Haryana State Board HBSE 7th Class Maths Solutions Chapter 1 Integers Ex 1.4 Textbook Exercise Questions and Answers.
Haryana Board 7th Class Maths Solutions Chapter 1 Integers Exercise 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)1
(h) [(-36) ÷ 12] ÷ 3
(i) [(-6)+ 5] ÷ [(-2) A -77
Solution:
(a) (-30) ÷ 10 = -3
(b) 50 ÷ (- 5) = -10
(c) (-36) ÷ (-9) = 4
(d) (-49) ÷ (49) = -1
(e) 13 ÷ (-1) = -13 (Meaningless)
(f) 0 ÷ (-12) = 0
(g) (- 31) ÷ [(- 30) + ( -1)]
= (-31) ÷ (-31) = 1
(h) [(- 36) ÷ 12] ÷ 3 = -3 ÷ 3 = – 1
(i) [(-6) + 6] ÷ [(-2) + 1]
= 0 ÷ (- 1) = 0 (Meaingless)
Question 2.
Verify that a ÷ (b + c) * (a ÷ b) + (a ÷ c) for each of the following values of a, b and c.
(а) a = 12, b = – 4, c = 2
(б) a = (- 10), 6 = 1, c = 1.
Solution:
(a) 12 ÷ (— 4 + 2) ≠ [12 ÷ (-4)]+ [12 ÷ 2]
12 ÷ (-2) ≠ (-3) + (6)
– 6 ≠ 3
(b) (- 10) ÷ (1 + 1) ≠ [(-10) ÷ 1] + [(- 10) ÷ 1]
(- 10) ÷ 2 ≠ (- 10) + (- 10)
– 5 ≠ – 20
Question 3.
Fill in the blanks :
(a) 369 ÷ = 369
(b) -75 ÷ = – 1
(c) (-206) + -1
(d) -87 = 87
(e) ÷ 1 = -87
(f) ÷ 48 = -l
(g) 20 ÷ = – 2
(h) ÷ (4) = – 3
Sol.
(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, 6) such that a ÷ b = – 3. One such pair is (6, – 2) because 6 ÷ (- 2) = (- 3).
Solution:
(i) (3, – 1) ⇒ .3 ÷ (- 1) = -3
(ii) (12,-4) ⇒ 12 ÷ (-4) = -3
(iii) (15,-5) ⇒ 15 ÷ (-5) = -3
(to) (18,-6) ⇒ 18 ÷ (-6) = -3
(v) (21,-7) ⇒ 21 ÷ (-7) = -3
Question 5.
The temperature at 12 noon was 10°C above zero. If it decreases at the rate of 2° per hour until mid-night, at what time would the temperature 8°C below zero ? What would be the temperature at midnight ?
Solution:
At 9 p.m. the temperature was 8 degree below zero and the temperature was – 14°C at mid night.
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? (iii) Rakesh scores 18 marks by attempting 16 questions. How many questions has he attempted correctly and how many has he attempted incorrectly?
Solution:
(i) Radhick scored = (3,000 x 8)
– (5,000 x 5)
Radhika has got 12 correct answers
= 12 x 3 = 36 marks
incorrect answers = 36-20 = 16 marks 16
hence no. of questions = 16/2 = 8
(ii) Mohini has got 7 correct answers
= 7 x 3 = 21 marks
incorrect answers = 21 – (- 5) = 26
hence no. of incorrect questions
= 26 ÷ 2 = 13
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.
Solution:
Rate of Shaft = 6m / min.
Distance of descent from ground level = 10m
Total Distance = 10m + 350m = 360
Time taken to reach the mine = \(\frac{360 \mathrm{~m}}{6 \mathrm{~m}}\)
= 60m
= 1 hour