CBSE Class 7 Mathematics Integers, Fractions and Decimals Worksheet Set 38

Answer: (c) 6. (−8) − (−14) = −8 + 14 = 6.

Teacher's Note:
1. Subtracting a negative number is the same as adding its positive.
2. Do the sum on the number line.

Answer: (d) 9.4249 m². 3.07 × 3.07 = 9.4249.

Teacher's Note:
1. Multiply the side by itself.
2. Remember that area is written in square units.

Answer: (a) −270. 30 × (−23 + 14) = 30 × (−9) = −270.

Teacher's Note:
1. Take out the common factor 30.
2. Then add the integers inside the bracket.

Answer: (a) −2 and −3 (b) 3 and 12, since 3 − 12 = −9 (c) 4 and −5 (d) 9 and −3.

Teacher's Note:
1. Many pairs work.
2. Check your pair by doing the operation.

Answer: (a) 3 + (−5) = −2 and 3 − 5 = −2. (b) −4 + (−3) = −7 and −4 − 3 = −7. Both sides are equal.

Teacher's Note:
1. Subtracting a negative number means adding the positive.
2. Compute both sides separately.

Answer: 32.50 × 24 = ₹780.

Teacher's Note:
1. Multiply as whole numbers and then place the decimal point.
2. Check by estimation: 30 × 24 = 720.

Answer: Number = \( \dfrac{32}{3} \div 20 = \dfrac{32}{60} = \dfrac{8}{15} \).

Teacher's Note:
1. Write the mixed number as an improper fraction.
2. Then divide it by 20.

Answer: 1243 × 99 + 1243 = 1243 × 100 = 1,24,300.

Teacher's Note:
1. Subtracting a negative gives a plus.
2. Combine using 99 + 1 = 100.

Answer: 105 ÷ (−7) = −15 and (−85) ÷ 17 = −5. So (−15) ÷ (−5) = 3.

Teacher's Note:
1. Work out each bracket first.
2. The quotient of two negatives is positive.

Answer: Not defined. Division by zero has no meaning.

Teacher's Note:
1. No number multiplied by 0 gives 50.
2. So the result cannot exist.

Answer: 889 × (1806 − 806) = 889 × 1000 = 8,89,000.

Teacher's Note:
1. Take 889 out as a common factor.
2. The bracket becomes a round number.

Answer: −20 − 15 + 31 − 18 = −22.

Teacher's Note:
1. Remove the brackets by applying the signs.
2. Add the positives and negatives separately.

Answer: −14 + 141 − 50 − 86 + 144 + 48 = 333 − 150 = 183.

Teacher's Note:
1. Positives: 141 + 144 + 48 = 333.
2. Negatives: 14 + 50 + 86 = 150.

Answer: The predecessor is −40 − 1 = −41.

Teacher's Note:
1. The predecessor is one less than the number.
2. On the number line it lies to the left.

Answer: 436 × 9 = 3924; with four decimal places the product is 0.3924.

Teacher's Note:
1. Multiply ignoring the decimals.
2. Add the decimal places of both numbers.

Answer: Multiply both by 100: 21735 ÷ 630 = 34.5.

Teacher's Note:
1. Make the divisor a whole number by shifting the decimal point.
2. Shift the dividend equally.

Answer: 780450 ÷ 10406 = 75.

Teacher's Note:
1. Shift the decimal point two places in both numbers.
2. Then divide as whole numbers.

Answer: Let it be x. Then \( \dfrac{-x}{-9} = \dfrac{1}{x} \), so x² = 9 and x = 3 or −3.

Teacher's Note:
1. Form an equation using the given condition.
2. Both a positive and a negative integer work.

Answer: 5 − (−3) = 8.

Teacher's Note:
1. Exceeding means subtracting the smaller from the larger.
2. Subtracting −3 adds 3.

Answer: −5 − (−8) = 3. So −8 is 3 less than −5.

Teacher's Note:
1. Subtract the smaller number from the larger.
2. Use the number line to check.

Answer: 25 × 75 = 1875.

Teacher's Note:
1. Think of 75 as 3 quarters of 100.
2. So 25 × 75 = 75 ÷ 4 × 100.

Answer: Number = \( \dfrac{8}{15} \div \dfrac{2}{3} = \dfrac{8}{15} \times \dfrac{3}{2} = \dfrac{4}{5} \).

Teacher's Note:
1. Divide by the fraction by multiplying with its reciprocal.
2. Then simplify.

Answer: 56.80 × 16.25 = ₹923.

Teacher's Note:
1. Multiply the price by the weight.
2. Round first to check: 57 × 16 ≈ 912.

Answer: \( \dfrac{118}{5} \times \dfrac{38}{7} = \dfrac{4484}{35} \approx \) ₹128.11.

Teacher's Note:
1. Change both mixed numbers to improper fractions.
2. Multiply and then convert.

Answer: Girls = \( \dfrac{2}{5} \times 75 \) = 30. Boys = 75 − 30 = 45.

Teacher's Note:
1. Find the fraction of the whole for the girls.
2. Subtract to get the boys.

Answer: (a) 14 ÷ 11 ≈ 1.27 but 2 + 3.5 = 5.5. (b) 12 ÷ (−5) = −2.4 but (−6) + (−4) = −10. In both cases the two sides differ.

Teacher's Note:
1. Evaluate each side with the numbers given.
2. The two sides are unequal, so division does not distribute over addition.

Answer: Fall = 8 × 8 = 64 °C. Temperature = 48 − 64 = −16 °C.

Teacher's Note:
1. Multiply the rate by the time.
2. Subtract from the starting temperature.

Answer: Distance = 30 + 390 = 420 m. Time = 420 ÷ 6 = 70 minutes.

Teacher's Note:
1. Add the distance above and below the ground.
2. Divide by the speed.

Answer: 2.34 m = 234 cm. Pieces = 234 ÷ 0.45 = 520.

Teacher's Note:
1. Convert metres to centimetres first.
2. Then divide the height by the thickness.

Answer: (a) 10 correct give 40, so 40 − 2x = 20 and x = 10. (b) 5 correct give 20, so 20 − 2x = −10 and x = 15.

Teacher's Note:
1. Find the marks from correct answers first.
2. The deficit comes from the incorrect ones, each costing 2 marks.