Andhra Pradesh SCERT Class 7 Maths Integers Question and Answers Solutions
Andhra Pradesh SCERT 7th Class Maths Solutions Chapter 1 Integers Question and answers. Students who are searching for Andhra Pradesh Class 7 Maths Chapter 1 can find here Solution of this chapter.
Board |
Andhra Pradesh (AP Board) |
Class |
7th |
Subject |
Maths |
Topic |
Solution |
EXERCISE 1.1
1.) Write down a pair of integers whose:
(a) sum is -7
ANSWER:
We have to write a pair of integers whose sum is -7
We write (-5,-2) pair.
-5 + (-2) = -7
(b) Difference is -10
ANSWER:
We have to write a pair of integers whose Difference is -10
We write (-20,-10) pair.
-20 – (-10) = -10
(c) Sum is 0
ANSWER:
We have to write a pair of integers whose sum is 0
We write (-5, 5)
-5 + 5 = 0
2.)
(a) Write a pair of negative integers whose difference gives 8.
ANSWER:
We have to write a pair of negative integers whose difference gives 8.
We write a pair of negative integers is ( -10,-18)
-10 – (-18) = 8
(b) Write a negative integer and a positive integer whose sum is -5.
ANSWER:
We have to write a negative integer and a positive integer whose sum is -5.
We write a negative integer and a positive integer whose sum is -5 is (-12,7)
-12 + 7 = -5
(c) Write a negative integer and a positive integer whose difference is -3.
ANSWER:
We have to write a negative integer and a positive integer whose difference is -3.
We write a negative integer and a positive integer whose sum is -3 is (-19,16)
-19 + 16 = -3
3.) In a quiz, team A scored -40, 10, 0 and team B scored 10, 0, -40 in three successive rounds. Which team scored more? Can we say that we can add integers in any order?
ANSWER:
Given,
Team A scored -40, 10, and 0
Team B scored 10, 0, -40 in three successive rounds.
Team A score = -40 + 10 + 0 = -30
Team B score = 10 + 0 + -40 = -30
Both team score equal.
Yes, we can add integers in any order.
4.) Fill in the blanks to make the following statements true:
(i) (-5)+(-8) = (-8) + (…………)
ANSWER:
Here, we have to fill blanks to make the statements true.
(-5)+(-8) = (-8) + (…………)
(-5)+(-8) = (-8) + (-5)
(ii) -53 + ……. =-53
ANSWER:
Here, we have to fill blanks to make the statements true.
-53 + ……. =-53
-53 + 0 = -53
(iii) 17+ ………… = 0
ANSWER:
Here, we have to fill blanks to make the statements true.
17+ ………… = 0
17+ (-17) = 0
(iv) [13+(-12)] + (…………) = 13+ [(-12) + (-7)]
ANSWER:
Here, we have to fill blanks to make the statements true.
[13+(-12)] + (…………) = 13+ [(-12) + (-7)]
[13+(-12)] + (-7) = 13+ [(-12) + (-7)]
(v) (-4)+ [15+(-3)] = [-4+15] + …………
ANSWER:
Here, we have to fill blanks to make the statements true.
(-4)+ [15+(-3)] = [-4+15] + …………
(-4)+ [15+(-3)] = [-4+15] + (-3)
EXERCISE 1.2
1.) Find each of the following products:
(a) 3 x (- 1)
ANSWER:
We have to find product of 3 x (- 1)
We know,
Product of 1 negative integer and 1 positive integer is always negative integer.
3 x (- 1) = -3
(b) (- 1) x 225
ANSWER:
We have to find product of (- 1) x 225
We know,
Product of 1 negative integer and 1 positive integer is always negative integer.
(- 1) x 225 = -225
(c) (- 21) x (- 30)
ANSWER:
We have to find product of (- 21) x (- 30)
We know,
Product of 2 negative integers is always positive integer.
(- 21) x (- 30) = 630
(d) (- 316) x (- 1)
ANSWER:
We have to find product of (- 316) x (- 1)
We know,
Product of 2 negative integers is always positive integer.
(- 316) x (- 1) = 316
(e) (- 15) x 0 x (- 18)
ANSWER:
We have to find product of (- 15) x 0 x (- 18)
We know,
When we multiply any number with 0 the product is always 0.
(- 15) x 0 x (- 18) = 0
(f) (- 12) x (- 11) x (10)
ANSWER:
We have to find product of (- 12) x (- 11) x (10)
We know,
Product of 2 negative integers is always positive integer.
(- 12) x (- 11) x (10) = [(- 12) x (- 11)] x (10)
[(- 12) x (- 11)] x (10) = 132 x 10
[(- 12) x (- 11)] x (10) = 1320
(g) 9 x (- 3) x (- 6)
ANSWER:
We have to find product of 9 x (- 3) x (- 6)
We know,
Product of 2 negative integers is always positive integer.
9 x (- 3) x (- 6) = 9 x [(- 3) x (- 6)]
9 x [(- 3) x (- 6)] = 9 x 18
9 x [(- 3) x (- 6)] = 162
(h) (- 18) x (- 5) x (- 4)
ANSWER:
We have to find product of (- 18) x (- 5) x (- 4)
We know,
Product of 3 negative integers is always negative integer.
(- 18) x (- 5) x (- 4) = -360
(i) (- 1) x (- 2) x (- 3) x 4
ANSWER:
We have to find product of (- 1) x (- 2) x (- 3) x 4
We know,
Product of 3 negative integers is always negative integer.
(- 1) x (- 2) x (- 3) x 4
= [(- 1) x (- 2) x (- 3)] x 4
= -6 x 4
(- 1) x (- 2) x (- 3) x 4 = -24
(j) (- 3) x (- 6) x (- 2) x (- 1)
ANSWER:
We have to find product of (- 3) x (- 6) x (- 2) x (- 1)
We know,
Product of 4 negative integers is always positive integer.
(- 3) x (- 6) x (- 2) x (- 1) = 36
2.) Verify the following:
(a) 18[7 + (- 3)] = [18 x 7] + [18 x (- 3)]
ANSWER:
We have to verify 18[7 + (- 3)] = [18 x 7] + [18 x (- 3)]
We take LHS of given.
We multiply 18 with bracket [7 + (- 3)] we get RHS.
18[7 + (- 3)] = [18 x 7] + [18 x (- 3)]
From this,
LHS = RHS
18[7 + (- 3)] = [18 x 7] + [18 x (- 3)]
(b) (- 21)[(- 4) + (- 6)] = [(- 21)(- 4)] + [(- 21)(- 6)]
ANSWER:
We have to verify (- 21)[(- 4) + (- 6)] = [(- 21)(- 4)] + [(- 21)(- 6)]
We take LHS of given.
(- 21)[(- 4) + (- 6)]
We multiply (-21) with bracket [(- 4) + (- 6)] we get RHS.
(- 21)[(- 4) + (- 6)] = [(- 21)(- 4)] + [(- 21)(- 6)]
From this,
LHS = RHS
(- 21)[(- 4) + (- 6)] = [(- 21)(- 4)] + [(- 21)(- 6)]
3.) (i) For any integer a, what is (- 1) x a equal to?
ANSWER:
For any integer a, we have to find (- 1) x a
(- 1) x a = -a
(ii) Determine the integer whose product with (-1) is
(a) -22
ANSWER:
We have to find the integer whose product with (-1) is -22
Let the integer is y.
Y x (-1) = -22
Y = 22
The integer is 22.
(b) 37
ANSWER:
We have to find the integer whose product with (-1) is 37
Let the integer is y.
Y x (-1) = 37
Y = -37
The integer is -37
(c) 0
ANSWER:
We have to find the integer whose product with (-1) is 0
Let the integer is y.
Y x (-1) = 0
Y = 0
The integer is 0.
EXERCISE 1.3
1.) Evaluate each of the following:
(a) (- 30) / 10
ANSWER:
We have to evaluate (- 30) / 10.
We know,
When we divide with 1 positive integer and negative integer answer we get is always negative integer.
Here, -30 is negative integer and 10 is positive integer.
(- 30) / 10 = -3
(b) 50 / (- 5)
ANSWER:
We have to evaluate 50 / (- 5)
We know,
When we divide with 1 positive integer and negative integer answer we get is always negative integer.
Here, -5 is negative integer and 50 is positive integer.
50 / (- 5) = -10
(c) (- 36) / (- 9)
ANSWER:
We have to evaluate (- 36) / (- 9)
We know,
When we divide with 2 positive or negative integer answer we get is always positive integer.
Here (- 36), (- 9) both are negative integers.
(- 36) / (- 9) = 4
(d) (- 49) / (49)
ANSWER:
We have to evaluate (- 49) / (49)
We know,
When we divide with 1 positive integer and negative integer answer we get is always negative integer.
Here, -49 is negative integer and 49 is positive integer.
(- 49) / (49) = -1
(e) 13 / [(- 2) + 1]
ANSWER:
We have to evaluate 13 / [(- 2) + 1]
We 1st simplify [(- 2) + 1] = -1
We have to evaluate 13 / -1
We know,
When we divide with 1 positive integer and negative integer answer we get is always negative integer.
Here, -1 is negative integer and 13 is positive integer.
13 / -1 = -13
(f) 0 / (- 12)
ANSWER:
We have to evaluate 0 / (- 12)
We know,
When we divide any number with 0 answer is always 0.
0 / (- 12) = 0
(g) (- 31) / [(- 30) + (- 1)]
ANSWER:
We have to evaluate (- 31) / [(- 30) + (- 1)]
We 1st simplify [(- 30) + (- 1)] = -31
We have to evaluate (- 31) /(- 31)
We know,
When we divide with 2 positive or negative integer answer we get is always positive integer.
Here both (- 31), (- 31) are negative integers.
(- 31) /(- 31) = 1
(h) [(- 36) / 12] / 3
ANSWER:
We have to evaluate [(- 36) / 12] / 3
We 1st simplify [(- 36) / 12] = -3
We have to evaluate (- 3) / (3)
We know,
When we divide with 1 positive integer and negative integer answer we get is always negative integer.
Here, -3 is negative integer and 3 is positive integer.
(- 3) / (3) = -1
(i) [(- 6) + 5)] / [(-2) +1]
ANSWER:
We have to evaluate [(- 6) + 5)] / [(-2) +1]
We 1st simplify [(- 6) + 5)] = -1
Now, we solve [(-2) +1] = -1
We have to evaluate -1 / -1
We know,
When we divide with 2 positive or negative integer answer we get is always positive integer.
Here both (- 1), (- 1) are negative integers.
-1 / -1 = 1
2.) Verify that a/ (b+c) not equal to (a / b) + (a / c) for each of the following values of a, b and c.
(a) a = 12 b = – 4 , c = 2
ANSWER:
We have to verify a/ (b+c) not equal to (a / b) + (a / c)
Given, a = 12 b = – 4 , c = 2
a/ (b+c) = 12 / (4 + 2) = 12/6 = 2
(a / b) + (a / c) = (12/4) + (12/2)
(a / b) + (a / c) = 3 + 6 = 9
We verify a/ (b+c) not equal to (a / b) + (a / c)
(b) a = (- 10) b = 1 c = 1
ANSWER:
We have to verify a/ (b+c) not equal to (a / b) + (a / c)
Given, a = (- 10) b = 1 c = 1
a/ (b+c) = (- 10) / (1 + 1) = -10 / 2 = -5
(a / b) + (a / c) = ((- 10) / 1) + ((- 10) / 1)
(a / b) + (a / c) = -10 + -10 = -20
3.) Fill in the blanks:
(a) 369/ ——– = 369
ANSWER:
Here, we have to fill blank.
369/ ——– = 369
369/ 1 = 369
(b) (- 75) / ——– =-1
ANSWER:
Here, we have to fill blank.
(- 75) / ——– =-1
(- 75) / 75 =-1
(c) (- 206) / ——– =1
ANSWER:
Here, we have to fill blank.
(- 206) / ——– =1
(- 206) / (- 206) =1
(d) – 87 / ———- =87
ANSWER:
Here, we have to fill blank.
– 87 / ———- =87
– 87 / -1 = 87
(e) ———- / 1 = – 87
ANSWER:
Here, we have to fill blank.
———- / 1 = – 87
– 87 / 1 = – 87
- f) ————— / 48 = – 1
ANSWER:
Here, we have to fill blank.
————— / 48 = – 1
-48 / 48 = – 1
(g) 20 / ————– =-2
ANSWER:
Here, we have to fill blank.
20 / ————– =-2
20 /-10 =-2
(h) ————- / (4) = – 3
ANSWER:
Here, we have to fill blank.
————- / (4) = – 3
-12 / (4) = – 3
4.) Write five pairs of integers (a, b) such that a / b = – 3 One such pair is (6, – 2) because 6 / (- 2) = (- 3)
ANSWER:
Here, we have to write five pairs of integers (a, b) such that a / b = – 3
1st pair is (-12, 4) because -12 / 4 = (- 3)
2nd pair is (-24, 8) because -24 / 8 = (- 3)
3rd pair is (-72, 24) because -72 / 24 = (- 3)
4th pair is (-15, 5) because -15 / 5 = (- 3)
5th pair is (-75, 25) because -75 / 25 = (- 3)
5.) The temperature at 12 noon was 100C above zero. If it decreases at the rate of 20C per hour until midnight, at what time would the temperature be 80C below zero? What would be the temperature at mid-night?
ANSWER:
Given that,
The temperature at 12 noon was 100C above zero.
It decreases at the rate of 20C per hour until midnight.
We have to find what time the temperature would be 80C below zero.
Also we have to find the temperature at mid-night.
There are total 12 hours from 12 noon to mid night.
Total Temperature Decrease = 12 x 2 = 240C
The temperature at 12 noon was 100C above zero.
The temperature at mid-night = 100C – 240C
The temperature at mid-night = – 140C
Time the temperature would be 80C below zero = 140C – 80C = 3 hours
Time the temperature would be 80C below zero = 9 P.M
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?
ANSWER:
Given,
In class test (3) marks are given for every correct answer and (-2) marks are given for every incorrect answer.
Radhika scored 20 marks. If she has got 12 correct answers.
We have to find how many questions has she attempted incorrectly.
She has got 12 correct answers. = 12 x 3 marks = 36 marks but Radhika scored 20 marks.
Questions has she attempted incorrectly = 36 – 20 = 16 marks.
But, (-2) marks are given for every incorrect answer.
16 / -2 = 8
Total 8 questions 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?
ANSWER:
Given,
In class test (3) marks are given for every correct answer and (-2) marks are given for every incorrect answer.
Mohini scores -5 marks in this test, though she has got 7 correct answers.
We have to find how many questions has she attempted incorrectly.
Mohini has got 7 correct answers = 7 x 3 marks = 21 marks.
But, she got -5 marks.
Questions has she attempted incorrectly = 21 – (-5) = 26 marks
But, (-2) marks are given for every incorrect answer
Questions has she attempted incorrectly = 26 / -2 = 13
13 questions she attempted incorrectly.
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 it will take to reach – 350 m.
ANSWER:
Given,
An elevator descends into a mine shaft at the rate of 6m / min.
The descent starts from 10 m above the ground level,
We have to find how long it will take to reach – 350 m.
We first find total distance that elevator descends into a mine shaft = 10 m + 350 m = 360 m
Time it will take to reach – 350 m. = 360 / 6m / min.
Time it will take to reach – 350 m. = 60 min or 1 hour