NCERT Solutions for Class 7 Maths Chapter 1 Integers Ex 1.4

Class 7 Maths NCERT Solutions Chapter 1 Integers Ex 1.4

Ex 1.4 Class 7 Maths Question 1.
Evaluate each of the following:

Solution.

Ex 1.4 Class 7 Maths Question 2.
values of a, b and c.
(a) a = 12, b = – 4, c = 2
(b) a = (- 10), b = 1, c = 1
Solution.

Ex 1.4 Class 7 Maths Question 3.
Fill in the blanks :

Solution.

Ex 1.4 Class 7 Maths Question 4.
Write five pairs of integers (a, b) such that \(a\div b\) = – 3. One such pair is (6, – 2) because \(6\div \left( – 2 \right) =\left( – 3 \right)\) .
Solution.
Five pairs of integers (a, b) such that a + b = -3 are:

1. [9, (-3)]
2. [12, (-4)]
3. [15, (-5)]
4. [-9, 3]
5. [-12, 4]

Ex 1.4 Class 7 Maths Question 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?
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.

Ex 1.4 Class 7 Maths 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 on this test though she has got 7 correct, answers. How many questions has she attempted incorrectly?
Solution.
(i) Marks given for 12 correct answers at the rate of + 3 marks for each answer = 3 x 12 = 36
Radhika’s score = 20 marks
∴ Marks deducted her for incorrect answers = 20 – 36 = – 16
Marks given for one incorrect answer = – 2
Number of incorrect answers \(=\left( -16 \right) \div \left( -2 \right) =8\)
(ii) Marks given for 7 correct answers at the rate of + 3 marks for each answer = 3 x 7 = 21
Mohini’s score = – 5
∴ Marks deducted for incorrect answers = -5 – 21 = -26
Marks given for one incorrect answer = -2
∴ Number of incorrect answers \(=\left( – 26 \right) \div \left( – 2 \right) =13\)

Ex 1.4 Class 7 Maths Question 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.
Answer.
Let ‘x’ minutes by the time taken to reach – 350 m.
According to the question, we get
x = \(\frac { (-10)+(-350) }{ 6 } \) = \(\frac { -360 }{ 6 } \) = -60
Negative sign indicates descent.
∴ x = 60 minutes = 1 hour

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