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Toggle## Class 7, Maths, Chapter 1, Exercise 1.4 Solutions

**Q.1. Evaluate each of the following:**

**(a) (–30) ÷ 10 **

**(b) 50 ÷ (–5) **

**(c) (–36) ÷ (–9)**

**(d) (– 49) ÷ (49) **

**(e) 13 ÷ [(–2) + 1] **

**(f) 0 ÷ (–12)**

**(g) (–31) ÷ [(–30) + (–1)] **

**(h) [(–36) ÷ 12] ÷ 3 **

**(i) [(– 6) + 5)] ÷ [(–2) + 1]**

**Ans: **

**(a) (-30) ÷ 10**

= (-30) **÷** 10

= – 3

When we divide a negative integer by a positive integer, we first divide them as whole numbers and then put minus sign (-) before the quotient.

**(b) 50 ÷ (-5)**

= (50) **÷** (-5)

= – 10

When we divide a positive integer by a negative integer, we first divide them as whole numbers and then put minus sign (-) before the quotient.

**(c) (-36) ÷ (-9)**

= (-36) **÷** (-9)

= 4

When we divide a negative integer by a negative integer, we first divide them as whole numbers and then put positive sign (+) before the quotient.

**(d) (- 49) ÷ (49)**

= (-49) **÷ **49

= – 1

When we divide a negative integer by a positive integer, we first divide them as whole

numbers and then put minus sign (-) before the quotient.

**(e) 13 ÷ [(-2) + 1]**

= 13 **÷** [(-2) +1]

= 13 **÷** (-1)

= – 13

When we divide a positive integer by a negative integer, we first divide them as whole numbers and then put minus sign (-) before the quotient.

**(f) 0 ÷ (-12)**

= 0 **÷** (-12)

= 0

When we divide zero by a negative integer gives zero.

**(g) (-31) ÷ [(-30) + (-1)]**

= (-31) **÷** [(-30) + (-1)] [Use BODMASS Rule]

= (-31) **÷** [-30 – 1]

= (-31) **÷** (-31)

= 1

When we divide a negative integer by a negative integer, we first divide them as whole numbers and then put positive sign (+) before the quotient.

**(h) [(-36) ÷ 12] ÷ 3**

First, we have to solve the integers with in the bracket,

= [(-36) **÷** 12]

= (-36) **÷** 12

= – 3

Then,

= (-3) **÷** 3

= – 1

When we divide a negative integer by a positive integer, we first divide them as whole numbers and then put minus sign (-) before the quotient.

**(i) [(- 6) + 5)] ÷ [(-2) + 1]**

The given question can be written as,

= [-1] **÷** [-1]

= 1

When we divide a negative integer by a negative integer, we first divide them as whole numbers and then put positive sign (4) before the quotient.

**Q.2. Verify that a ÷ (b + c) ≠ (a ÷ b) + (a ÷c) for each of the following values of a, b and c.**

**(a) a = 12, b = – 4, c = 2 **

**(b) a = (–10), b = 1, c = 1**

**Q.3. Fill in the blanks:**

**(a) 369 ÷ _____ = 369 **

**(b) (–75) ÷ _____ = –1**

**(c) (–206) ÷ _____ = 1 **

**(d) – 87 ÷ _____ = 87**

**(e) _____ ÷ 1 = – 87 **

**(f) _____ ÷ 48 = –1**

**(g) 20 ÷ _____ = –2 **

**(h) _____ ÷ (4) = –3**

**Q.4. Write five pairs of integers (a, b) such that a ÷ b = –3. One such pair is (6, –2) because 6 ÷ (–2) = (–3).**

**Ans: **

(i) (15, -5) Because, 15 **÷** (-5) = (-3)

(ii) (-15, 5) Because, (-15) **÷** (5) = (-3)

(iii) (18, -6) Because, 18 **÷** (-6) = (-3)

(iv) (-18, 6) Because, (-18) **÷** 6 = (-3)

(v) (21, -7) Because, 21 **÷** (-7) = (-3)

**Q.5. The temperature at 12 noon was 10°C above zero. If it decreases at the rate of 2°C per hour until midnight, at what time would the temperature be 8°C below zero? What would be the temperature at mid-night?**

**Q.6. In a class test (+ 3) marks are given for every correct answer and (–2) marks are given for every incorrect answer and no marks for not attempting any question. **

**(i) Radhika scored 20 marks. If she has got 12 correct answers, how many questions has she attempted incorrectly? **

**(ii) Mohini scores –5 marks in this test, though she has got 7 correct answers. How many questions has she attempted incorrectly?**

**Q.7. An elevator descends into a mine shaft at the rate of 6 m/min. If the descent starts from 10 m above the ground level, how long will it take to reach – 350 m.**