Chapter 1: Integers

Q11Written answer

Water level in a well was 20m below ground level. During rainy season, rain water collected in different water tanks was drained into the well and the water level rises 5 m above the previous level. The wall of the well is 1m 20 cm high and a pulley is fixed at a height of 80 cm. Raghu wants to draw water from the well. The minimum length of the rope that he can use is

NCERT Exemplars Class 7 Maths Solutions Chapter 1 Image 4

(a) 17 m (b) 18 m (c) 96 m (d) 97 m

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Worked solution

(a) 17 m

Given,

Height of the wall of the well = 1m 20 cm = 1.2 m

Height of the fixed pulley = 80 cm = 0.8 m

Initially water was available at a depth of 20 m below ground level.

Later, due to rain the water level was raised by 5 m.

Hence, the new depth at which water is available = 20 – 5 = 15 m

Thus,

The minimum length of the rope required to draw water from the well will be

(1.2 + 0.8 + 15) m = 17 m

Q12Written answer

(– 11) × 7 is not equal to

(a) 11 × (– 7) (b) – (11 × 7) (c) (– 11) × (– 7) (d) 7 × (– 11)

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Worked solution

(c) (– 11) × (– 7)

We have,

11 x (-7) = -77

– (11 x 7) = -77 and

7 x (-11) = -77

But, (-11) x (-7) = 77

Q13Written answer

(– 10) × (– 5) + (– 7) is equal to

(a) – 57 (b) 57 (c) – 43 (d) 43

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Worked solution

(d) 43

Using BODMAS rule,

(-10) x (-5) + (-7) = 50 – 7 = 43

Q14Written answer

Which of the following is not the additive inverse of a?

(a) – (– a) (b) a × (– 1) (c) – a (d) a ÷ (–1)

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Worked solution

(a) – (-a)

The additive inverse of a is – a

But, – (-a) = a

Q15Written answer

Which of the following is the multiplicative identity for an integer a?

(a) a (b) 1 (c) 0 (d) – 1

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Worked solution

(b) 1

The multiplicative identity of an integer a is 1. [As a x 1 = a]

Q16Written answer

[(– 8) × (– 3)] × (– 4) is not equal to

(a) (– 8) × [(– 3) × (– 4)] (b) [(– 8) × (– 4)] × (– 3)

(c) [(– 3) × (– 8)] × (– 4) (d) (– 8) × (– 3) – (– 8) × (– 4)

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Worked solution

(d) (– 8) × (– 3) – (– 8) × (– 4)

= (– 8) × [(– 3) × (– 4)]

= [(– 8) × (– 4)] × (– 3)

= [(– 3) × (– 8)] × (– 4)

But, [(– 8) × (– 3)] × (– 4) ≠ (– 8) × (– 3) – (-8) × (– 4)

Q17Written answer

(– 25) × [6 + 4] is not same as

(a) (– 25) × 10 (b) (– 25) × 6 + (– 25) × 4 (c) (– 25) × 6 × 4 (d) – 250

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Worked solution

(c) (– 25) × 6 × 4

(– 25) × [6 + 4]

= (– 25) × 10

= (– 25) × 6 + (– 25) × 4

= – 250

But, (– 25) × [6 + 4] ≠ (– 25) × 6 × 4

Q18Written answer

– 35 × 107 is not same as

(a) – 35 × (100 + 7) (b) (– 35) × 7 + ( – 35) × 100

(c) – 35 × 7 + 100 (d) (– 30 – 5) × 107

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Worked solution

(c) – 35 × 7 + 100

– 35 × 107 = (– 30 – 5) × 107 = – 35 × (100 + 7) = (– 35) × 7 + ( – 35) × 100

But, – 35 × 107 ≠ – 35 × 7 + 100

Q19Written answer

(– 43) × (– 99) + 43 is equal to

(a) 4300 (b) – 4300 (c) 4257 (d) – 4214

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Worked solution

(a) 4300

By BODMAS rule,

(– 43) × (– 99) + 43 = [(– 43) × (– 99)] + 43 = 4257 + 43 = 4300

Q20Written answer

(– 16) ÷ 4 is not same as

(a) ( – 4) ÷ 16 (b) – ( 16 ÷ 4) (c) 16 ÷ (– 4) (d) – 4

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Worked solution

(a) ( – 4) ÷ 16

(– 16) ÷ 4 = -4

But, ( – 4) ÷ 16 = -1/4

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