Worksheet Solutions: Far and Near

Q1: 250 cm = ? m
(a) 2.5 m
(b) 25 m
(c) 0.25 m
(d) 2500 m
Sol: (a) 2.5 m

1 meter = 100 centimeters
So, 250 ÷ 100 = 2.5 meters

Q2: A rope is 600 cm long. If cut into 10 equal pieces, the length of each piece is:
(a) 60 m
(b) 60 cm
(c) 6 m
(d) 600 m
Sol: (b) 60 cm

Total length = 600 cm
Number of pieces = 10
Each piece = 600 ÷ 10 = 60 cm

Q3: 5 km = ? m
(a) 500
(b) 5000
(c) 50
(d) 50,000
Sol: (b) 5000

1 kilometer = 1000 meters
So, 5 × 1000 = 5000 meters

Q4: A train is 250 m long. What is its length in kilometers?
(a) 0.025 km
(b) 2.5 km
(c) 0.25 km
(d) 25 km
Sol: (c) 0.25 km

1 kilometer = 1000 meters
So, 250 ÷ 1000 = 0.25 kilometers

Q5: A ribbon is 36 m long. If each piece is 4 m long, how many pieces can be cut?
(a) 8
(b) 9
(c) 10
(d) 12
Sol: (b) 9

Total length = 36 meters
Each piece = 4 meters
Number of pieces = 36 ÷ 4 = 9

Q6: Convert the following into centimeters.

(i) 66 mm

(ii) 32 dm

(iii) 4 cm 8 mm

(iv) 63 km

(v) 16 m

(vi) 1.5 dm

Sol: We use:

  • 1 cm = 10 mm
  • 1 dm = 10 cm
  • 1 m = 100 cm
  • 1 km = 1000 m = 100,000 cm

(i) 66 mm
Since 10 mm = 1 cm
66 mm = 66 ÷ 10 = 6.6 cm

(ii) 32 dm
Since 1 dm = 10 cm
32 dm = 32 × 10 = 320 cm

(iii) 4 cm 8 mm
8 mm = 0.8 cm
So, 4 cm + 0.8 cm = 4.8 cm

(iv) 63 km
1 km = 100,000 cm
63 km = 63 × 100,000 = 6,300,000 cm

(v) 16 m
1 m = 100 cm
16 m = 16 × 100 = 1600 cm

(vi) 1.5 dm
1 dm = 10 cm
1.5 dm = 1.5 × 10 = 15 cm

Q7: Convert the following into kilometers.

(i) 14 m

(ii) 59 hm

(iii) 136 dam

(iv) 207 dam

(v) 5600 cm

(vi) 10000 cm

Sol: We use:

  • 1 km = 1000 m
  • 1 hm (hectometer) = 100 m
  • 1 dam (decameter) = 10 m
  • 1 m = 100 cm

(i) 14 m
1 km = 1000 m
14 m = 14 ÷ 1000 = 0.014 km

(ii) 59 hm
1 hm = 100 m
59 hm = 59 × 100 = 5900 m
5900 ÷ 1000 = 5.9 km

(iii) 136 dam
1 dam = 10 m
136 dam = 136 × 10 = 1360 m
1360 ÷ 1000 = 1.36 km

(iv) 207 dam
207 dam = 207 × 10 = 2070 m
2070 ÷ 1000 = 2.07 km

(v) 5600 cm
1 m = 100 cm → 5600 cm = 5600 ÷ 100 = 56 m
Now, 56 ÷ 1000 = 0.056 km

(vi) 10000 cm
10000 ÷ 100 = 100 m
100 ÷ 1000 = 0.1 km

Q8: Compare the following using >, < or = sign:

(i) 702 cm ………. 503 cm

(ii) 2 m ………. 9 m

(iii) 800 cm ………. 80 m

(iv) 702 cm ………. 5 m

(v) 8 km ………. 7000 m

(vi) 625 cm ………. 9 m

(vii) 10 m ………. 4 cm

(viii) 1000 m ………. 1000 km

(ix) 100 cm ………. 100 m

(x) 1 km ………. 1000 m

Sol: (i) 702 cm > 503 cm 
So, 702 cm > 503 cm

(ii) 2 m … 9 m
Clearly, 2 m < 9 m

(iii) 800 cm … 80 m
Convert: 800 cm = 8 m.
So, 8 m < 80 m 
→ 800 cm < 80 m

(iv) 702 cm … 5 m
Convert: 702 cm = 7 m 2 cm = 7.02 m.
So, 7.02 m > 5 m 
→ 702 cm > 5 m

(v) 8 km … 7000 m
Convert: 8 km = 8000 m.
So, 8000 m > 7000 m 
→ 8 km > 7000 m

(vi) 625 cm … 9 m
Convert: 625 cm = 6 m 25 cm = 6.25 m.
So, 6.25 m < 9 m 
→ 625 cm < 9 m

(vii) 10 m … 4 cm
Convert: 10 m = 1000 cm.
So, 1000 cm > 4 cm 
→ 10 m > 4 cm

(viii) 1000 m … 1000 km
Convert: 1000 m = 1 km.
So, 1 km < 1000 km 

→ 1000 m < 1000 km

(ix) 100 cm … 100 m
Convert: 100 cm = 1 m.
So, 1 m < 100 m 
→ 100 cm < 100 m

(x) 1 km … 1000 m
Convert: 1 km = 1000 m.
So, 1 km = 1000 m

Q9: A road between two villages is 8 km 250 m long. Out of this, workers have repaired 5 km 750 m. How much road is still left to repair?

Sol: Total length of road = 8 km 250 m
Repaired length = 5 km 750 m

First, convert both into metres:

  • 8 km 250 m = 8000 + 250 = 8250 m
  • 5 km 750 m = 5000 + 750 = 5750 m

Length left to repair = 8250 – 5750 = 2500 m

Now convert back into km and m:
2500 m = 2 km 500 m

2 km 500 m of road is still left to repair.

Q10: A cloth merchant bought a roll of cloth 45 m long. He sold 12 m 40 cm to one customer and 18 m 60 cm to another. How much cloth is left with him?

Sol: Total length of cloth = 45 m

Sold cloth:

  • To first customer = 12 m 40 cm = 12.40 m
  • To second customer = 18 m 60 cm = 18.60 m

Total cloth sold = 12.40 m + 18.60 m = 31.00 m

Cloth left = 45.00 m – 31.00 m = 14.00 m

14 m cloth is left with the merchant.

Q11: The distance from a school to the railway station is 4 km 300 m. The bus travels this distance in the morning and returns in the afternoon. What is the total distance covered by the bus in a day?

Sol: Distance from school to railway station = 4 km 300 m

Since the bus goes in the morning and comes back in the afternoon, the distance is covered two times.

Convert into metres first:
4 km 300 m = 4000 + 300 = 4300 m

Total distance = 2 × 4300 = 8600 m

Now convert back into km and m:
8600 m = 8 km 600 m 

The bus covers 8 km 600 m in a day.

Q12: A ribbon is 96 m long. It is cut into 12 equal pieces. What is the length of each piece?

Sol: Total length of ribbon = 96 m
Number of equal pieces = 12

Length of each piece = 96 ÷ 12 = 8 m

Each piece is 8 m long.

Q13: A man walks 3 km every day. How many kilometers will he walk in 15 days?

Sol: Distance walked in 1 day = 3 km
Number of days = 15

Total distance = 3 × 15 = 45 km

The man will walk 45 km in 15 days.

Q14: A train travels 125 km in 1 hour. How much distance will it cover in 8 hours?

Sol: Distance covered in 1 hour = 125 km
Time = 8 hours

Total distance = 125 × 8 = 1000 km

The train will cover 1000 km in 8 hours.

Q15: A road is 420 m long. It is divided into 7 equal sections. What is the length of each section?

Sol: Total length of road = 420 m
Number of equal sections = 7

Length of each section = 420 ÷ 7 = 60 m

Each section is 60 m long.

Worksheet: Far and Near

Q1: 250 cm = ? m
(a) 2.5 m
(b) 25 m
(c) 0.25 m
(d) 2500 m

Q2: A rope is 600 cm long. If cut into 10 equal pieces, the length of each piece is:
(a60 m
(b) 60 cm
(c) 6 m
(d600 m

Q3: 5 km = ? m
(a) 500
(b) 5000
(c) 50
(d) 50,000

Q4: A train is 250 m long. What is its length in kilometers?
(a) 0.025 km
(b) 2.5 km
(c) 0.25 km
(d) 25 km

Q5: A ribbon is 36 m long. If each piece is 4 m long, how many pieces can be cut?
(a) 8
(b) 9
(c) 10
(d) 12

Q6: Convert the following into centimeters.

(i) 66 mm

(ii) 32 dm

(iii) 4 cm 8 mm

(iv) 63 km

(v) 16 m

(vi) 1.5 dm

Q7: Convert the following into kilometers.

(i) 14 m

(ii) 59 hm

(iii) 136 dam

(iv) 207 dam

(v) 5600 cm

(vi) 10000 cm

Q8: Compare the following using >, < or = sign:

(i) 702 cm ………. 503 cm

(ii) 2 m ………. 9 m

(iii) 800 cm ………. 80 m

(iv) 702 cm ………. 5 m

(v) 8 km ………. 7000 m

(vi) 625 cm ………. 9 m

(vii) 10 m ………. 4 cm

(viii) 1000 m ………. 1000 km

(ix) 100 cm ………. 100 m

(x) 1 km ………. 1000 m

Q9: A road between two villages is 8 km 250 m long. Out of this, workers have repaired 5 km 750 m. How much road is still left to repair?

Q10: A cloth merchant bought a roll of cloth 45 m long. He sold 12 m 40 cm to one customer and 18 m 60 cm to another. How much cloth is left with him?

Q11: The distance from a school to the railway station is 4 km 300 m. The bus travels this distance in the morning and returns in the afternoon. What is the total distance covered by the bus in a day?

Q12: A ribbon is 96 m long. It is cut into 12 equal pieces. What is the length of each piece?

Q13: A man walks 3 km every day. How many kilometers will he walk in 15 days?

Q14: A train travels 125 km in 1 hour. How much distance will it cover in 8 hours?

Q15: A road is 420 m long. It is divided into 7 equal sections. What is the length of each section?

Worksheet Solutions: We the Travellers—II

Q1: Arrange in columns and add:
(a) 215, 340 and 100

Ans:

= 215 + 340 + 100 = 650

(b) 321, 436 and 157

= 321 + 436 + 157 = 914

Q2:  Add:

(a) 

Ans: 

(b) 

Ans: 

 (c)

Ans: 


Q3: Fill in thewith the correct digits:

(a) 

(b) 
Ans: (a) The missing numbers are 8724, 0142, 1013.

  • First number = 8724
  • Second number = 0142
  • Third number = 1013
  • Sum = 9879

(b) The missing numbers are 3057, 5610, 1202.

  • First number = 3057
  • Second number = 5610
  • Third number = 1202
  • Sum = 9869

Q4: Monika had Rs 2,183 in her bank account. She again deposited Rs 1,345. What is the amount in Monika’s bank account now?
AnsAmount of money Monika had in the bank = Rs 2,183
Amount Monika deposited in the bank again = Rs 1,345. 

Total amount submitted by Monika = Rs. (2183 + 1345) = Rs. 3528

Q5: Arrange in columns and find the sum:
(a) 2,751 + 3,201 + 536
(b) 205 + 6,879 + 2,752
(c) 5196 + 2,861 + 1,674

Ans(a) 2,751 + 3,201 + 536 = 6488

(b) 205 + 6,879 + 2,752 = 9836

(c) 5196 + 2,861 + 1,674 = 9731

Q6: What is 100 more than:

(a) 9,175 + 100 = 9,275
Ans: Start from the hundreds place in 9,175. 
Adding 100 gives:
9,175 + 100 = 9,275.

(b) 7,132 + 100 = 7,232
Ans: Start from the hundreds place in 7,132. 
Adding 100 gives:
7,132 + 100 = 7,232.

(c) 3,721 + 100 = 3,821
Ans: Start from the hundreds place in 3,721. 
Adding 100 gives:
3,721 + 100 = 3,821.

Q7: What is one more than:

(a) 2,738 + 1 = 2,739
Ans: Start from the ones place in 2,738. 
Adding 1 gives:
2,738 + 1 = 2,739.

(b) 8,643 + 1 = 8,644
Ans: Start from the ones place in 8,643. 
Adding 1 gives:
8,643 + 1 = 8,644.

Q8: Fill in the blanks:
(a) ______+ 2,432 = 2,432 + ______= 2,432
(b) 1,937 + 3,132 = 3,132 + ______.
Ans:
(a) 0 + 2,432 = 2,432 + = 2,432 (Since zero added to any number is the number itself)
(b) 1,937 + 3,132 = 3,132 + 1937  (By using the commutative property of addition which  is a fundamental property in maths that states that the order in which you add two numbers does not affect the sum.)

Q9: In an examination, 6,381 boys and 2,954 girls appeared. How many students in all appeared for the examination?
AnsNumber of boys who appeared for exam = 6381
Number of girls who appeared for exam = 2954

Total number of students = 9335


Q10: At a meeting addressed by a political leader, there were 2,649 men 3,259 women and 837 children. How many people were present at the meeting?
AnsNumber of men = 2649
Number of women = 3259
Number of children = 837
Total number of people at the meeting = 2649  + 3259 + 837

Therefore, total number of people present in the meeting = 6745
Q11: Subtract:

(a) 
(b) 
Ans: (a)  400 – 321 = 79
(b) 591 – 360 = 231

Q12: Find the difference between : 
(
a) 153 and 256
(b) 781 and 651

Ans:
(a) 153 and 256 = 256 – 153 = 103
(b) 781 and 651 = 781 – 651 = 130

Q13: Fill in the boxes:
(a) 

Ans

  • Top number = 8617
  • Bottom number = 4223
  • Result = 4394

(b) 

Ans: 

  • Top number = 6328
  • Bottom number = 2725
  • Result = 3603

Q14: Fill in the blanks:
(a) 6,821 – 10 = ______.
(b) 491 – 10 = ______.
(c) 9,386- 100  ______.
Ans:

(a) 6,821 – 10 = 6,811.
(b) 491 – 10 = 481.
(c) 9,386- 100  = 9,286.

Q15: In the year 2010, a poultry farm produced 6,134 eggs. In 2011, it produced 1,785 eggs less than that in 2010. How many eggs were produced in 2011?
Ans: Number of eggs produced by poultry farm in 2010 = 6134
Number of eggs produced in 2011 = Number of eggs produced in 2010 = 6134 – 1785
Therefore, Eggs produced in 2011 = 4349


Q16: What must be added to 2,176 to get 5, 158?
AnsTo know which number should be added to 2176 to get 5158, we have to subtract the two numbers = 5158 – 2176 = 2982 should be added to 2176 to get 5158
Q17: In an examination, 8380 candidates appeared. Out of these, 4,090 candidates failed. How many candidates passed?
AnsNumber of candidates appeared = 8380
Number of candidates failed = 4090
Number of candidates passed = 8380 – 4090 = 4290


Q18: Last year, a cycle factory produced 8,319 cycles. This year the production came down by 5, 761 cycles. What is the production this year?
AnsLast year, a cycle factory produced = 8319
This year a cycle factory produced less by = 5761
The production this year = 2558 cycles

Q19: To find the difference between two numbers, we always subtract the ______ number from the ______ number.

AnsTo find the difference between two numbers, we always subtract the greater number from the smaller number.

Q20: I am a 5 digit number. My tens digit is 2. My ones and hundreds digit is twice the tens digit. My thousands digit is one subtracted from the product of the ones and tens digit. My ten thousands digit is the difference between the thousands and the tens digit. What number am ‘I’?

Ans: Tens digit = 2
∴ Ones digit = 2×2=4
Hundreds digit = 2×2=4
Thousands digit = (2×4) – 1= 7
Ten thousand digit = 7-2 = 5
∴ The number is
TTh Th H T O
5 7 4 2 4

Worksheet: We the Travellers—II

Q1: Arrange in columns and add:
(a) 215, 340 and 100
(b) 321, 436 and 157
You can take the help of this example to solve the above questions:
Addition of 293 and 146:  

Worksheet: We the Travellers—IIQ2:  Add:
(a) 
(b)  
(c)

You can take the help of this example to solve the above questions:
Addition of 6134 and 2423: Worksheet: We the Travellers—II

Q3: Fill in theWorksheet: We the Travellers—IIwith the correct digits:

(a) Worksheet: We the Travellers—II

(b) Worksheet: We the Travellers—IIYou can take the help of this example to solve the above questions:
Addition of 6134 and 2423:

Q4: Monika had Rs 2,183 in her bank account. She again deposited Rs 1,345. What is the amount in Monika’s bank account now?

Q5: Arrange in columns and find the sum:
(a)
 2,751 + 3,201 + 536
(b) 205 + 6,879 + 2,752
(c) 5196 + 2,861 + 1,674
You can take the help of this example to solve the above questions:

Worksheet: We the Travellers—II

Worksheet: We the Travellers—IIQ6: What is 100 more than:
(a) 9,175 ______.
(b) 7,132 ______.
(c) 3,721 ______.

Q7: What is one more than:
(a) 2,738 ______.
(b) 8,643 ______.

Q8: Fill in the blanks:
(a)
 ______+ 2,432 = 2,432 + ______= 2,432
(b)
 1,937 + 3,132 = 3,132 + ______.

Q9: In an examination 6,381 boys and 2,954 girls appeared. How many students in all appeared for the examination?

Q10: At a meeting addressed by a political leader, there were 2,649 men 3,259 women and 837 children. How many people were present at the meeting?

Q11: Subtract:
(a) 
(b) 

Q12: Find the difference between :
(a)
 153 and 256
(b) 781 and 651

Q13: Fill in the boxes:
(a) 

(b) 

Q14: Fill in the blanks:
(a) 
6,821 – 10 = ______.
(b) 491 – 10 = ______.
(c) 9,386- 100  ______.

Q15: In year 2010, a poultry farm produced 6,134 eggs. In 2011, it produced 1,785 eggs less than that in 2010. How many eggs were produced in 2011?

Q16: What must be added to 2,176 to get 5, 158?

Q17: In an examination 8,380 candidates appeared. Out of these, 4,090 candidates failed. How many candidates passed?

Q18: Last year, a cycle factory produced 8,319 cycles. This year the production came down by 5, 761 cycles. What is the production this year?

Worksheet: We the Travellers—II

Q19: To find the difference between two numbers, we always subtract the ______ number from the ______ number.

Q20: I am a 5-digit number. My tens digit is 2. My ones and hundreds digit is twice the tens digit. My thousands digit is one subtracted from the product of the ones and tens digit. My ten thousand digit is the difference between the thousands and the tens digit. What number am ‘I’?

Worksheet (Solutions): Angles as Turns

Q1: A full turn is equal to how many degrees?
​(a) 90°
(b) 180°
(c) 270°
(d) 360°
Ans: (d)

Q2: Two half turns in the same direction are equal to:
(a) A quarter turn
(b) A full turn
(c) Three-quarter turn
(d) No turn
Ans: (b)

Q3: How many quarter turns make a full turn?
(a) 2
(b) 3
(c) 4
(d) 6
Ans: (c)

Q4: How many degrees are in one quarter turn?
(a) 45°
(b) 60°
(c) 90°
(d) 120°
Ans: (c)

Q5: A reflex angle is always:
(a) 
Less than 90°
(b) Between 90° and 180°
(c) Between 180° and 360°
(d) Equal to 90°
Ans: (c)

Q6: For each arrow turn, guess the size in degrees and state the type. 

(a) 1 quarter turn clockwise → ______ ° → type: __________

(b) 3 quarter turns anti‑clockwise → ______ ° → type: __________

(c) 1/2 of a full turn → ______ ° → type: __________

(d) 2/3 of a full turn  → ______ ° → type: __________

(a) 1 quarter turn clockwise
= 90°
→ type: Right angle

(b) 3 quarter turns anti-clockwise
= 3 × 90° = 270°
→ type: Reflex angle (since it’s more than 180° but less than 360°)

(c) 1/2 of a full turn
= 360° ÷ 2 = 180°
→ type: Straight angle

(d) 2/3 of a full turn
= (2/3) × 360° = 240°
→ type: Reflex angle

Q7: A robot starts facing East. It makes the following sequence of turns:

  • 1 quarter turn clockwise,
  • 1 half turn anti‑clockwise,
  • 3 quarter turns clockwise.

(a) What direction is it facing now? __________
(b) What is the net turn (in degrees) relative to the start? __________°

Ans: 

Start: Facing East.

  1. 1 quarter turn clockwise → from East → South.
  2. 1 half turn anti-clockwise → from South → turn 180° left → North.
  3. 3 quarter turns clockwise → 270° right from North → West.

So final direction = West.

Now, net turn relative to start (East):

  • East → West is a 180° turn.
  • Since the robot ended up on the opposite side of its start, the net turn is ±180°.
  • Conventionally, we write it as −180° (anticlockwise) or +180° (clockwise)

Final answers (a) West
(b) Net 180°

Q8: Identify the type of angles given below: 

Ans: 

a. Right Angle 

b. Acute Angle 

c. Obtuse Angle

Q9. Draw angles with the following degree measures:

a. 60°

b. 45°

c. 180°

Ans:

 a.b.c.

Q10: Draw The following angles 

(a) a right angle and label it as ∠ABC.
Ans: 

(b) an acute angle and label it as ∠XYZ.
Ans: 

(c) a straight angle and label it as ∠PQR.
Ans: 

Worksheet: Angles as Turns

Q1: A full turn is equal to how many degrees?
​(a) 90°
(b) 180°
(c) 270°
(d) 360°

Q2: Two half turns in the same direction are equal to:
(a) A quarter turn
(b) A full turn
(c) Three-quarter turn
(d) No turn

Q3: How many quarter turns make a full turn?
(a) 2
(b) 3
(c) 4
(d) 6

Q4: How many degrees are in one quarter turn?
(a) 45°
(b) 60°
(c) 90°
(d) 120°

Q5: A reflex angle is always:
(a) 
Less than 90°
(b) Between 90° and 180°
(c) Between 180° and 360°
(d) Equal to 90°

Q6: For each arrow turn, guess the size in degrees and state the type. 

(a) 1 quarter turn clockwise → ______ ° → type: __________

(b) 3 quarter turns anti‑clockwise → ______ ° → type: __________

(c) 1/2 of a full turn → ______ ° → type: __________

(d) 2/3 of a full turn  → ______ ° → type: __________

Q7: A robot starts facing East. It makes the following sequence of turns:

  • 1 quarter turn clockwise,
  • 1 half turn anti‑clockwise,
  • 3 quarter turns clockwise.

(a) What direction is it facing now? __________
(b) What is the net turn (in degrees) relative to the start? __________°

Q8: Identify the type of angles given below: 

Worksheet: Angles as Turns

Q9. Draw angles with the following degree measures:

a. 60°

b. 45°

c. 180°

Q10: Draw the following angles:

(a) a right angle and label it as ∠ABC.

(b) an acute angle and label it as ∠XYZ.

(c) a straight angle and label it as ∠PQR.

Worksheet Solutions: Fractions

Q1: Divide each collection into two equal parts by dotted lines:

(i) 

(ii) 

(iii) 

Ans:

Q2: In each of the following write the fraction representing the shaded portion:

(i) 

Ans: = 1/3

(ii)      
Ans: = 1/4

(iii) 
Ans: = 1/3

Q3: Write the fraction whose.
(i) Numerator is 7 and denominator is 15.
Ans:
 7/15

(ii) Numerator is 22 and denominator is 35.
Ans: 
22/35

Q4: Divide each collection into a suitable number of equal parts and fill in the blanks:

(i) 

1/2 of 8 = ______.

Ans: 4

(ii) 

1/8 of 16 = ______.

Ans: 2

(iii) 

5/6 of 18 = ______.
Ans: 
15

Q5: Draw a collection of objects. Divide the collection into suitable number of equal parts and find

(i) 1/3 of 9

Ans:

= 3

(ii) 3/7 of 14
Ans:

= 6

(iii) 4/9 of 18
Ans:

= 8

Q6: Write the next three equivalent fractions of each of the following

(i) 1/4
Ans:
2/8, 4/16, 8/32

(ii) 2/3
Ans: 4/6, 8/12, 16/24

(iii) 5/9
Ans:
 10/18, 20/36, 40/72

(iv) 4/7
Ans:
 8/14, 16/28, 32/56

Q7: Fill in the missing numerators to make the statement true:
(i) 

Ans: 15

(ii) 

Ans: 5

(iii) 
Ans: 5

Q8: Find an equivalent fraction of 3/4 with:
(i) Numerator 15
Ans:
 Equivalent fraction of 3/4 with numerator 15: (3/4) × (5/5) = 15/20.

(ii) Denominator 48
Ans: 
Equivalent fraction of 3/4 with denominator 48: (3/4) x (12/12) = 36/48.

(iii) denominator 24
Ans:
 Equivalent fraction of 3/4 with denominator 24: (3/4) × (6/6) = 18/24.

Q9: Fill in the missing denominators to make the statement true:
(i) 

Ans: 21

(ii) 
Ans: 9

(iii) 

Ans: 40

Q10: Check whether the given fractions are equivalent:

(i) 3/15, 1/5

Ans: 3/15 in the simplest form is 1/5, thus equivalent.

(ii) 2/11, 6/21
Ans: 6/21 in the simplest form is 2/7, thus not equivalent.

(iii) 4/9, 8/18
Ans: 8/18 in the simplest form is 4/9, thus equivalent.

Q11: State whether the fraction is in its lowest terms or not:
(i) 12/20 
Ans: 
NO
The simplest form of 12/20 is 3/5.

(ii) 4/6
Ans: NO
The simplest form of 4/6 is 2/3.

(iii) 80/81
Ans: 
YES
The simplest form of 80/81 is 80/81 itself.

Q12: Reduce to the lowest terms: 
(i) 21/28
Ans: The simplest form of 21/28 is 3/4.

(ii) 45/60
Ans: The simplest form of 45/60 is 3/4.

(iii) 36/54
Ans: The simplest form of 36/54 is 2/3.

Q13: Encircle the fraction which is in its lowest terms:
(i) 

(ii) 

Ans:

Q14: Fill in the blanks by putting > or < in each of the following to make the statement true:

(i) 

Ans: >

(ii) Ans: <

(iii) Ans: >

Q15: Which is smaller in each of the following pairs of fractions?
(i) 3/16, 21/32
Ans: We need to make the denominator equal first,
3/16 x 2/2 = 6/32
6/32 < 21/32

(ii) 18/25, 2/5
Ans:
 We need to make the denominator equal first,
2/5 x 5/5 = 10/25
18/25 > 10/25

(iii) 8/21, 7/20
Ans: We need to make the denominator equal first,
LCM = 420
8/21 x 20/20 = 160/420
7/20 x 21/21 = 147/420

Q16: Find the sum:
(i) 1/8 + 2/8 + 3/8
Ans: 
6/8

(ii) 1/13 + 3/13 + 8/13
Ans: 12/13

(iii) 9/35 + 2/35 + 11/35
Ans: 22/35

Q17: Write the fractions whose numerator is 6 and denominator is 19.
Ans: 
6/19

Q18: ______ = ______.
Ans: (1+2+4)/7 = 1.

Worksheet: Fractions

Q1: Divide each collection into two equal parts by dotted lines:

(i) 

(ii) 

(iii) 

Q2: In each of the following write the fraction representing the shaded portion:

(i) 

(ii) 

(iii) 

Q3: Write the fraction whose
(i) Numerator is 7 and denominator is 15.

(ii) Numerator is 22 and denominator is 35.

Q4: Divide each collection into suitable number of equal parts and fill in the blanks:

(i) 
1/2 of 8 = ______.

(ii) 

1/8 of 16 = ______.

(iii) 

5/6 of 18 = ______.

Q5: Draw a collection of objects. Divide the collection into suitable number of equal parts and find:
(i) 1/3 of 9

(ii) 3/7 of 14

(iii) 4/9 of 18

Q6: Write the next three equivalent fractions of each of the following
(i) 1/4

(ii) 2/3

(iii) 5/9

(iv) 4/7

Q7: Fill in the missing numerators to make the statement true:

(i) 

(ii) 

(iii) 

Q8: Find an equivalent fraction of 3/4 with:
(i) Numerator 15

(ii) Denominator 48

(iii) denominator 24

Q9: Fill in the missing denominators to make the statement true:

(i) 

(ii) 

(iii) 

Q10: Check whether the given fractions are equivalent:
(i) 3/15, 1/5

(ii) 2/11, 6/21

(iii) 4/9, 8/18

Q11: State whether the fraction is in its lowest terms or not:
(i) 12/20

(ii) 4/6

(iii) 80/81

Q12: Reduce to the lowest terms:
(i) 21/28

(ii) 45/60

(iii) 36/54

Q13: Encircle the fraction which is in its lowest terms:

(i) 

(ii) 

Q14: Fill in the blanks by putting > or < in each of the following to make the statement true:

(i) 

(ii) 

(iii) 

Q15: Which is smaller in each of the following pairs of fractions?
(i) 3/16, 21/32

(ii) 18/25, 2/5

(iii) 8/21, 7/20

Q16Find the sum:

(i) 

(ii) 

(iii) 

Q17: Write the fractions whose numerator is 6 and denominator is 19.

Q18: ______ = ______.

Worksheet Solutions: We the Travellers—I (Part – 2)

Q1: Write the number that has 5 thousands, 7 hundreds, 8 tens, and 4 ones. 

(a) 5,748 

(b) 5,784 

(c) 5,874 

(d) 5,847

Ans: (b) 5,784

Q2: What is the value of the digit 3 in the number 5,327? 

(a) 3 

(b) 30 

(c) 300 

(d) 3,000

Ans: (c) 300

Q3: In the number 4,218, which digit is in the hundreds place? 

(a) 4 

(b) 2 

(c) 1 

(d) 8

Ans: (b) 2

Q4: Write the expanded form of the number 6,493. 

(a) 6000 + 400 + 90 + 3 

(b) 600 + 400 + 90 + 3 

(c) 6000 + 400 + 9 + 30 

(d) 6000 + 40 + 90 + 3

Ans: (a) 6000 + 400 + 90 + 3

Q5: If you add 300 to the number 1,472, what is the new number? 

(a) 1,772 

(b) 1,742 

(c) 1,770 

(d) 1,732

Ans: (a) 1,772

Q6: Round 96 to the nearest ten.
(a) 95
(b) 100
(c) 90
(d) 80

Ans: (b) 100

Q7: A store had 7,600 candies. They sold 3,250 candies. How many candies are left? 

(a) 4,250 

(b) 4,350 

(c) 4,340 

(d) 4,300

Ans: (a) 4,350

Q8: John has 1,234 stamps and his brother has 567 stamps. How many stamps do they have together? 

(a) 1,801 

(b) 1,701 

(c) 1,800 

(d) 1,700

Ans: (a) 1,801

Q9: If you have 6 thousands, 3 hundreds, 5 tens, and 8 ones, what is the number? 

(a) 6,358 

(b) 6,538 

(c) 6,835 

(d) 6,385

Ans: (a) 6,358

Q10: Choose the missing sign.
902 ___ 902
(a) >
(b) <
(c) =

Ans: (c)
Q11: Who am I?
(i) I am the smallest 5-digit number: _______________
(ii) I am the predecessor of 8,25,481: _______________
(iii) I am one more than 99,999: _______________
(iv) My place value in 9,83,351 is ten thousand: _______________
(v) I am the largest 6 – digit number: _______________

Ans:
(i) 10,000
(ii) 8,25,480
(iii) 1,00,000
(iv) 80,000
(v) 9,99,999

Q12: Write the number names for the following numerals.
(i) 89,53,828
(ii) 25,87,463
(iii) 341,906,235
(iv) 54,928,329
(v) 8,842,935

Ans:
(i) Eighty-nine lakh fifty-three thousand eight hundred twenty-eight
(ii) Twenty-five lakh eighty-seven thousand four hundred sixty-three
(iii)Three hundred forty-one million nine hundred six thousand two hundred thirty-five
(iv) Fifty-four million nine hundred twenty-eight thousand three hundred twenty-nine
(v) Eight million eight hundred forty-two thousand nine hundred thirty-five

Q13: Write the numerals for the following number names.
(i) Seventy nine lakhs ninety six thousand, two hundred and thirty eight.
(ii) Four hundred and thirty one million, nine hundred and seven thousand, five hundred and sixty three.
(iii) Two crores, seventy three lakhs, fifty six thousand, eight hundred and seventeen.
(iv) Seventy million four hundred and eight.

Ans:
(i) 79,96,238
(ii) 431,907,563
(iii) 2,73,56,817
(iv) 70,000,408

Q14: (a) Write the Number names for the following Numerals.
(i) 24,998
(ii) 1,84,305
(iii) 3,10,706

Ans:

(i) Twenty-four thousand nine hundred ninety-eight.
(ii) One lakh eighty-four thousand three hundred five.
(iii) Three lakh ten thousand seven hundred six.

(b) Write the numerals for the following number names.
(i) Three lakh twenty three thousand four hundred two
(ii) Six lakh ten thousand three hundred seven

Ans:
(i) 3,23,402
(ii) 6,10,307

Q15: Form the largest and smallest 5 or 6–digit numbers using the given digits.
(i) 3,  9,  4,  1,  7
(ii) 9,  6,  1,  5,  2
(iii) 3,  0,  8,  2,  7,  1

Ans: (i) 97,431; 13,479
(ii) 96,521; 12,569
(iii) 8,73,210; 1,02,378

Worksheet: We the Travellers—I (Part – 2)

Q1: Write the number that has 5 thousands, 7 hundreds, 8 tens, and 4 ones. 

(a) 5,748 

(b) 5,784 

(c) 5,874 

(d) 5,847

Q2: What is the value of the digit 3 in the number 5,327? 

(a) 3 

(b) 30 

(c) 300 

(d) 3,000

Q3: In the number 4,218, which digit is in the hundreds place? 

(a) 

(b) 2 

(c) 

(d) 8

Q4: Write the expanded form of the number 6,493. 

(a) 6000 + 400 + 90 + 3 

(b) 600 + 400 + 90 + 3 

(c) 6000 + 400 + 9 + 30 

(d) 6000 + 40 + 90 + 3

Q5: If you add 300 to the number 1,472, what is the new number? 

(a) 1,772 

(b) 1,742 

(c) 1,770

(d) 1,732

Q6: Round 96 to the nearest ten.
(a) 95

(b) 100

(c) 90

(d) 80

Q7: A store had 7,600 candies. They sold 3,250 candies. How many candies are left? 

(a) 4,250 

(b) 4,350 

(c) 4,340 

(d) 4,300

Q8: John has 1,234 stamps and his brother has 567 stamps. How many stamps do they have together? 

(a) 1,801 

(b) 1,701 

(c) 1,800 

(d) 1,700

Q9: If you have 6 thousands, 3 hundreds, 5 tens, and 8 ones, what is the number? 

(a) 6,358 

(b) 6,538 

(c) 6,835 

(d) 6,385


Q11: Who am I?
(i) I am the smallest 5-digit number: _______________
(ii) 
I am the predecessor of 8,25,481: _______________
(iii)
 I am one more than 99,999: _______________
(iv) 
My place value in 9,83,351 is ten thousand: _______________
(v) 
I am the largest 6 – digit number: _______________

Q12: Write the number names for the following numerals.
(i)
 89,53,828
(ii) 
25,87,463
(iii) 
341,906,235
(iv) 
54,928,329
(v) 
8,842,935

Q13: Write the numerals for the following number names.
(i) 
Seventy-nine lakh ninety-six thousand, two hundred and thirty-eight.
(ii) 
Four hundred and thirty-one million nine hundred and seven thousand five hundred and sixty-three.
(iii) 
Two crores seventy-three lakh fifty-six thousand eight hundred and seventeen.
(iv) 
Seventy million four hundred and eight.

Q14: (a) Write the Number names for the following Numerals.
(i) 24,998
(ii) 1,84,305
(iii) 3,10,706

(b) Write the numerals for the following number names.
(i) Three lakh twenty-three thousand four hundred two
(ii) Six lakh ten thousand three hundred seven

Q15: Form the largest and smallest 5 or 6–digit numbers using the given digits.
(i) 3,  9,  4,  1,  7
(ii
) 9,  6,  1,  5,  2
(iii)
 3,  0,  8,  2,  7,  1