.
How many rupees is 75 paise?
Locating and Comparing Decimals
What are Decimals?
Decimals are numbers that show values smaller than 1. They help us measure things more accurately, like length, weight, and money.
How to Show Decimals on a Number Line?
To place a decimal like 1.4 on a number line:
First, see which two whole numbers it lies between. 1.4 lies between 1 and 2.
Then divide the gap between 1 and 2 into 10 equal parts.
The 4th division after 1 is 1.4.
So, 1.4 = 1 unit and 4 tenths.
Does Adding Zeros Change the Value?
Let’s compare:
0.2 = 0.20 = 0.200 — All same (2 tenths)
But:
0.02 = 2 hundredths 0.002 = 2 thousandths These are different.
Adding zeros to the right after decimal digits doesn’t change the value. But changing the place value (tenths, hundredths, thousandths) does.
Try yourself:
What does a decimal point separate in a number?
A.Large numbers from small numbers
B.Whole numbers from fractional parts
C.Even numbers from odd numbers
D.Positive numbers from negative numbers
View Solution
Ordering Decimal Numbers
Look at these numbers:
4.5, 4.05, 4.005, 4.050, 4.50
Let’s convert them all to the same format (3 decimal places):
4.500
4.050
4.005
4.050
4.500
Now, it’s easier to compare:
Smallest = 4.005
Largest = 4.500
4.5 = 4.50
4.05 = 4.050
Closest Decimals
This concept teaches you how to compare decimal numbers and figure out which decimal is closest to a given number.
Let’s compare the numbers: 0.9, 1.1, 1.01, and 1.11
Which one is closest to 1?
Step 1: Arrange the numbers in order: 0.9 < 1 < 1.01 < 1.1 < 1.11
Step 2: See how far each number is from 1:
0.9 is 0.1 away (10/100)
1.1 is also 0.1 away
1.01 is just 0.01 away (1/100)
So, 1.01 is closest to 1.
This improves your understanding of how place value affects the size of decimal numbers.
Addition and Subtraction of Decimals
This concept teaches how to add and subtract numbers with decimals (like 2.7, 3.5, etc.), just like you do with whole numbers. The only difference is that you have to align the decimal points and work carefully with tenths, hundredths, or thousandths.
Example 6: Priya needs 2.7 m of cloth and Shylaja needs 3.5 m of cloth. How much cloth is needed in total?
Sol: We add: 2.7 + 3.5 = 6.2 m
How?
2.7 = 2 + 7/10
3.5 = 3 + 5/10
Add: (2 + 3) + (7/10 + 5/10) = 5 + 12/10
12/10 = 1 whole and 2/10
Total = 6 + 2/10 = 6.2 m
Example 7: How much longer is Shylaja’s cloth compared to Priya’s?
Sol: We subtract: 3.5 – 2.7 = 0.8 m
In fractions:
3.5 = 3 + 5/10
2.7 = 2 + 7/10So, difference = 8/10 = 0.8
Detailed Decimal Addition (Place Value Style)
Let’s add: 75.345 + 86.691
Each digit is added based on place value:
Decimal Sequences
A sequence is a list of numbers that follow a pattern.
In a decimal sequence, each number includes a decimal point and the numbers change in a regular way.
What is the pattern?
Let’s look at this example:4.4, 4.8, 5.2, 5.6, 6.0…
What’s happening here?
Each number is increasing by 0.4.
So, to continue the sequence, we keep adding 0.4:
6.0 + 0.4 = 6.4
6.4 + 0.4 = 6.8
6.8 + 0.4 = 7.2
The next 3 terms are: 6.4, 6.8, 7.2.
Try yourself:Which number is closest to 1?A.0.9B.1.1C.1.01D.1.11View Solution
Estimating Sums and Differences
Sometimes, when we add or subtract decimal numbers, we want to quickly estimate the answer before calculating exactly. Estimating helps us check if our final answer is reasonable.
Sonu noticed an interesting pattern and made a smart observation:
“If we add two decimal numbers, the answer will always be more than the sum of their whole number parts, but less than 2 more than that.”
Example:
1. Let’s take the numbers 25.936 and 8.202
Whole number parts: 25 and 8
Their sum is: 25 + 8 = 33
So, Sonu says the final sum should be:
More than 33
Less than 33 + 2 = 35
Let’s check:
Actual sum = 25.936 + 8.202 = 34.138
Yes! It lies between 33 and 35 – so Sonu’s idea works here.
2. Let’s say you want to subtract two decimals, like:
9.6 – 2.3
Whole number parts are 9 and 2
The answer will lie between 9 – 2 = 7 and 9 – 2 + 1 = 8
Actual answer: 7.3, which lies between 7 and 8
Conclusion:
Think of the whole number part first.
Then remember:
For addition: the answer is a little more than just adding the whole numbers.
For subtraction: the answer is a little less than just subtracting the whole numbers.
More on the Decimal System
Decimal numbers use a dot (called the decimal point) to separate the whole part of a number from the fractional part. For example:
1.5 means one and a half
0.05 means five hundredths
Sometimes, small mistakes in placing or reading this decimal point can lead to huge real-world problems which are as follows:
1. Amsterdam’s Money Mistake (2013):
They meant to send €1.8 million.
But due to a decimal error, they sent €188 million.
Why? Because the amount was entered in euro-cents instead of euros (1 euro = 100 cents).
That’s 100 times more money!
2. The Plane Fuel Disaster (1983):
Ground staff gave fuel in pounds instead of kilograms.
The plane had half the fuel it actually needed.
The decimal error could’ve cost lives, but thankfully, everyone survived.
3. Medical Mistakes:
If a doctor reads 0.05 mg as 0.5 mg, that’s 10 times the correct amount.
This could be dangerous when giving medicine.
Deceptive Decimal Notation
1. Decimal Confusion in Time (Deceptive Decimal Notation):
When you see 4.5 hours, don’t think it’s 4 hours and 5 minutes.
0.5 hours actually means 30 minutes, not 5 minutes!
So, 4.5 hours after noon is 4:30 PM, not 4:05 PM.
2. Real-Life Measurement Mistake:
If someone says 2.5 feet, it means 2 feet 6 inches (because 0.5 ft = 6 inches).
But if they actually meant 2 feet 5 inches, the door or object won’t fit correctly.
This shows why it’s important to know what decimals mean in real measurements.
3. Decimal Notation in Sports (Like Cricket):
In cricket, 5.5 overs means 5 overs + 5 balls (because 1 over = 6 balls).
So, 5.5 ≠ 5 overs 50%; it means 5 overs and 5 balls = 5.833 overs in true decimal form!
Try yourself:
What does Sonu observe about adding two decimal numbers?
A.The answer is exactly the sum of whole numbers.
B.The answer is equal to two times the whole numbers.
C.The answer is more than the sum of whole numbers.
D.The answer is less than the sum of whole numbers.
View Solution
A Pinch of History – Decimal Notation Over Time
Ancient mathematicians like Shridhara and Abu’l Hassan used fractions like 1/10, 1/100.
In 15th century, people marked decimal parts in different colors or added little superscript numbers (like 3⁶).
In 16th century, John Napier and Christopher Clavius introduced the use of a dot (.) to separate whole numbers and decimals (like 2.5).
Some countries today use comma instead of a dot (e.g., 1,000.5 becomes 1.000,5).
Have you ever noticed how we combine numbers and operations like addition (+), subtraction (-), multiplication (×), and division (÷) to represent situations or solve problems? Phrases like “13 + 2” (13 plus 2), “20 – 4” (20 minus 4), or “12 × 5” (12 times 5) are common in mathematics. These combinations are called arithmetic expressions.
In this chapter, we will delve deeper into the world of arithmetic expressions.
Simple Expressions
Every arithmetic expression has a specific value, which is the single number it represents. For instance, the expression “13 + 2” has a value of 15.
We use the equals sign (=) to show this relationship: 13 + 2 = 15.
Think about Mallika spending ₹25 each weekday (Monday to Friday) for lunch. To find her total weekly spending, we can write the expression 5 × 25. This expression represents “5 times 25,” and its value tells us the total amount spent.
An important point is that different expressions can result in the same value. Consider the number 12. It can be represented by various expressions:
10 + 2 = 12
15 – 3 = 12
3 × 4 = 12
24 ÷ 2 = 12
This flexibility allows us to express the same mathematical idea in multiple ways, which can be useful in different contexts or for simplifying problems.
Comparing Expressions
Just as we compare individual numbers using symbols like equals (=), greater than (>), and less than (<), we can also compare arithmetic expressions. This comparison is based on the values that the expressions evaluate to.
For example, let’s compare the expressions 10 + 2 and 7 + 1:
The value of 10 + 2 is 12.
The value of 7 + 1 is 8.
Since 12 is greater than 8, we can write: 10 + 2 > 7 + 1.
Similarly, let’s compare 13 – 2 and 4 × 3:
The value of 13 – 2 is 11.
The value of 4 × 3 is 12.
Since 11 is less than 12, we write: 13 – 2 < 4 × 3.
Reading and Evaluating Complex Expressions
Simple expressions usually involve just one operation. But what happens when an expression combines multiple operations, like 30 + 5 × 4? Without a clear context or rule, how do we know whether to add first or multiply first? This ambiguity can lead to different answers.
Consider the language example from the textbook:
Sentence (a): “Shalini sat next to a friend with toys”. (Meaning: The friend has toys, Shalini sat next to her).
Sentence (b): “Shalini sat next to a friend, with toys”. (Meaning: Shalini has the toys, and she sat next to her friend).
The comma in sentence (b) acts like punctuation, clarifying the meaning. Without it, the sentence could be interpreted in two ways. Similarly, in mathematics, we need rules and tools to ensure everyone evaluates a complex expression the same way.
Let’s look at this example: Mallesh brought 30 marbles, and Arun brought 5 bags with 4 marbles each. The total number of marbles can be written as 30 + 5 × 4.
Purna’s calculation: Added 30 and 5 first (30 + 5 = 35), then multiplied by 4 (35 × 4 = 140).
Mallesh’s calculation: Multiplied 5 and 4 first (5 × 4 = 20), then added 30 (30 + 20 = 50).
⇒ In the context of the story, Mallesh’s calculation (50 marbles) makes sense. Purna’s calculation (140 marbles) doesn’t fit the situation. ⇒ This highlights that just looking at the expression 30 + 5 × 4 isn’t enough; we need a standard order of operations.
⇒ To resolve such confusion and ensure consistent evaluation, mathematics uses specific tools and conventions, primarily brackets and the concept of terms, which we will explore next.
Try yourself:
What is the value of the expression 13 + 2?
A.10
B.20
C.15
D.12
View Solution
Brackets in Expressions
One of the primary tools used in mathematics to clarify the order of operations in complex expressions is brackets ( ).
When an expression contains brackets, the part of the expression inside the brackets must be evaluated first, before performing operations outside the brackets.
Let’s revisit the expression for the total number of marbles Mallesh and Arun brought: 30 + 5 × 4. We determined that multiplication should happen before addition based on the context. We can make this explicit using brackets:
30 + (5 × 4)
To evaluate this:
First, calculate the value inside the brackets: 5 × 4 = 20.
Then, perform the remaining operation: 30 + 20 = 50.
This use of brackets removes ambiguity and ensures the expression correctly represents the intended calculation.
Example 1: Irfan buys biscuits for ₹15 and toor dal for ₹56. He pays with ₹100. How much change does he get?
Ans: Irfan spent ₹15 on a biscuit packet and ₹56 on toor dal.
So, the total cost in rupees is 15 + 56.
He gave ₹100 to the shopkeeper. So, he should get back 100 minus the total cost.
Can we write that expression as— 100 – 15 + 56 ?
Can we first subtract 15 from 100 and then add 56 to the result?
We will get 141.
It is absurd that he gets more money than he paid the shopkeeper!
We can use brackets in this case:
100 – (15 + 56).
Evaluating the expression within the brackets first, we get 100 minus 71, which is 29.
So, Irfan will get back ₹29.
Example 2: Rani went to a stationery shop. She bought a notebook for ₹40 and a pen for ₹25. She gave the shopkeeper ₹100. How much money will she get back?
Step 1: Total cost of the items ₹40 + ₹25 = ₹65
Step 2: Amount given to the shopkeeper ₹100
Step 3: Expression to find the balance 100 – (40 + 25)
Step 4: Solve using brackets = 100 – 65 = ₹35
Ans: Rani will get back ₹35.
Terms in Expressions
What if an expression has multiple operations but no brackets to specify the order, like 30 + 5 × 4? While brackets are one way to clarify order, another fundamental concept used is that of terms.
Terms are the parts of an expression separated by addition (+) signs.
To identify terms correctly, we first need to handle subtraction. Remember that subtracting a number is the same as adding its inverse (the number with the opposite sign). So, before identifying terms, we convert all subtractions into additions of negative numbers.
Let’s see some examples:
Expression:12 + 7
Already in addition form.
Terms: 12 and 7.
Marked: 12 + 7
Expression:83 – 14
Convert subtraction: 83 + (–14)
Terms: 83 and –14.
Marked: 83 + (–14)
Expression:–18 – 3
Convert subtraction: –18 + (–3)
Terms: –18 and –3.
Marked: –18 + (–3)
Expression:6 × 5 + 3
Already in addition form.
Notice that 6 × 5 does not contain an addition sign separating the 6 and 5. It represents a single value obtained through multiplication.
Terms: 6 × 5 and 3.
Marked: (6 × 5) + 3
Expression:2 – 10 + 4 × 6
Convert subtraction: 2 + (–10) + 4 × 6
Terms: 2, –10, and 4 × 6.
Marked: 2 + (–10) + (4 × 6)
Identifying terms is crucial for the standard order of operations:
1. Evaluate each term first: Perform all multiplications and divisions within each term.
2. Add the resulting values of the terms: Once each term has been simplified to a single number, perform the additions (including the additions that came from converted subtractions).
Let’s re-evaluate 30 + 5 × 4 using terms:
Identify terms: 30 and 5 × 4.
Evaluate each term: The term 30 is already evaluated. The term 5 × 4 evaluates to 20.
Add the term values: 30 + 20 = 50.
This process of identifying and evaluating terms provides a systematic way to handle expressions with multiple operations, even without brackets, ensuring a consistent result.
Swapping and Grouping
Once we have identified the terms in an expression (after converting all subtractions to additions), does the order in which we add these terms matter? Let’s investigate.
Consider the expression 6 – 4. Converting to addition gives 6 + (–4).
The terms are 6 and –4.
The value is 6 + (–4) = 2.
What if we swap the terms? –4 + 6.
The value is –4 + 6 = 2.
The value remains the same! This isn’t just true for positive numbers; it holds even when negative numbers are involved. Swapping any two terms in an addition expression does not change the final value.
This property is formally known as the Commutative Property of Addition.
Now, consider an expression with three terms, like (–7) + 10 + (–11).
Let’s try adding them in different groups:
Group the first two terms:( (–7) + 10 ) + (–11)= ( 3 ) + (–11)= –8
Group the last two terms:(–7) + ( 10 + (–11) )= (–7) + ( –1 )= –8
Again, the value is the same regardless of how we group the terms for addition. This also holds true for expressions with more than three terms and when negative numbers are involved.
This property is formally known as the Associative Property of Addition.
Try yourself:
What is the name of the property that states the grouping of terms does not affect the sum?
A.Identity Property of Addition
B.Distributive Property
C.Commutative Property of Addition
D.Associative Property of Addition
View Solution
Conclusion: Order Doesn’t Matter for Addition
Because of the commutative and associative properties, when an expression only involves addition (after converting subtractions), we can add the terms in any order or grouping we find convenient, and the result will always be the same.
For example, in (–7) + 10 + (–11), we could add the negative terms first: (–7) + (–11) = –18, and then add the positive term: –18 + 10 = –8.
In mathematics we use the phrase commutative property of addition instead of saying “swapping terms does not change the sum”. Similarly, “grouping does not change the sum” is called the associative property of addition.
Swapping the Order of Things in Everyday Life
Manasa’s mom says: “Wear your hat and shoes.”
Manasa can do either:
Wear her hat first, then her shoes, or
Wear her shoes first, then her hat.
Result: Manasa will still be ready to go out and look the same either way. ➡ Here, the order does not matter.
In math, this is like: 2 + 3 = 5 and 3 + 2 = 5 Addition can be done in any order — it won’t change the answer
Order Does Matter
Now her mom says: “Wear your socks and shoes.”
This time:
If Manasa wears socks first, then shoes — ✅ that’s the correct way.
But if she wears shoes first, then tries to wear socks — ❌ it’s wrong and uncomfortable!
Result: She’ll look odd and it won’t work properly. ➡ Here, the order matters.
In math, this is like: 8 – 5 = 3, but 5 – 8 = -3 So in subtraction, changing the order changes the answer.
More Expressions and Their Terms
Let’s look at a few more examples from the textbook to solidify our understanding of writing expressions and identifying their terms in different scenarios.
Example: Amu, Charan, Madhu, and John went to a hotel and ordered four dosas. Each dosa cost ₹23, and they wish to thank the waiter by tipping ₹5. Write an expression describing the total cost.
Situation: 4 friends order 4 dosas at ₹23 each and want to leave a ₹5 tip.
Expression for total cost: The cost of the dosas is 4 × 23. The tip is 5. The total cost is the sum: 4 × 23 + 5.
Identifying Terms: The expression is already a sum. The terms are 4 × 23 and 5.
Evaluation:
Evaluate terms: 4 × 23 = 92. The term 5 is already evaluated.
Add term values: 92 + 5 = 97.
Total Cost: ₹97.
Example : Children in a class are playing “Fire in the mountain, run, run, run!”. Whenever the teacher calls out a number, students are supposed to arrange themselves in groups of that number. Whoever is not part of the announced group size, is out. Ruby wanted to rest and sat on one side. The other 33 students were playing the game in the class. The teacher called out ‘5’.
Situation: 33 students are playing. The teacher calls out ‘5’. Students form groups of 5. Ruby observes.
Observation: Ruby sees 6 full groups of 5, with 3 students left over.
Expression: Ruby writes 6 × 5 + 3 (representing 6 groups of 5, plus the 3 remaining).
Identifying Terms: The terms are 6 × 5 and 3.
Evaluation:(6 × 5) + 3 = 30 + 3 = 33 (the total number of students playing).
Variations:
If the teacher called ‘4’: There would be 8 groups of 4 with 1 left over. Expression: 8 × 4 + 1. Terms: 8 × 4 and 1.
If the teacher called ‘7’: There would be 4 groups of 7 with 5 left over. Expression: 4 × 7 + 5. Terms: 4 × 7 and 5.
Example: Raghu bought 100 kg of rice from the wholesale market and packed them into 2 kg packets. He already had four 2 kg packets. Write an expression for the number of 2 kg packets of rice he has now and identify the terms.
Situation: Raghu buys 100 kg rice, packs it into 2 kg bags. He already had 4 such bags.
Expression for total bags: Number of new bags = 100 ÷ 2 (or 100/2). Total bags = 4 + 100 ÷ 2.
Identifying Terms: The terms are 4 and 100 ÷ 2.
Evaluation:
Evaluate terms: 4 is evaluated. 100 ÷ 2 = 50.
Add term values: 4 + 50 = 54.
Total Bags: 54 bags.
Example: Kannan has to pay ₹432 to a shopkeeper using coins of ₹1 and ₹5, and notes of ₹10, ₹20, ₹50 and ₹100. How can he do it?
Situation: Paying ₹432 using various denominations.
This shows how expressions can represent real-world combinations, and identifying terms helps understand the structure.
Example: Here are two pictures. Which of these two arrangements matches with the expression 5 × 2 + 3?
Which image is correct?
Expression:5 × 2 + 3
Identifying Terms:5 × 2 and 3.
Evaluation:
Interpretation: The expression means “3 more than 5 groups of 2”. This matches the picture showing 5 pairs of items plus 3 individual items.This Image is correct
Removing Brackets — I
Let us find the value of this expression,
200 – (40 + 3).
We first evaluate the expression inside the bracket to 43 and then subtract it from 200. But it is simpler to first subtract 40 from 200:
200 – 40 = 160.
And then subtract 3 from 160:
160 – 3 = 157.
What we did here was 200 – 40 – 3. Notice, that we did not do
200 – 40 + 3.
So,
200 – (40 + 3) = 200 – 40 – 3.
Removing Brackets – II
Example: Lhamo and Norbu went to a hotel. Each of them ordered a vegetable cutlet and a rasgulla. A vegetable cutlet costs ₹43 and a rasgulla costs ₹24. Write an expression for the amount they will have to pay.
Situation: Lhamo and Norbu each buy:
1 vegetable cutlet = ₹43
1 rasgulla = ₹24
So, the amount one person pays is: 43 + 24
There are two people, so together they pay: (43 + 24) + (43 + 24) Instead of writing it this way, we can simplify using brackets and multiplication: 2 × (43 + 24)
Why use brackets? Brackets tell us to first add the items, and then multiply the total by 2 (for two people). So, 2 × (43 + 24) = 2 × 67 = ₹134
This is much simpler than adding 43 + 24 twice!
What if another friend, Sangmu joins?
If a third person, Sangmu, joins and buys the same items, then the expression becomes: 3 × (43 + 24) That means: 3 × 67 = ₹201
Example: In the Republic Day parade, there are boy scouts and girl guides marching together. The scouts march in 4 rows with 5 scouts in each row. The guides march in 3 rows with 5 guides in each row (see the figure below). How many scouts and guides are marching in this parade?
Boy scouts: 4 rows × 5 boys = 20 Girl guides: 3 rows × 5 girls = 15
So total people = 20 + 15 = 35
But we can do this smarter: Instead of calculating separately, first add the rows: (4 + 3) × 5
Computing these expressions, we get
(4 + 3) × 5 = 7 × 5 = 35
What’s the lesson here?
Using brackets helps us to group numbers and make multiplication or subtraction easier. For example:
Have you ever thought about how many grains of rice are in a single bag, or how many stars twinkle in the night sky? Numbers are everywhere, helping us count, measure, and understand the world around us. Sometimes, these numbers are small, like the number of fingers on your hand. But often, especially when we talk about populations, distances between cities, or even the variety of life on Earth, the numbers become very, very large!
Imagine a farmer named Eshwarappa, walking through a market in Karnataka. He overhears a conversation about rice – not just any rice, but lakhs of varieties that used to exist in India! A lakh!Eshwarappa hearing a conversationThat sounds like a huge number. Eshwarappa Eshwarappa shared this incident with his daughter Roxie and son Estu . They wonder,
“Can a person taste all 1 lakh rice varieties in their lifetime?”
Let’s Calculate!
There are 365 days in a year. So if someone lives for 100 years, the number of days is:100×365=36,500 days.
So, if someone eats 3 different types of rice every single day for 100 years, they can taste all 1 lakh rice varieties! This story from your textbook introduces us to the fascinating world of large numbers. It makes us question: How big is a lakh? How do we even write or say such big numbers?
In this chapter, we will embark on a journey to explore these “Large Numbers Around Us.”
Getting a Feel for Large Numbers
Sometimes, we hear big numbers like 180 metres or 450 metres—but it’s hard to imagine how tall that really is. So we compare it to something we know.
Let’s Look at Somu’s Building
Somu is 1 metre tall.
Each floor is about 4 times his height. So, 1 floor = 4 metres.
There are 10 floors, so the total height of the building is:
10×4=40 metres
Q1: Which is taller — The Statue of Unity or Somu’s building? How much taller?
Statue of Unity = 180 metres
Somu’s building = 40 metres
180−40=140180−40=140 metres taller
Answer: The Statue of Unity is taller by 140 metres.
Q2: How much taller is the Kunchikal waterfall than Somu’s building?
Waterfall height = 450 metres
Building height = 40 metres
450−40=410450−40=410 metres taller
Answer: The waterfall is 410 metres taller than Somu’s building.
Q3: How many floors should Somu’s building have to be as tall as the waterfall?
Waterfall = 450 metres
1 floor = 4 metres
450÷4=112.5450÷4=112.5
We can’t have half a floor in reality, so we round up to 113.
Answer: Somu’s building should have 113 floors to be as tall as the waterfall!
Is One Lakh a Very Large Number?
This is actually a very interesting question because…
Sometimes 1 lakh feels very big and sometimes it feels small, depending on what we are talking about.
Let’s see why:
Roxie gives three examples to show how huge one lakh can feel:
1 Lakh Varieties of Rice
Imagine tasting a new type of rice every day.
It would take 274 years to try them all!
We live only about 70–80 years. So, we’ll never finish them!
Living for 1 Lakh Days
One year has 365 days.
1,00,000 ÷ 365 ≈ 274 years!
That’s like living three lifetimes. So yes, it’s big.
1 Lakh People Standing in a Line
If each person takes about 0.38 meters of space, then:
1,00,000 people = 38 km long line.
That’s like a line from one city to another!
Estu gives a different view. He shows how small 1 lakh can feel:
Stadium Seats
The cricket stadium in Ahmedabad holds more than 1 lakh people.
They all fit in one place — that feels not so big, right?
Hair on a Human Head
An average person has 80,000 to 1,20,000 hairs.
That means 1 lakh hairs fit on your head!
So, in a tiny space, you can already have 1 lakh things.
Fish Eggs
Some fish can lay 1 lakh eggs at once!
Even 10 lakh (a million) in some species!
That makes 1 lakh seem small in nature.
Q: So,is 1 lakh big or small?
Ans: It depends on what you’re comparing it with.
If you’re saving ₹1 lakh, it feels like a lot of money.
But if a government spends ₹1 lakh on a city, it’s very little.
If you’re counting people or things in small spaces, 1 lakh may not feel big.
But if you want to do something 1 lakh times, it’s a huge effort.
Reading and Writing Large Numbers
Now that we have a better feel for large numbers like lakhs, how do we actually read and write them clearly?
The Indian Place Value System
In the Indian system, numbers are grouped into hundreds, thousands, lakhs, crores, and so on. Here’s a breakdown:
Units: The first three digits from the right are the units, tens, and hundreds.
Thousands: The next two digits are the thousands.
Lakhs: The next two digits are the lakhs.
Crores: The digits after lakhs are the crores.
Indian Place Value Chart
Comma Rules:
The first comma comes after 3 digits from the right (thousands group).
Next commas come after 2 digits each.
Example: 12,78,830 is grouped as 12 (lakhs), 78 (thousands), 830 (hundreds & below)
Q: Write these in words:
(a) 3,00,600 Ans: Three lakh six hundred
(b) 5,04,085 Ans: Five lakh four thousand eighty-five
(d) 70,53,138 Ans: Seventy lakh fifty-three thousand one hundred thirty-eight
Writing Number Names as Numbers
Now let’s go the other way — you are given the number in words, and you need to write it in figures (numbers).
Q: Write the numbers
(a) One lakh twenty-three thousand four hundred and fifty-six Ans: 1,23,456
(b) Four lakh seven thousand seven hundred and four Ans: 4,07,704
(c) Fifty lakhs five thousand and fifty Ans: 50,05,050
(d) Ten lakhs two hundred and thirty-five Ans: 10,00,235
Try yourself:
What is the height of Somu’s building?
A.40 metres
B.180 metres
C.450 metres
D.100 metres
View Solution
The Land of Tens
Understanding place value is like having a secret code for numbers. Each digit in a number holds a specific value based on its position. The “Land of Tens” analogy from the chapter helps illustrate this beautifully using special calculators.
Imagine calculators with limited buttons:
Thoughtful Thousands (+1000 button): To make 3,000, you press it 3 times. To make 10,000, you press it 10 times. To make one lakh (1,00,000), you need to press it 100 times (since 1 lakh = 100 thousands).
Tedious Tens (+10 button): To make 500, you press it 50 times (50 x 10 = 500). To make 1,000, you press it 100 times (100 x 10 = 1000). To make one lakh (1,00,000), you need a whopping 10,000 presses (10,000 x 10 = 1,00,000)!
Handy Hundreds (+100 button): To make 3,700, you press it 37 times (37 x 100 = 3700). To make 10,000, you press it 100 times (100 x 100 = 10,000). To make one lakh (1,00,000), you press it 1,000 times (1,000 x 100 = 1,00,000).
This shows how many smaller units make up larger ones: 100 thousands make a lakh, 10,000 tens make a lakh, and 1,000 hundreds make a lakh.
What is Place Value?
Place value defines the value of each digit in a number based on its position. Each position, or “place,” in a number has a unique value that helps determine the overall number.
Example 1: What are the place values of each digit in the number 92,735? Ans:
5 is Ones
3 is Tens
7 is Hundreds
2 is Thousands
9 is Ten thousands
The diagram below illustrates the above example in more detail.
Now, let’s meet Creative Chitti, a calculator with buttons for +1, +10, +100, +1000, +10000, +100000, etc. I am Creative ChittiChitti shows that numbers can be made in many ways. For example, 5072 could be:
(50 x 100) + (7 x 10) + (2 x 1) = 5000 + 70 + 2 = 5072
(3 x 1000) + (20 x 100) + (72 x 1) = 3000 + 2000 + 72 = 5072
Another way: (4 x 1000) + (10 x 100) + (6 x 10) + (12 x 1) = 4000 + 1000 + 60 + 12 = 5072
This leads us to the idea of expanded form. While Chitti is creative, Systematic Sippy wants to use the fewest button clicks possible. To make 5072 with the fewest clicks, Sippy would press:
+1000 button: 5 times (for 5000)
+100 button: 0 times (for 0 hundreds)
+10 button: 7 times (for 70)
+1 button: 2 times (for 2)
Total clicks = 5 + 0 + 7 + 2 = 14 clicks. The expression is: (5 x 1000) + (0 x 100) + (7 x 10) + (2 x 1) = 5072.
Notice something important? The way Systematic Sippy makes the number with the fewest clicks directly corresponds to the standard expanded form based on place value! Each digit is multiplied by its place value (ones, tens, hundreds, thousands, etc.).
Expanded Form: When we write a number in expanded form, we break it down to show the value of each digit. It’s like stretching the number out to see each part clearly.
Example 2: Write in expanded form: 4,582 Sol: Let’s expand 4,582:
Thousands place: The digit 4 is in the thousands place, so its value is 4,000.
Hundreds place: The digit 5 is in the hundreds place, so its value is 500.
Tens place: The digit 8 is in the tens place, so its value is 80.
Ones place: The digit 2 is in the ones place, so its value is 2.
Putting it all together: 4,582 = 4,000 + 500 + 80 + 2
Of Crores and Crores!
We’ve talked about lakhs, but the world of large numbers doesn’t stop there! What happens when we have numbers even bigger than ten lakhs?
As numbers get bigger, it becomes difficult to read and understand them unless they are written properly with commas. To help us, two main systems are used around the world:
The Indian Number System
The International Number System (also called the American System)
In the Indian system, the next major milestone after lakh is the crore as we already discussed above.
1 Crore = 100 Lakhs
1 Crore = 1,00,00,000 (That’s a 1 followed by seven zeros!)
Think back to the Creative Chitti calculator. If you pressed the +10,00,000 (ten lakh) button ten times, you would reach 1,00,00,000, which is one crore.
Just like lakhs, crores help us talk about very large quantities, such as the population of large cities or entire states, or the cost of major projects.
And it doesn’t stop at crores! The next step in the traditional Indian system is the arab.
1 Arab = 100 Crores
1 Arab = 1,00,00,00,000 (A 1 followed by nine zeros!)
International System of Writing Numbers
The number 100000 is read as one hundred thousand or 1 lakh. It is a 6-digit numeral.
In the International System, the number 10 lakh or ten hundred thousand, that is, a thousand thousand, is called a million.
It is written as under:
Instead of lakhs, crores, etc. as periods, we use millions, billions, etc.
Let us write the smallest 8-digit number in the two systems of numerations.
The International place value chart is given below.
The chart can be expanded to include more than nine places.
The section just before the millions is known as the billions section.
Next, we have the trillions section.
The places before the hundred billions are referred to as: – trillions place – ten trillions place – hundred trillions place
When we compare the two systems of counting, we can see the following connections.
Note that in the Indian system, starting from the right after the first period of 3 digits all other periods are of 2 digits but in the International system, each period consists of three digits.
We place a comma or leave space after every 3 digits.
The abacus shows the number six million eight hundred forty-nine thousand two hundred forty.
To make the task of reading and writing such large numbers easy, start counting digits from the right by threes and leave some space or put a comma after every three digits as shown below.
Try yourself:
What are the two main systems used to write large numbers around the world?
A.Metric and Imperial
B.Indian and International
C.American and European
D.Local and Global
View Solution
Number Names – Indian vs. American
Let’s take an example number:
→ 9876501234
In the Indian system, we place commas like this:
9,87,65,01,234 We read it as: 9 arab 87 crore 65 lakh 1 thousand 234 or 987 crore 65 lakh 1 thousand 234
In the American system, commas look like this:
9,876,501,234 We read it as: 9 billion 876 million 501 thousand 234
Understanding Zeros in Large Numbers
1 thousand = 1,000 → 3 zeros
1 lakh = 1,00,000 → 5 zeros
1 crore = 1,00,00,000 → 7 zeros
1 arab = 1,00,00,00,000 → 9 zeros
Now let’s answer these questions:
Q: How many zeros in a thousand lakh?
1 lakh = 1,00,000
1,000 × 1,00,000 = 1,00,00,00,000 → 8 zeros
But let’s calculate more carefully:
1000×1,00,000=1,00,00,00,000(which is actually 10 crores)
So the number has 8 zeros.
Q: How many zeros in a hundred thousand?
1 thousand = 1,000
100 × 1,000 = 1,00,000 → 5 zeros
So Ans: 5 zeros
Exact and Approximate Values
Read the image above. Does this mean exactly 100,000 people walked through the gates? Probably not! It’s likely an approximation or an estimate. The actual number might have been 98,543 or maybe 101,210. For a headline, saying “about 1 lakh” gives a good enough idea of the crowd size without needing the precise count.
This brings us to the important concept of estimation. Often, especially with large numbers, we don’t need the exact value. An approximate value is easier to understand, remember, and use.
Why do we use approximate numbers?
Example:
The exact population of Chintamani town is 76,068.
But saying “about 75,000 people live there” gives a quick idea without needing to know the exact count.
Two Common Ways of Rounding:
1. Rounding Up:
When we increase the number to a higher, easier number.
Example: A school has 732 people. The principal may round it up and order 750 sweets.
2. Rounding Down:
When we reduce the number a little to make it simpler.
Example: An item costs ₹470, but the shopkeeper might say it’s around ₹450.
Let’s Summarise:
Nearest Neighbours
A common way to estimate is by rounding to the nearest ten, hundred, thousand, lakh, crore, etc. This involves looking at the digit to the right of the place value you’re rounding to.
Rule: If the digit to the right is 5 or greater, round up the digit in the target place value. If the digit to the right is 4 or less, keep the digit in the target place value the same. All digits to the right of the target place value become zeros.
Let’s find the nearest neighbours for 6,72,85,183:
Nearest Thousand: Look at the hundreds digit (1). Since 1 < 5, keep the thousands digit (5) the same. 6,72,85,000
Nearest Ten Thousand: Look at the thousands digit (5). Since 5 ≥ 5, round up the ten thousands digit (8) to 9. 6,72,90,000
Nearest Lakh: Look at the ten thousands digit (8). Since 8 ≥ 5, round up the lakhs digit (2) to 3. 6,73,00,000
Nearest Ten Lakh: Look at the lakhs digit (2). Since 2 < 5, keep the ten lakhs digit (7) the same. 6,70,00,000
Nearest Crore: Look at the ten lakhs digit (7). Since 7 ≥ 5, round up the crores digit (6) to 7. 7,00,00,000
Patterns in Products
Instead of multiplying directly by numbers like 5, 25, or 50, Roxie and Estu uses a shortcut based on how those numbers relate to 10, 100, or 1000.
These shortcuts are possible because:
5 = 10 ÷ 2
25 = 100 ÷ 4
50 = 100 ÷ 2
125 = 1000 ÷ 8
So, multiplying a number by 5 is the same as:
Dividing the number by 2 and then multiplying by 10 → a × 5 = (a ÷ 2) × 10
And multiplying a number by 25 is the same as:
Dividing the number by 4 and then multiplying by 100 → a × 25 = (a ÷ 4) × 100
These are based on properties of multiplication and division:
Multiplication is associative and distributive
You can rearrange factors in multiplication for easier calculation
For example: a × 5 = a × (10 ÷ 2) = (a ÷ 2) × 10 This works because multiplication and division are inverse operations that can be grouped like this for easier solving.
Example 1: 116 × 5
Instead of directly multiplying 116 × 5, Roxie breaks it into:
116 × 5 = (116 ÷ 2) × 10
Why does this work?
Because 5 = 10 ÷ 2, so multiplying by 5 is the same as dividing the number by 2 and then multiplying the result by 10.
So,
116 ÷ 2 = 58
Then, 58 × 10 = 580Example 2: 824 × 25
Estu applies a similar shortcut: 824 × 25 = (824 ÷ 4) × 100 Why?
Because 25 = 100 ÷ 4, so multiplying by 25 is like dividing by 4 and then multiplying the result by 100.
So,
824 ÷ 4 = 206
Then, 206 × 100 = 20600
Fascinating Facts about Large Numbers
This lesson uses real-world facts involving huge numbers to show how multiplication and divisionhelp us understand large quantities — like distances, weights, populations, and more.
1. Using Multiplication to Discover Big Facts
2. Using Division to Break Down Big Facts
Try yourself:How many zeros are in a crore?A.5 zerosB.7 zerosC.9 zerosD.8 zerosView Solution
Did You Ever Wonder….?
Estu’s Question:
Can the entire population of Mumbai fit into 1 lakh buses?
Step 1: Understand the Numbers
1 lakh buses = 1,00,000 buses
Each bus holds = 50 people
So, total people in 1 lakh buses = 1,00,000 × 50 = 50,00,000 = 50 lakh people
Step 2: Compare with Mumbai’s Population
Population of Mumbai = 1 crore 24 lakh = 1,24,00,000 people
People buses can carry = 50 lakh
So, can everyone fit into the buses? No! Because 1 crore 24 lakh is more than double50 lakh.
Conclusion: The whole population of Mumbai cannot fit in 1 lakh buses.
Now think about the Titanic Ship:
Can the population of Mumbai fit into 5000 Titanic-like ships?
Step 1: How many people fit in 1 ship?
Each Titanic can carry = 2,500 people
So, 5000 ships can carry = 5000 × 2500 = 1,25,00,000 = 1 crore 25 lakh people
Step 2: Compare again
Mumbai’s population = 1 crore 24 lakh
Space on ships = 1 crore 25 lakh
Yes! The population of Mumbai can fit into 5000 Titanic-like ships.
Solved Examples
Example 1: Write the number 70,53,138 in words using the Indian system. Ans: Seventy lakh fifty-three thousand one hundred thirty-eight.
Example 2: Write the number name “Fifty lakh five thousand fifty” in figures using the Indian system. Ans: 50,05,050
Example 3: Compare 500 lakhs and 5 million. Use ‘<‘, ‘>’, or ‘=’.
Ans: 500 lakhs = 500 x 1,00,000 = 5,00,00,000
5 million = 5 x 1,000,000 = 5,000,000
Since 5,00,00,000 is much larger than 5,000,000,
500 lakhs > 5 million
Example 4: Using Systematic Sippy’s method (fewest clicks), how would you make the number 3,67,813? Write the expression.
This story is about Rani Abbakka, a brave queen of Ullal who fought against the Portuguese to protect her land’s freedom.
It shows her courage, determination, and leadership as she stood up to a powerful enemy.
She inspired her people and other rulers to defend their country.
Explanation of the Story
Rani Abbakka and the Portuguese Threat
The story begins with Rani Abbakka, the queen of Ullal, a small coastal kingdom in India. At the time, Ullal was under pressure from the Portuguese, who had captured it and demanded tribute (money or goods) to maintain control. Rani Abbakka, however, believed Ullal was a sovereign (free) country and boldly refused to pay. When a Portuguese envoy visited to collect the overdue tribute, she firmly declared,
“We are a sovereign country. We don’t pay tribute to Portugal. And we don’t take orders from the Portuguese!” Though the envoy warned her of the consequences, Abbakka stood her ground.
Conflict at Home
Soon after her coronation (the ceremony of becoming queen), Abbakka shared her plan to resist the Portuguese with her husband, Veera Narasimha, the king of Bangadi. While she was determined to fight for Ullal’s independence, he was worried. He feared that her bold move might anger the Portuguese, bringing danger to his own kingdom. He called her decision rash and tried to persuade her to change her mind. Despite his concerns, Abbakka refused to back down. When she declared she wasn’t afraid of the Portuguese, Veera Narasimha even ordered his soldiers to stop her. But Abbakka’s determination remained strong.
Gathering Allies and Strategic Planning
Rani Abbakka reached out to local rajas (kings) for support. She held a meeting to unite them against the Portuguese threat. Although many of the rajas were unsure if their small forces could match the Portuguese army, Abbakka’s confidence and leadership encouraged them. To further strengthen Ullal, she ordered the building of merchant ships and formed an alliance with the Zamorin of Kozhikode, a powerful coastal ruler. This move allowed her to defy the Portuguese and establish successful trade with Arabia, boosting Ullal’s economy and position in the region.
The Battle for Ullal
Furious at her defiance, the Portuguese launched an attack on Ullal. Rani Abbakka bravely led her soldiers into battle, fighting alongside them. The battle lasted four days, with the people of Ullal showing great courage. In the end, the Portuguese were defeated and forced to retreat, never to trouble Ullal again. Abbakka even attacked the Portuguese fort, displaying her dauntless spirit and fierce commitment to her people and land.
Legacy of a Brave Queen
The people of Ullal stood by Abbakka, inspired by her courage and strong leadership. Her victory over the powerful Portuguese brought great pride to the kingdom and inspired other Indian rulers to resist foreign powers. Rani Abbakka’s story is a powerful reminder that with unity, strategic thinking, and fearless leadership, even the strongest enemies can be defeated.
Moral of the Story
The story teaches us the importance of courage, determination, and standing up for what is right.
Rani Abbakka’s bravery shows that even in the face of a powerful enemy, one person’s leadership and belief in freedom can inspire others and lead to victory.
It encourages us to value independence and work together for a common goal.
Difficult Words
Vassal: A state controlled by a more powerful country, forced to pay money or goods.
Coronation: A ceremony where someone is officially made king or queen.
Successor: A person who takes over a position or role from someone else.
Rash: Acting quickly without thinking about the results.
Sovereign: Free and independent, not controlled by others.
League: A partnership or alliance.
Wrath: Extreme anger.
Seize: To take something suddenly or by force.
Resolve: Strong determination to achieve a goal.
Raged: Happened in a fierce or violent way.
Decisive: Able to make decisions quickly and effectively.
This poem is a heartfelt tribute to soldiers who protect the nation with courage and dedication.
It celebrates their sacrifices, bravery, and tireless efforts in guarding the country under tough conditions.
The poet expresses deep gratitude and prays for their well-being, highlighting their selfless service.
ExplanationStanza 1
Oh! Defenders of borders You are great sons of my land When we are all asleep You still hold on to your deed
Explanation The poet begins by addressing soldiers as “Defenders of borders,” showing their role in protecting the country’s boundaries. Calling them “great sons” (meaning all soldiers, men and women) reflects their importance to the nation. While people sleep peacefully, soldiers stay awake, committed to their duty of safeguarding the country. This highlights their vigilance and sacrifice.
Stanza 2
Windy season or snowy days Or scorching sun’s sweltering rays You are there guarding all the time awake Treading the lonely expanses as yogis
Explanation This stanza describes the harsh conditions soldiers face. Whether it’s windy, snowy, or extremely hot, they remain on duty, always alert. The phrase “treading the lonely expanses as yogis” compares soldiers to yogis (spiritual seekers) who walk alone with focus. It shows their determination and strength in patrolling remote, lonely areas.
Stanza 3
Climbing the heights or striding the valleys Defending the deserts or guarding the marshes Surveillance in seas and by securing the air Prime of your youth given to the nation!!
Explanation The poet explains the diverse terrains where soldiers work—mountains, valleys, deserts, marshes, seas, and air. They climb high peaks, patrol lowlands, and monitor all areas to keep the nation safe. The line “Prime of your youth given to the nation” emphasizes that soldiers dedicate their youthful years, a precious time, to serve the country, showing their immense sacrifice.
Stanza 4
Wind chimes of my land vibrate your feat We pray for you brave men!! May the Lord bless you all!!
Explanation In the final stanza, the poet uses “wind chimes” to symbolise the nation’s pride and respect for soldiers’ brave actions (“feat”). The poet, along with the people, prays for the soldiers’ safety and well-being, asking for divine blessings. This shows gratitude and admiration for their courage and service.
Moral of the Poem
The poem teaches us to value and respect the sacrifices made by soldiers.
It encourages gratitude for their selfless service, as they protect the nation under tough conditions.
They give up personal comforts and safety.
We should honour their dedication and pray for their strength and safety.
Difficult Words
Defenders: Protectors or guardians.
Borders: Boundaries of a country.
Deed: Duty or task.
Scorching: Very hot.
Sweltering: Uncomfortably hot.
Treading: Walking or stepping on.
Expanses: Large, open areas.
Yogis: Spiritual people who meditate and live simply.
This lesson is a letter exchange between two friends, Soumya and Ananda, who share their feelings about brave soldiers who fought for India.
Soumya writes about her visit to the National War Memorial in New Delhi, describing how it honours soldiers who died in wars.
She shares stories of heroes and the memorial’s features, like the eternal flame and circles representing bravery and sacrifice.
Ananda replies, expressing gratitude and inspiration to join the Armed Forces.
The lesson teaches us to respect and remember soldiers’ sacrifices for our freedom.
Explanation of the Story
The story is told through two letters between Soumya, who lives in Bengaluru, and Ananda, who lives in Chandigarh. It focuses on their thoughts about soldiers and Soumya’s visit to the National War Memorial.
Soumya’s Letter (14 April):
Soumya writes to Ananda, reminding him of their earlier conversation about war and peace. She reflects on India’s journey—its fight for independence and the wars fought after 1947 to defend the nation. Curious about the brave soldiers who sacrificed their lives, Soumya finds some answers during her school trip to New Delhi, where she visits the National War Memorial.
Her teacher explains that the memorial, built between April 2018 and February 2019 near India Gate and inaugurated by Prime Minister Narendra Modi, honours soldiers who died in conflicts such as the Indo-China War (1962), Indo-Pak Wars (1965 and 1971), and the Kargil War (1999). The memorial holds 29,000 tablets with over 26,000 names of fallen heroes.
Soumya also learns about bravery awards like the Param Vir Chakra (PVC), awarded to 21 soldiers, starting with Major Somnath Sharma in 1947. Other notable heroes include Lance Naik Albert Ekka, Flying Officer Nirmal Jit Singh Sekhon, Second Lieutenant Arun Khetarpal, and Major Hoshiar Singh. Captain Mahendra Nath Mulla, a Navy officer, received the Maha Vir Chakra (MVC).
Inspired by the story of Lance Naik Albert Ekka, who bravely fought and died in the 1971 war despite serious injuries, Soumya feels a deep desire to one day serve the nation like him.
The National War Memorial has several symbolic sections:
Amar Chakra (Circle of Immortality): Home to the eternal flame, symbolising that soldiers’ spirits live on.
Veerta Chakra (Circle of Bravery): Displays six bronze murals of heroic battles.
Tyag Chakra (Circle of Sacrifice): Walls shaped like a Chakravyuh formation, listing soldiers’ names.
Raksha Chakra (Circle of Protection): Rows of trees representing the protectors of the nation.
Soumya describes the memorial’s beauty—the respectful wreaths, the lighting that changes from dawn to dusk, and the pride mixed with sadness she felt. Her class is preparing presentations about soldiers, and she chooses Major Padmapani Acharya, a 1999 Kargil War hero who, despite severe injuries, led his men to victory and was posthumously awarded the MVC. Soumya ends her letter excitedly, sharing a website link about the memorial.Ananda’s Letter (24 April)
Ananda is deeply moved by Soumya’s letter. He praises her vivid description and agrees that the National War Memorial is not just a monument but a symbol of gratitude for those who gave their lives for India’s freedom. Inspired by her experience, he too dreams of joining the Armed Forces.
He recalls visiting a war memorial in Chandigarh’s Bougainvillaea Garden, where people laid flowers to honour fallen soldiers. This visit reminds him of the famous Hindi poem Pushp ki Abhilasha by Makhanlal Chaturvedi, where a flower wishes to fall on the path of brave soldiers rather than be used for mere decoration.
Ananda shares his admiration for Captain Anuj Nayyar, another MVC awardee from the Kargil War, whose mother wrote a heartfelt book about him. Ananda mentions an interview where Captain Nayyar’s mother talks about the pain and pride of keeping her son’s memory alive.
Excited about the National War Memorial and Museum app, which provides information in 21 languages and showcases murals, Ananda expresses his wish to visit the memorial one day. He also plans to suggest creating a collage of inspiring heroes at school.
Before ending, Ananda warmly shares his love for philately—stamp collecting—and appreciates Soumya’s beautifully stamped letters. He concludes by telling her that her letter truly inspired him.
Moral of the Story
The lesson teaches us to be thankful for soldiers who gave their lives so we can live in a free and safe country.
It encourages us to honour their bravery by remembering their stories, visiting memorials, and learning about their sacrifices.
The story also inspires us to be courageous, serve our nation, and live in a way that respects the freedom soldiers fought for.
Difficult Words
Here are the meanings of some words from the lesson, explained simply:
Homage: Showing respect publicly for someone.
Memorial: A place or statue built to remember people who died.
Patriotism: Love and loyalty for one’s country.
Sacrifices: Giving up something important, like life, for a cause.
Inaugurated: Officially opened or started.
Tribute: An act to show respect or gratitude.
Etched: Carved or written permanently, like names on stone.
Gallantry: Great courage, especially in battle.
Posthumously: After someone has died.
Citation: A description of someone’s brave actions for an award.
Awestruck: Feeling amazed and impressed.
Commemorates: Honors and remembers officially.
Obelisk: A tall, pointed stone pillar.
Wreaths: Rings of flowers used to show respect for the dead.
Interminable: Never-ending, like an eternal flame.
Murals: Large paintings or designs on walls.
Valour: Great bravery in danger.
Solemn: Serious and respectful.
Sovereignty: A country’s independence and control over itself.
This chapter tells the inspiring story of a young woman who faced a life-changing accident but refused to give up.
With strong will and determination, she overcame challenges to achieve something extraordinary.
It is a story of courage, hope, and never giving up on dreams, no matter how tough things get.
Explanation of the Story
Early Life and Dreams
Arunima Sinha, a 24-year-old from Ambedkar Nagar, Uttar Pradesh, was always passionate about sports. Her father was an army engineer, and her mother worked as a health supervisor. Arunima excelled in sports, especially volleyball, and after completing her law degree, she planned to join the paramilitary forces. This would allow her to pursue her love for sports while building a career.
A Life-Changing Incident
On April 11, 2011, Arunima’s life took a dramatic turn when she met with a terrible train accident. She lost one of her legs, and doctors had to fit her with an artificial limb. While recovering in the hospital, Arunima, refusing to give up, found new inspiration. She read about Mount Everest and decided she would climb it, despite her injury. Many thought this dream was impossible, but Arunima was firm in her resolve.
The Climb to Mount Everest
To achieve her dream, Arunima trained rigorously. She enrolled at the Nehru Institute of Mountaineering in Uttarkashi and underwent 18 months of intense preparation. She was guided by Bachendri Pal, the first Indian woman to climb Mount Everest, who believed that Arunima had already won by daring to dream so big.
After 52 challenging days of climbing, on May 21, 2013, Arunima reached the summit of Mount Everest. She proudly planted the Indian flag and placed a photograph of Swami Vivekananda, her inspiration, at the top. She became the first Indian woman with an artificial leg to achieve this remarkable feat.
Conquering the Seven Summits
Arunima’s achievements didn’t stop with Everest. By July 2016, she had conquered the highest peaks of all seven continents, including mountains in Europe, Africa, Australia, South America, North America, and Antarctica. In January 2019, she became the first woman amputee to climb Mount Vinson in Antarctica, completing her mission to conquer the Seven Summits.
The Spirit of Arunima’s Journey
Arunima’s story is not just about physical endurance but about incredible mental strength and courage. Her journey proves that with determination, perseverance, and belief in oneself, even the most impossible challenges can be overcome.
Moral of the Story
The story teaches us that no matter how difficult life gets, we should never give up on our dreams.
With courage, hard work, and belief in ourselves, we can achieve great things, even when others think it’s impossible.
Arunima’s journey shows that challenges can make us stronger if we face them with determination.
Difficult Words
Beacon: A source of inspiration or guidance, like a light that shows the way.
Resilience: The ability to bounce back from tough situations.
Amputated: When a part of the body, like a leg, is surgically removed.
Prosthetic leg: An artificial leg that helps a person move and walk.
Feat: A great achievement or success.
Harrowing: Something very upsetting or scary.
Rigorous: Very strict or tough, like hard training.
Endeavour: A serious effort to achieve something.
Surge: A sudden strong feeling or increase, like a wave of emotions.
Endurance: The ability to keep doing something difficult for a long time.
This short and lively poem, written by Edna St. Vincent Millay, expresses a deep love for travel and adventure through the speaker’s fascination with trains.
The speaker imagines the sounds and sights of trains passing by, even when they are far away, and feels a strong urge to hop on any train, no matter its destination.
The poem captures the excitement of exploring new places and the joy of making friends, while highlighting the speaker’s restless spirit and longing for new experiences.
Explanation of the Poem Stanza 1
The railroad track is miles away, And the day is loud with voices speaking, Yet there isn’t a train goes by all day But I hear its whistle shrieking.
Explanation:
In this stanza, the speaker describes how the railway tracks are far from where they are, and the day is noisy with people talking. Despite the distance and the absence of trains passing nearby, the speaker imagines hearing the loud, piercing whistle of a train every time one goes by. The word “shrieking” makes the whistle sound sharp and exciting, showing how the speaker’s mind is always on trains. This reflects their strong fascination with travel, as the idea of a train’s journey captures their attention even in a busy, noisy day, pulling them away from the chatter around them.
Stanza 2
All night there isn’t a train goes by, Though the night is still for sleep and dreaming, But I see its cinders red on the sky, And hear its engine steaming.
Explanation:
Here, the speaker talks about the quiet night, a time meant for sleeping and dreaming. Even though no trains pass close by, the speaker imagines seeing the train’s red cinders—glowing sparks from the engine—lighting up the night sky and hearing the sound of the engine puffing steam. This vivid picture shows how the speaker’s imagination keeps the train alive in their mind, even in the calm and silent night. The cinders and steaming engine add a sense of movement and energy, revealing the speaker’s excitement about trains and the adventures they represent, keeping them awake with thoughts of travel.
Stanza 3
My heart is warm with the friends I make, And better friends I’ll not be knowing; Yet there isn’t a train I wouldn’t take, No matter where it’s going.
Explanation:
In the final stanza, the speaker shares their love for the friends they’ve made, describing their heart as “warm” with affection and saying they couldn’t find better friends. However, despite this happiness, the speaker admits they would jump on any train, no matter where it’s headed. This shows a powerful pull toward travel and exploration that is stronger than their ties to friends. The phrase “no matter where it’s going” highlights the speaker’s adventurous spirit, ready to embrace the unknown just for the thrill of the journey. It balances the comfort of friendship with the irresistible call of new experiences.
Moral of the Poem
The poem teaches us that a love for adventure and exploration can live alongside strong connections with friends.
It encourages us to embrace curiosity and be open to new experiences, even if it means leaving the familiar behind.
The speaker’s excitement for travel shows that following your passions can lead to a fuller, more exciting life.
Difficult Words
Here are the meanings of some difficult words from the poem, explained simply:
Railroad: A track made of steel rails for trains to travel on.
Shrieking: Making a loud, high-pitched sound, like a sharp whistle.
Cinders: Small pieces of burnt coal or wood, like glowing sparks from a train’s engine.
Steaming: Giving off steam, like the puffing sound from a train’s engine.
Warm: Full of love or affection, like feeling happy and close to friends.
This exciting story, written by Ruskin Bond, follows Suraj, a young boy who loves adventure and is fascinated by trains.
Set in a jungle near a railway tunnel, the story describes Suraj’s visit to watch a steam train burst out of the tunnel and his unexpected meeting with Sunder Singh, the watchman who looks after the tunnel.
Together, they share a thrilling moment when they face a leopard in the tunnel, forming a special friendship.
The story is full of vivid descriptions of the jungle and the train, capturing the thrill of exploration and bravery.
Explanation of the Story
Suraj’s Fascination with the Jungle Train
The story begins on a hot noon in a jungle where a railway track cuts through towering evergreen trees. Suraj, a young boy, waits near a tunnel, eager to watch the midday steam train burst out. He isn’t catching a train; he simply loves the sight of it, finding it magical. He has cycled from town, hidden his bike in a nearby village, and walked over a hill to reach the tunnel’s exit.
As he waits, he hears the distant whistle and rumble. The train bursts out like a green, black, and gold dragon, spitting sparks and roaring past, stirring the jungle into motion. After the train passes, Suraj, curious, decides to walk through the tunnel. Inside, it’s damp, smoky, and dark, with a bat and a lizard startling him. Emerging into sunlight on the other side, he notices a flash of orange and gold on the hillside—a swishing tail disappearing among the trees.
Meeting Sunder Singh, the Watchman
Nearby, Suraj finds a small hut belonging to Sunder Singh, the tunnel’s watchman. His job is to inspect the tunnel and signal trains if anything is wrong—using a red flag by day or an oil lamp at night. Sunder Singh welcomes Suraj warmly, joking that the tunnel is “his,” though officially it belongs to the government.
As they chat, Suraj mentions the flash he saw, and Sunder Singh explains it was “his” leopard—a familiar visitor to the area, harmless unless provoked. He also tells Suraj about the night train at 9 p.m., inviting him to return and promising to escort him home safely. Suraj leaves, planning to get his parents’ permission.
The Night Adventure
The next evening, Suraj returns. As the jungle cools and darkens, they enjoy tea, surrounded by the sounds of birds and forest creatures. When darkness falls, Sunder Singh checks the tunnel with his oil lamp while Suraj waits.
Suddenly, they hear a sawing sound from the tunnel. Realising the leopard is inside and could be hit by the oncoming train, Sunder Singh decides to scare it away. Taking an axe for safety and reassuring Suraj, they both enter the tunnel. Their shouts and lamp startle the leopard, which flees into the jungle. After ensuring the tracks are clear, they step aside just in time as the night train roars through, leaving the jungle still and silent once again.
Suraj’s Farewell to the Jungle
A week later, Suraj rides the same night train with his father, who is heading to Delhi on business. As the train crosses bridges and villages, Suraj recognises the tunnel. Peering out into the darkness, he spots a familiar glow—the oil lamp of Sunder Singh, standing watch. As the train speeds through and the jungle fades behind, Suraj thinks fondly of the lonely watchman who lights up the darkness for both trains and leopards.
Moral of the Story
The story teaches us that courage and curiosity can lead to exciting adventures and unexpected friendships.
Suraj’s bravery in exploring the tunnel and facing the leopard with Sunder Singh shows that stepping out of your comfort zone can bring rewarding experiences.
It also highlights the importance of kindness and trust, as seen in the bond between Suraj and Sunder Singh, who work together to protect the leopard.
Difficult Words
Here are the meanings of some difficult words from the story, explained simply:
Shimmered: Shined with a soft, wavy light.
Embankment: A wall of stones or earth to support a railway.
Cutting: A narrow path dug through a hill for a railway.
Scrub-covered: Covered with short trees and bushes.
Serpents: Snakes, used here to describe the railway tracks.
Snorting: Making a loud sound through the nose, like the train’s engine.
Puffing: Blowing out air or steam in short bursts.
Instinctively: Doing something without thinking, like a reflex.
Flinch: To pull back quickly from something surprising or scary.
Plume: A long, thin cloud, like smoke trailing behind.
Shisham: A type of tree found in northern India.
Contemplation: Deep thinking or daydreaming.
Reassure: To make someone feel calm or safe.
Scuttled: Ran quickly with small steps.
Dazzled: Blinded or amazed by bright light.
Swishing: Moving with a soft, sweeping sound, like a tail.
Obstacles: Things that block or get in the way.
Porcupine: A small animal with sharp spines on its back.
Range: An area or region, like where the leopard roams.
Yawned: Opened the mouth wide, usually when tired.
Swooped: Moved down quickly through the air, like birds flying.
Scent: A pleasant smell, like of flowers.
Tailorbird: A small bird known for sewing leaves to make a nest.
Twilight: The soft light just after sunset or before sunrise.
Quaint: Unusual or old-fashioned in a charming way.
Nightjar: A bird active at night with a short beak.
Flexing: Bending or stretching, like limbs moving.
Trimming: Adjusting, like fixing the wick of a lamp.
Padded: Soft, quiet steps, like an animal’s footsteps.
Rustle: A soft sound, like leaves moving.
Sawing: A back-and-forth sound, like cutting wood.
Lithe: Slim and graceful in movement.
Sinewy: Lean and strong, with visible muscles.
Snarling: Growling with teeth shown, like an angry animal.
Twitching: Making small, sudden movements.
Defying: Challenging or standing up against something.
Tremor: A slight shaking or vibration.
Scribbling: Writing quickly or messily.
Fringe: The edge or border, like the jungle’s boundary.
Flickering: Shining with an unsteady, wavering light.
This story follows Shaana, a young girl from Rameswaram island, who travels across India with her parents.
Through postcards written to her friends, she shares her experiences of visiting different places, exploring diverse landscapes, and learning about India’s rich geography and culture.
The story highlights the beauty and variety of India’s regions.
ExplanationShaana’s travel adventure takes her across various parts of India, each with its unique geography, weather, and wildlife. Her journey reflects her curiosity, playful spirit, and growing confidence.
Kashmir (North) – Glaciers and SnowballsIn her 30 April postcard, Shaana writes from Thajiwas Glacier in Kashmir, high up in the north. She describes the white and blue glaciers and how they all had to wear four layers of clothes because of the freezing cold. Her parents enjoy throwing snowballs at each other and love the place. However, they notice that there was more snow the previous year, hinting at possible climate changes. Shaana likes the snow but feels so cold that her hands shake from not wearing gloves. She ends her note by sending love to her PT teacher and Library Ma’am.
Thajiwas Glacier
Himachal Pradesh – Mountains and Playful ImaginationOn 10 May, Shaana reaches Himachal Pradesh. She enjoys the peaceful mountains and is woken up each morning by the chirping of colourful birds. At night, she hears growling sounds and imagines they are bears, but her mother says it’s just her father snoring. She even jokes about wanting to hug a bear, showing her playful imagination and adventurous spirit.
Arunachal Pradesh – Forests and Red PandasIn her 17 May postcard, Shaana travels all the way east to Arunachal Pradesh, which she learns is far from Himachal Pradesh. The journey includes two trains and a long drive through a dense forest, where they reach a treehouse. The forest is so thick that Shaana warns that if you blink or stop to tie your shoelace, you could get lost. She declares Arunachal her favourite stop so far and hopes to see red pandas, reflecting her growing love for nature and wildlife.
Red Pandas
Sundarbans, West Bengal – Mangroves and Crocodiles
By 24 May, Shaana reaches the Sundarbans in West Bengal, a wetland area where mangrove trees grow in seawater. She is surprised to learn this and feels amazed. During a boat ride, she spots crocodiles and a lonely snake, which makes her both nervous and excited. Her mother expresses sadness about how much the area floods now, gently introducing the topic of climate change.
Sundarbans
Gujarat – Deserts and Surprise Test
In her 30 May postcard, Shaana shares that they’ve crossed the entire country from east to west, reaching Gujarat. She finds the desert hot, dry, and sandy, calling it a beach without the sea. Although she dislikes the heat, she loves the colourful clothes worn by people in the region. Her mother surprises her with a holiday test, and Shaana proudly says she scored 88%, showing she’s still learning even while travelling.
Narmada River – Rafting and Water Thrills
On 7 June, Shaana writes about travelling to the Narmada River in central India, after leaving the desert. She tries rafting, which she finds wild and fast, unlike the calm image she had of rivers. She ends up soaked, while her father is so scared he swears never to go rafting again. Shaana, on the other hand, loves the water and wants to do it again.
Goa – Plateaus, Beaches, and Tunnels
Shaana writes from Goa on 12 June, describing the beautiful plateaus, hills, and beaches. She travels by train through many tunnels, something she used to fear but now enjoys. She says she would love to go on a plateau tour with her friends in the future, showing how her confidence has grown.
Chennai and Puducherry – Surfing and Family Fun
In her 17 June postcard, Shaana returns to Tamil Nadu, visiting Chennai and then Puducherry. She learns to surf and only falls twice, proudly saying she’s good at it now. Her parents play in the water like children, and she jokes about having to control them. She also observes that the waves and water here are different from those on her island.
Olaikaadu Beach – Floating and Pebble Treasures
On 24 June, before heading home, Shaana’s family stops at Olaikaadu beach. She wants to learn diving, but there aren’t any suits in her size, so she spends the day floating and watching fish while her parents dive. She also collects pretty pebbles, which she plans to gift her classmates.
Back Home in Rameswaram – Reflections and Farewell
In her final letter dated 25 June, Shaana writes to her parents, amazed that they travelled across the entire country. She fondly remembers the forests, glaciers, deserts, wetlands, rivers, plateaus, and beaches, as well as the different languages and people they encountered. She expresses a desire to travel again and take her friends along next time.
Conclusion: A Journey Through India’s DiversityShaana’s adventure captures the geographical and cultural richness of India—from the snowy glaciers of the north to the sandy deserts of the west, the thick forests of the east to the beaches of the south. Through her postcards, she shares her joy, imagination, fears, and growing confidence. Her journey is both an exploration of nature and a discovery of herself, showing that travel is not just about visiting places—but about seeing the world with curiosity and wonder.
Moral of the Story
The story teaches us to appreciate the beauty and diversity of our country.
It encourages curiosity and openness to new experiences, as Shaana learns about different landscapes, animals, and environmental changes.
It also shows the importance of sharing experiences with others, fostering a sense of connection and understanding.
Difficult Words
Glacier: A large mass of ice that moves slowly over land.
Chirping: Short, sharp sounds made by birds.
Snoring: Loud breathing noises made while sleeping.
Treehouse: A small house built in a tree.
Wetlands: Areas of land covered with water, like marshes or swamps.
Mangroves: Trees that grow in salty coastal waters.
Plateaus: Flat, elevated areas of land.
Rafting: Traveling on a river using a small inflatable boat.
Yes, one screw was bit longer than the other
is read as “four and one-tenth”
is read as “forty-one and one-tenth”
The other is marked in quarters (¼, ½, ¾…)
Dividing one-tenth (1/10) by 10 gives one-hundredth (1/100).
…and so on!
Fractional Parts (tenths, hundredths, etc.) are to the right of the decimal point.
The 4th division after 1 is 1.4.
Total = 6 + 2/10 = 6.2 m
2.7 = 2 + 7/10So, difference = 8/10 = 0.8
This could be dangerous when giving medicine.
This shows why it’s important to know what decimals mean in real measurements.
Some countries today use comma instead of a dot (e.g., 1,000.5 becomes 1.000,5).
Group the first two terms:
Group the last two terms:
Wear her hat first, then her shoes, or
Wear her shoes first, then her hat.
This Image is correct
Each floor is about 4 times his height.
1 Lakh Varieties of Rice
But saying “about 75,000 people live there” gives a quick idea without needing to know the exact count.
Then, 206 × 100 = 20600
