NCERT Solutions for Class 7 Maths Chapter 1 Integers Ex 1.4 are part of NCERT Solutions for Class 7 Maths. Here we have given NCERT Solutions for Class 7 Maths Chapter 1 Integers Ex 1.4.

Board |
CBSE |

Textbook |
NCERT |

Class |
Class 7 |

Subject |
Maths |

Chapter |
Chapter 1 |

Chapter Name |
Integers |

Exercise |
Ex 1.4 |

Number of Questions Solved |
7 |

Category |
NCERT Solutions |

## NCERT Solutions for Class 7 Maths Chapter 1 Integers Ex 1.4

**Question 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].

**Solution:**

**(a)** (- 30) + 10 = – 3

**(b)** 50 +(-5) = – 10

**(c)** (-36) +(-9) = 4

**(d)** (- 49) + (49) = – 1

**(e)** 13 + [(- 2) + 1] = 13 + (- 1) = – 13

**(f)** 0 + (- 12) = 0

**(g)** (- 31) + [(- 30) + (- 1)] = (- 31) + (- 31) = 1

**(h)** [(- 36) + 12] + 3 = (- 3) + 3 = – 1

**(i)** [(- 6) + 5] + [(- 2) + 1] = (- 1) + (- 1) = 1.

**Question 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 = l.

**Solution:**

**(a)** a + (b + c) = 12 ÷ [(- 4) + 2] = 12 + (- 2) = – 6

(a ÷ b) + (a ÷ c) = 12 ÷ (- 4) + 12 ÷ 2 = -3 + 6 = 3

So, a + (b + c) ≠ (a + b) + (a + c)

**(b)** a ÷ (b + c) = (- 10) + (1 + 1) = (- 10) + 2 = – 5

a ÷ b + a ÷ c = (- 10) ÷ 1 + (- 10) ÷ 1 = (- 10) + (- 10) = – 20

So, a ÷ (b + c) ≠ (a ÷ b) + (a ÷ c).

**Question 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.

**Solution:**

**(a)** 369 ÷ **1** = 369

**(b)** – 75 ÷ **75** = -1

**(c)** (- 206) ÷ **(- 206)** = 1

**(d)** – 87 ÷ **– 1** = 87

**(e)** **– 87** ÷ 1 = – 87

**(f)** **– 48** ÷ 48 = – 1

**(g)** 20 ÷ **(-10)** = – 2

**(h)** **– 12** ÷ (4) = – 3.

**Question 4.**

Write five pairs of integers (a, b) such that a + b = -3. One such pair is (6, -2) because 6 +(-2) = (-3).

**Solution:**

Five pairs of integers (a, b) such that a + b = – 3 are:

- [9, (- 3)]
- [12, (- 4)]
- [15, (-5)]
- [-9, 3]
- [-12, 4].

**Question 5.**

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

**Solution:**

Temperature at 12 noon = + 10°C

Temperature at 1 P.M.= 10°C – 2°C = 8°C

Temperature at 2 P.M. = 8°C – 2°C = 6°C

Temperature at 3 P.M. = 6°C – 2°C = 4°C

Temperature at 4 P.M. = 4°C – 2°C = 2°C

Temperature at 5 P.M. = 2°C – 2°C = 0°C

Temperature at 6 P.M. = 0°C – 2°C = – 2°C

Temperature at 7 P.M. = – 2°C – 2°C = – 4°C

Temperature at 8 P.M. = – 4°C – 2°C = – 6°C

Temperature at 9 P.M. = – 6°C – 2°C = – 8°C

So, the temperature was 8°C below zero at 9 P.M.

Temperature at 10 P.M. = – 8°C – 2°C = – 10°C

Temperature at 11 P.M. = – 10°C – 2°C = – 12°C

Temperature at 12 P.M. = – 12°C – 2°C = – 14°C

So, the temperature at mid-night was 14 degrees below zero.

**Aliter:**

Difference between the temperatures 10°C above zero and 8°C below zero

= 10°C – (- 8°C)

= 10°C + 8°C = 18°C

Time for this degrees

= 18 ÷ 2 = 9 hours

So, the temperature was 8°C below zero at 9 P.M.

Difference between the times 12 noon and mid-night = 12 hours

Degrees in temperature in 12 hours = 12 × 2 = 24°C

So, temperature at mid night

= 10°C – 24°C = – 14°C.

**Question 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 ?

**Solution:**

**(i)** Let ‘x’ be the number of incorrect question attempted by Radhika.

According to the question, we get

(+ 3) × 12 + x × (-2) = 20

⇒ 36 – 2x = 20

⇒ 2x = 36 – 20

⇒ x = = 8

Therefore, Radhika attempted 8 incorrect questions.

**(ii)** Let ‘x’ be the number of incorrect question attempted by Mohini.

According to the question, we get

(+ 3) × 7 + x × (- 2) = – 5

⇒ 21 – 2x = -5

⇒ 2x = 21 + 5

⇒ x = = 13

Therefore, Mohini attempted 13 incorrect questions.

**Question 7.**

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

**Solution:**

Let ‘x’ minutes be the time taken to reach – 350 m.

According to the question, we get

x = = = -60

Negative sign indicates descent.

∴ x = 60 minutes = 1 hour

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