Text Book Solutions All Class

Q1: Simplify:

Ans: LCM of 9 and 3 = 9.

Q2: Simplify: 

Ans: 

Q3: Find: 

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Q4: Simplify: 

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Q5: A chocolate bar weighskg. If  kg is eaten, how much is left?

Ans: 

Q6: If a wall is 5/6 painted, how much is unpainted?

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Q7: Convert  into an improper fraction and subtract.

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Q8: Convert into an improper fraction and divide it by .

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Q1: Can a triangle exist with side lengths 4 cm, 5 cm, and 10 cm? 

Ans: No.
Explanation: Apply the triangle inequality: 4 + 5 = 9 < 10, so the condition fails. A triangle cannot exist.

Q2: What is the third angle in a triangle with angles 35 degrees and 65 degrees? 

Ans: 80 degrees.
Explanation: The angle sum property gives: 
35° + 65° + Angle 3 = 180°. 
Thus, Angle 3 = 180° – 100° = 80°

Q3: Is a triangle with side lengths 7 cm, 7 cm, and 7 cm equilateral? 

Ans: Yes.
Explanation: All sides are equal (7 cm), so by definition, the triangle is equilateral.

Q4: Find the exterior angle at vertex B in triangle ABC if angle A = 40 degrees and angle C = 60 degrees. 

Ans: 100°.
Explanation: First, angle B = 180° – (40° + 60°) = 80°. 
The exterior angle at B is 180° – 80° = 100°.

Q5: If two sides of a triangle are 6 cm and 8 cm, what is the minimum integer length of the third side? 

Ans: 3 cm
Explanation: The triangle inequality requires 6 + x > 8, so x > 2. 
The smallest integer is 3 cm.

Q6: In triangle DEF, if angle D = 90 degrees and angle E = 45 degrees, what is angle F? 

Ans: 45°.
Explanation: Angle sum: 90°+ 45° + Angle F = 180°. 
Thus, Angle F = 180° – 135° = 45°.

Q7: Can a triangle have angles 50 degrees, 60 degrees, and 80 degrees? 

Ans: ​No
Explanation: Sum of angles:
 50 + 60 + 80 = 190 > 180, so a triangle cannot exist with these angles. 

Q8: What is the largest possible integer length of the third side in a triangle with sides 5 cm and 9 cm? 

Ans: 13 cm.
Explanation: Triangle inequality: 5 + 9 > x, so x < 14. 
The largest integer is 13 cm.

Q9 Classify a triangle with angles 30 degrees, 60 degrees, and 90 degrees by angle type. 

Ans: Right-angled.
Explanation: One angle is 90 degrees, so the triangle is right-angled.

Q10: In triangle XYZ, if angle X = angle Y and angle Z = 50 degrees, what is angle X? 

Ans: 65°.
Explanation: Since angle X = angle Y, let each be x. 
Angle sum: x + x + 50° = 180°. 
Thus, 2x = 130°
⇒ x = 65°.

Q1: What is the 20th even number in the sequence 2, 4, 6, 8, ...?

Ans: 40
Explanation: The nth even number is 2n. For n = 20, 2 × 20 = 40.

Q2: Meera has 5 boxes and odd number cards (1, 3, 5, …). Can she pick 5 cards that add to 50?

Ans:No
Explanation: Adding 5 odd numbers always gives an odd sum (each odd number adds an unpaired unit). 
Since 50 is even, it’s impossible.

Q3: Sana adds 6 odd numbers. Is the sum even or odd?

Ans:Even
Explanation: Each odd number has one unpaired unit. 
For 6 odd numbers, the 6 unpaired units pair up (6 ÷ 2 = 3 pairs), so the sum is even.

Q4: Raj has a 14 × 19 grid. Is the number of small squares even or odd?

Ans: Even
Explanation: The number of squares is 14 × 19. 
Since 14 is even and 19 is odd, even × odd = even, 
so the total is even.

Q5: What is the 30th odd number in the sequence 1, 3, 5, …?

Ans:59
Explanation: The nth odd number is 2n – 1. 
For n = 30, 2 × 30 – 1 = 60 – 1 = 59.

Q6: In a 3 × 3 magic square with numbers 1 to 9, what is the sum of each row?

Ans:15
Explanation: The sum of numbers 1 to 9 is 45. 
In a magic square, each of the 3 rows sums to the same value, 
so 45 ÷ 3 = 15.

Q7: Tara writes the Virahãnka sequence: 1, 2, 3, 5, 8, 13, 21, 34, 55, 89. What is the next number?

Ans:144
Explanation: Each number in the Virahãnka sequence is the sum of the two previous numbers. So, 55 + 89 = 144.

Q8: In the puzzle K + K + K = LK, where K and L are digits, what is K?

Ans: 5
Explanation: 3K = LK (a two-digit number with units digit K). 
So, 3K = 10L + K. (expansion of a two digit number = 10p + q)
Subtract K: 2K = 10L. 
Thus, K = 5L. 
Since K and L are digits, L = 1, K = 5. 
Check: 5 + 5 + 5 = 15, and LK = 15.

Q9: A bulb is ON. Vijay toggles it 63 times. Is the bulb ON or OFF?

Ans: OFF
Explanation: Each toggle switches the bulb (ON to OFF or OFF to ON). 
Starting ON, 63 toggles (odd number) means it ends OFF.

Q10: In the Virahãnka sequence, two numbers are 377 and 610. What is the next number?

Ans: 987
Explanation: In the Virahãnka sequence, the next number is the sum of the two previous ones. 
So, 377 + 610 = 987.

Q1: Define vertically opposite angles. Are they always equal?
Ans: Vertically opposite angles are the angles opposite each other when two lines intersect. Yes, they are always equal.

Q2: Two angles form a linear pair. If one is 125°, find the other.
Ans: The other angle = 180° − 125° = 55°

Q3: Name a pair of lines that never intersect.
Ans: Parallel lines

Q4: A transversal cuts two lines and ∠1 = ∠5. What kind of angles are these, and what can you conclude about the lines?
Ans: Corresponding angles; the lines are parallel.

Q5: If ∠x and ∠y are supplementary and ∠x = 2∠y, find the angles.
Ans: ∠y = 60°, ∠x = 120°

Q6: ∠3 and ∠6 are equal and lie between two lines on opposite sides of the transversal. What type are they?
Ans: Alternate interior angles

Q7: Which angles lie between the two lines and on the same side of a transversal?
Ans: Co-interior (or consecutive interior) angles

Q8: How many pairs of corresponding angles are formed when a transversal cuts two lines?
Ans: 4 pairs

Q1: If Priya’s age is p = 25 years, find Rahul’s age using the expression r = p – 4. 

Ans: r = 21 years. 
Explanation: The expression r = p – 4 means Rahul’s age is 4 years less than Priya’s age. 
Substitute p = 25: r = 25 – 4 = 21 
Thus, Rahul is 21 years old.

Q2: How many matchsticks are needed to make 9 T’s, given the expression 3n, where n is the number of T’s? 

Ans: 27 matchsticks. 
Explanation: The expression 3n indicates each T requires 3 matchsticks. 
For n = 9 T’s: 3 x 9 = 27 
Therefore, 27 matchsticks are needed.

Q3: The cost of one mango is ₹40 and the cost of 1 kg of sugar is ₹50. Write and evaluate an expression to calculate the total cost for 6 mangoes and 4 kg of sugar.

Ans: ₹440 
Explanation: Cost of 6 mangoes = 6 × Cost of 1 mango = 6 × 40 = ₹240
Cost of 4 kg sugar = 4 × Cost of 1 kg sugar = 4 × 50 = ₹200
Total Cost = Cost of mangoes + Cost of sugar = 240 + 200 = ₹440

Q4: Find the perimeter of a square with side length s = 8 cm using the expression 4s. 

Ans: 32 cm 
Explanation: The perimeter of a square is given by 4s, where s is the side length. 
Substitute s = 8: 4 x 8 = 32 
The perimeter is 32 cm.

Q5: Evaluate the arithmetic expression 30 – 8 x 3. 

Ans: 6 
Explanation: Follow the order of operations (BODMAS/PEMDAS): 
multiplication before subtraction. 
Calculate 8 x 3 = 24, 
then: 30 – 24 = 6 
The value of the expression is 6.

Q6: Find the value of the expression 4k + 5 when k = 3. 

Ans: 17 
Explanation: Substitute k = 3 into the expression 4k + 5: 4 x 3 + 5 = 12 + 5 = 17 
The value is 17.

Q7: Simplify the expression 7p + 2p + 5p to find the total money earned from selling pens.

Ans: 14p 
Explanation: Combine like terms by adding the coefficients of p: 7p + 2p + 5p = (7 + 2 + 5)p = 14p 
The simplified expression for the total money earned is 14p.

Q8: Calculate Anjali’s score in the first round of a quiz if x = 5 and y = 2, using the expression 6x – 4y. 

Ans: 22
Explanation: Substitute x = 5 and y = 2 into the expression 
6x – 4y: 6 x 5 – 4 x 2 = 30 – 8 = 22 
Anjali’s score is 22.

Q9: Find the number of matchsticks needed for Step 20 in a matchstick pattern using the expression 3y + 2, where y is the step number. 

Ans: 62 matchsticks 
Explanation: Substitute y = 20 into the expression 
3y + 2: 3 x 20 + 2 = 60 + 2 = 62 
Thus, 62 matchsticks are needed for Step 20.

Q10: Determine the total amount paid for renting 4 chairs and 2 tables using the simplified expression 30c + 70t, where c represents number of chairs and t represents number of tables.

Ans: ₹260 
Explanation: The expression 30c + 70t gives the net cost for renting c chairs at ₹30 each and t tables at ₹70 each after returns. Substitute c = 4 and 
t = 2: 30 x 4 + 70 x 2 = 120 + 140 = 260 
The total amount paid is ₹260.

Q1. Estimate the sum of 25.936 and 8.202. Then calculate the exact sum. Is your estimation close?

Solution:
Estimate:
25.936 ≈ 26
8.202 ≈ 8
Estimated sum = 26 + 8 = 34

Actual sum = 25.936 + 8.202 = 34.138

Yes, estimation is close to actual.

Q2. Convert the following to decimals:

(a) 6 ones and 5 tenths
(b) 125 tenths

Solution:
(a) 6 + 5/10 = 6.5
(b) 125 ÷ 10 = 12.5

Q3. A chocolate bar weighs 0.85 kg. What is the total weight of 6 such bars?

Solution:

0.85 × 6 = 5.10 kg

Q4. Convert the following:

(a) 6.2 cm to mm
(b) 46 mm to meters

Solution:

(a) 6.2 × 10 = 62 mm
(b) 46 ÷ 1000 = 0.046 meters

Q5. Estimate the sum of 39.847 and 11.205 by rounding off the numbers. Then find the exact sum. Compare both.

Solution:

Estimate:

39.847 ≈ 40

11.205 ≈ 11

Estimated sum = 40 + 11 = 51

Exact sum = 39.847 + 11.205 = 51.052
Comparison: The estimate (51) is very close to the actual sum (51.052), showing estimation is useful for quick checks.

Q6. Express 328 grams in kilograms.

Solution:

328 ÷ 1000 = 0.328 kg

Q7. Rahul walked 2.9 km in the morning and 4.7 km in the evening. What was the total distance he walked? Express your answer as a decimal and a mixed fraction.

Solution:

2.9 + 4.7 = 7.6 km

7.6 = 7 + 6/10 =

Q8. A roll of cloth is 14.4 meters long. If it is divided equally among 6 tailors, how much does each get?

Solution:

14.4 ÷ 6 = 2.4 meters per tailor

Q9. Convert the mixed fraction  to decimal form.

Solution:

 = 4 + 0.3 = 4.3

Q10. Subtract 4.36 from 9.15.

Solution:

9.15 – 4.36 = 4.79

Q1: Find the values of the following expressions by writing the terms in each case.

(a) 35 – 8 + 9

Ans: Terms: 35, -8, 9. 

Expression: 35 + (-8) + 9 = 
27 + 9 = 36.

(b) 50 – 3 × 7 + 13

Ans: Terms: 50, -3 × 7, 13. 
Expression: 50 + (-21) + 13 
= 50 – 21 + 13 = 42.

(c) 60 – 15 + 5 + 10

Ans: Terms: 60, -15, 5, 10. 
Expression: 60 + (-15) + 5 + 10 
= 45 + 5 + 10 = 60.

Q2: Use ‘>’ or ‘<’ or ‘=’ in each of the following expressions to compare them. Can you do it without complicated calculations? Explain your thinking in each case.

(a) 322 + 215 ____ 324 + 213

Ans: Left side: 322 + 215 = 537

Right side: 324 + 213 = 537

322 + 215 = 324 + 213 (They are equal)

(b) 571 + 432 ____ 570 + 434

Ans: Left side: 571 + 432 = 1003
Right side: 570 + 434 = 1004

571 + 432 < 570 + 434

(c) 418 – 234 ____ 414 – 238

Ans: Left side: 418 – 234 = 184

Right side: 414 – 238 = 176
418 – 234 > 414 – 238

Q3: Compare and answer if LHS = RHS .

(a) 4 × (5 + 8) = 4 × 5 + 4 × 8

​Ans: This is already correct.
4 × (5 + 8) = 4 × 13 = 52
4 × 5 + 4 × 8 = 20 + 32 = 52

(b) 6 × (3 + 7) = 6 × 3 + 6 × 7

Ans: This is already correct.
6 × (3 + 7) = 6 × 10 = 60
6 × 3 + 6 × 7 = 18 + 42 = 60

Q4: Fill in the blanks to make the expressions equal on both sides of the = sign:

(a) 15 + 6 = _____ + 8

Ans: 15 + 6 = 21, 
so 13 + 8 = 21.
The blank is 13.

(b) 30 + _____ = 5 × 8

Ans: 5 × 8 = 40, 
so 30 + 10 = 40. 
The blank is 10.

(c) 9 × _____ = 72 ÷ 3

Ans: 
72 ÷ 3 = 24, 
so 9 × 4 = 24. 
The blank is 4.

(d) 50 – _____ = 40

Ans: 50 – 10 = 40. 
The blank is 10.

Q5: Compare the following pairs of expressions using ‘<‘, ‘>’, or ‘=’

(a) 72 × 34 – 15 ___ 72 × 30 – 15

Ans: 72 × 34 = 72 × (30 + 4) = 72 × 30 + 72 × 4.
So, 72 × 34 – 15 = 72 × 30 + 72 × 4 – 15, and 72 × 30 – 15 = 72 × 30 – 15.
So, 72 × 34 – 15 > 72 × 30 – 15

(b) 63 – 9 + 5 ___ 63 – 9 + 5

Ans: Same expression.
So, 63 – 9 + 5 = 63 – 9 + 5.

Q1: Rounding 4,78,942 to the nearest thousand gives ______.

Ans: 4,79,000

As 942 is greater than 500 so we round up

Q2: Convert 7,300,000 into the Indian number system.

Ans: 73,00,000 (Seventy-three lakh)

Q3: Write the following numbers in Indian Place Value Notation: 

One crore one lakh one thousand ten 

Ans: 1,01,01,010

Step-by-step (Indian Number System):

• One crore = 1,00,00,000
• One lakh = 1,00,000
• One thousand = 1,000
• Ten = 10
• Now add them all, we get: 1,01,01,010

Q4: True or False: 1 crore = 100 lakhs

Ans: True

1 crore = 100 lakhs.

Q5: Write the numbers 6,345,210 in words using the International system.

Ans: Six million three hundred forty-five thousand two hundred ten

Q6: Round 3,19,612 to the nearest ten thousand.

Ans: 3,20,000

(Since the thousands digit is 9, we round up)

Q7: Using any digits from 0 to 9 without repeating, write the greatest 5-digit number that is a multiple of 5.

Ans: A number is divisible by 5 if it ends in 0 or 5.
For maximum value, use the largest digits: 9, 8, 7, 6.
Case 1: Ends in 5: 98765 (digits 9, 8, 7, 6, 5, distinct, divisible by 5).
Case 2: Ends in 0: 98760 (digits 9, 8, 7, 6, 0, distinct, divisible by 5).
Compare: 98765 > 98760 (5 > 0 in units).
So, 98765 is the greatest 5-digit number that is a multiple of 5.

Q8: Calculate the product in a quick way

116 x 5

Ans:

116 x (10/2) as 10/2 = 5
58 x 10
580

Q9: Arrange the following in ascending order: 45,210; 54,120; 40,250; 49,500

Ans: 40,250 < 45,210 < 49,500 < 54,120