Integers Class 7 Ex. 1.3;
New Ncert Solution for Class 7 Maths Chapter 1 Integers Free Solution;
Exercise 1.3
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 1:-
(a) (-30) ÷ 10 = −30/10 = -3 ;
(b) 50 ÷ (-5) = 50/−5 = -10 ;
(c) (-36) ÷ (-9) = −36/−9 = 4 ;
(d) (-49) ÷ (49) = −49/49 = -1 ;
(e) 13 ÷ [(-2) + 1] = 13 ÷ -1 = 13/−1 = -13
(f) 0 ÷ (-12) = 0/−12 = 0 ;
(g) (-31) ÷ [(-30) + (-1)] = (-31) ÷ (-31) = −31/−31 = 1 ;
(h) [(-36) ÷ 12] ÷ 3 = [−(36/12)] ÷ 3 = -3 ÷ 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.
(а) a = 12, b = – 4, c = 2 ;
(b) a = (-10), b = 1, c = 1 ;
Solution 2:-
(a) From given, a = 12, b = – 4, c = 2 ;
For R.H.S, a ÷ (b + c) =
12 ÷ [(-4) + 2] = 12 ÷ (-2) = 12÷(-2) = -6 ;
For L.H.S, (a ÷ b) + (a ÷ c) =
[12 ÷ (-4)] + [12 ÷ 2] =12÷(−4)+(12÷2) = −3+6 = 3 ;
Since, L.H.S ≠ R.H.S
Hence, a ÷ (b + c) ≠ (a ÷ b) + (a ÷ c), verified.
(b) From given, a = (-10), b = 1, c = 1 ;
For L.H.S, a ÷ (b + c) =
(-10) ÷ (1 + 1) =(-10) ÷ 2 = −10/2 = -5 ;
For R.H.S, (a ÷ b) + (a ÷ c) =
[(-10) ÷ 1] + [(-10) ÷ 1] =(−10)/1+(−10)/1 = (-10) + (-10) = -20 ;
Since, L.H.S ≠ R.H.S
Hence, a ÷ (b + c) ≠ (a ÷ b) + (a ÷ c) , verified.
Question 3 :- Fill in the blanks:
(a) 369 ÷ ___ = 369
(b) (-75) ÷ ___ = -1
(c) (-206) ÷ ___ =1
(d) -87 ÷ ___ = 87
(e) ___ ÷ 1 = -87
(g) 20 ÷ ___ = -2
(h) ____÷ (4) = -3
Solution 3:-
(a) 369 ÷ ___ = 369
369 ÷ 1 = 369 .
(b) (-75) ÷ ___ = -1
(-75) ÷ 75 = -1 .
(c) (-206) ÷ ___ = 1
(-206) ÷ (-206) = 1.
(d) -87 ÷ ___ = 87
-87 ÷ (-1) = 87.
(e) ___ ÷ 1 = -87
-87 ÷ 1 = -87.
(f) ___ ÷ 48 = -1
(-48) ÷ 48 = -1.
(g) 20 + ___ = -2
20 ÷ (-10) = -2.
(h) ___ + (4) = -3
(-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 4:-
(a) (9, -3) because 9 ÷ (-3) = -3 ;
(b) (-36, 12) because (-36) ÷ 12 = -3 ;
(c) (21, -7) because 21 ÷ (-7) = -3 ;
(d) (18, -6) because 18 ÷ (-6) = -3 ;
(e) (24, -8) because 24 ÷ (-8) = -3 ;
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 midnight?
Solution 5:-
The temperature at 12 noon, was 10°C above zero = +10°C ;
Rate of decrease, in temperature per hour = 2°C ;
Number of hours, from 12 noon to midnight = 12 hours;
Since, the change in temperature in 12 hours
= 12 × (-2°C) = -24°C
So, the temperature at midnight
= +10°C + (-24°C) = -14°C
Hence, the required temperature at midnight =-14°C
Temperature decrease 2°C = 1 hour ;
Temperature decrease 1°C = 1/2 hour ;
Temperature decrease 18°C = (1/2) x 18 hour = 9 hour ;
Total time = 12 noon + 9 hour = 21 hour = 9 pm;
So, at 9 pm the temprature would be 8°C below 0°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 6:-
Given that,
For each-correct answer marks given = +3 marks;
For each incorrect answer marks given = -2 marks;
Zero marks for not attempted questions.
(i) Marks obtained by Radhika for 12 correct answers = (+3) × 12 = 36
Marks obtained by Radhika for correct answers = 12 × 3 = 36
Total marks obtained by Radhika = 20
Since, marks obtained by Radhika for incorrect answers = 20 – 36 = -16
So, number of incorrect answers = (−16)÷(−2) = 16/2 = 8;
Therefore, the number of incorrect answers = 8.
(ii) Marks scored by Mohini = -5
Number of correct answers = 7
Since, marks obtained by Mohini for 7 correct answers = 7 × (+3) = + 21;
Since, marks obtained for incorrect answers = -5 – 21 = (-26)
So, the number of incorrect answers = (-26) ÷ (-2) = 13;
Therefore, the number of incorrect answers = 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 7:-
The present position of the elevator is at 10 m above the ground level.
Since, the distance moved by the elevator below the ground level = 350 m
So, the total distance moved by the elevator = 350 m + 10 m = 360 m
Rate of descent = 6 m/min.
Total time taken by the elevator =360/6 = 60 minutes = 1 hour
Hence, the required time = 1 hour.
Chapter-1, Integer Class-7 Exercise-1.3 for Free