## ML Aggarwal Class 7 Solutions for ICSE Maths Chapter 1 Integers Objective Type Questions

Mental Maths

Question 1.
Fill in the blanks:
(i) ………… is the greatest negative integer.
(ii) ((-10) + 3) + (-12) = (-10) + (3 + …..)
(iii) The product of two negative integers and the product of two positive integers is a ………. integer.
(iv) The division of any integer by zero is ……..
(v) The integer whose product with (-1) is 22 is ………
(vi) (-15) × …….. = 120
(vii) ……… ÷ (-6) = -12
(viii) (-10) × ((-15) + 33) = ……. × (-15) + (-10) × 33
(ix) ……… ÷ (-25) = 0
(x) ((-8) × (-13)) × 27 = (-8) × ((……) × 27)
(xi) 13 × (-6) = -(……. × ………) = …….
(xii) (-a) + b = b + additive inverse of ……….
(xiii) When we divide a negative integer by a positive integer, we divide them as whole numbers and put a ……… sign before the quotient.
(xiv) When -25 is divided by ……… the quotient is 5.
(xv) There are …….. pairs of integers satisfying a ÷ b = -1.
(xvi) The value of the expression ((-60) ÷ 12) (-5) is ……….
Solution:
(i) -1 is the greatest negative integer.
(ii) [(-10) + 3] + (-12) = (-10) + (3 + ……..)
[(-10 + 3] + (-12) = (-10) + [3 + (-12)] (Associative law of addition)
(iii) The product of two negative integers and the product of two positive integers is a positive integer.
(iv) The division of any integer by zero is meaningless.
(v) The integer whose product with (-1) is 22 is -22. [∵ (-1) × (-22) = 22]
(vi) (-15) × ……. = 120
$$\frac { 120 }{ -15 }$$ = -8
(-15) × (-8) = 120
(vii) …….. ÷ (-6) = -12
-6 × (-12) = 72
72 ÷ (-6) = -12
(viii) (-10) × {(-15) + 33} = ……… × (-15) + (-10) × 33
= (-10) × {(-15) + 33}
= (-10) × (-15) + (-10) × 33 (Distributive law of multiplication)
(ix) 0 ÷ (-25) = 0 (∵ 0 divided by every integer excepted is zero)
(x) {(-8) × (-13)} × 27 = (-8) × {(-13) × 27} (Associative law of mutliplication)
(xi) 13 × (-6) = -(13 × 6) = -78
(xii) (-a) + b = b + additive inverse of a.
(xiii) When we divide a negative integer by a positive integer, we divide them as whole numbers and put a negative sign before the quotient.
quotient.
(xiv) When -25 is divided by (-5) the quotient is 5.
(xv) There are infinite pairs of integers satisfying a ÷ b = -1.
(xvi) The value of the expression ((-60) ÷ 12) (-5) is 1.
{∵ $$\frac { -60 }{ 12 }$$ = -5 ÷ (-5) = $$\frac { -5 }{ -5 }$$ = 1}

Question 2.
State whether the following statements are True (T) or False (F):
(i) For every integer a, |a| is either positive or zero.
(ii) The difference of two negative integers cannot be a positive integer.
(iii) We can write a pair of integers whose sum is not an integer.
(iv) Going 300 metres towards east first and then 100 m back is the same as going 100 m towards west first and then going 300 back.
(v) If we multiply an integer by (-1), then the result is the additive inverse of the integer.
(vi) If we divide an integer by (-1), then the result is the additive inverse of the integer.
(vii) 1 is the additive identity of integers.
(viii) (-17) × 6 is a whole number.
(ix) (-5) × (-8) × o is a positive integer.
(x) (-237) × 0 is same as 0 × (-89).
(xi) The product of 5 negative integers is a negative integer.
(xii) Closure property holds for subtraction of integers.
(xiii) Commutative property does not hold for subtraction of integers.
(xiv) Associative property holds for subtraction of integers.
(xv) Closure property holds for division of integers.
(xvi) Commutative property does not hold for division of integers.
(xvii) (-1) is not a mutliplicative identity of integers.
(xviii) Multiplication fact (-8) × (-12) = 96 is same as division fact 96 ÷ (-12) = -8.
(xix) [(-32 ÷ 8] ÷ 2 = (-32) ÷ (8 ÷ 2)
(xx) For every integer a, a ÷ a = 1.
(xxi) The successor of 0 × (-10) is 1 × (-10).
Solution:
(i) For every integer a, |a| is either positive or zero. (True)
(ii) The difference of two negative integers cannot be a positive integer. (False)
Correct:
Difference of -3 and -5 = -3 – (-5) = -3 + 5 = 2 which is positive
(iii) We can write a pair of integers whose sum is not an integer. (False)
Correct:
As sum of two integers is always an integer.
(iv) Going 300 metres towards east first and then 100 m back is the same as going 100 m towards west first and then going 300 back. (True)
(v) If we multiply an integer by (-1), then the result is the additive inverse of the integer. (True)
(vi) If we divide an integer by (-1), then the result is the additive inverse of the integer. (True)
(vii) 1 is the additive identity of integers. (False)
Correct:
0 is a additive identity not 1.
(viii) (-17) × 6 is a whole number. (False)
Correct:
(-17) × 6 = -102 is not a whole number as a whole numebr is zero or positive.
(ix) (-5) × (-8) × 0 is a positive integer. (False)
Correct:
(-5) × (-8) × 0 which is neither positive nor-negative.
(x) (-237) × 0 is same as 0 × (-89). (True)
(xi) The product of 5 negative integers is a negative integer. (True)
(xii) Closure property holds for subtraction of integers. (True)
(xiii) Commutative property does not hold for subtraction of integers. (True)
(xiv) Associative property holds for subtraction of integers. (False)
Correct:
It does not holds as
= 15 – 7 = 8
= 7 – 15 = -8
So, 8 ≠ (-8)
(xv) Closure property holds for division of integers. (False)
Correct:
As $$\frac { 15 }{ 5 }$$ = 3 but $$\frac { 5 }{ 15 }$$ = $$\frac { 1 }{ 3 }$$
So, 3 ≠ $$\frac { 1 }{ 3 }$$
(xvi) Commutative property does not hold for division of integers. (True)
(xvii) (-1) is not a mutliplicative identity of integers. (True)
(xviii) Multiplication fact (-8) × (-12) = 96 is same as division fact 96 ÷ (-12) = -8. (True)
(xix) [(-32 ÷ 8] ÷ 2 = (-32) ÷ (8 ÷ 2) (False)
Correct:
[(-32) ÷ 8} ÷ 2 = -4 ÷ 2 = -2
and (-32) ÷ (8 ÷ 2) = -32 ÷ 4 = -8
So, it is false.
(xx) For every integer a, a ÷ a = 1. (False)
Correct:
As 0 ÷ 0 ≠ 1
(xxi) The successor of 0 × (-10) is 1 × (-10). (False)
Correct:
As 0 × (-10) = 0 and successor of 0 is 1 but 1 × (-10) = -10

Question 3.
State whether the following statements are true or false. Justify your answer.
(i) The sum of a positive integer and a negative integer is always a positive integer.
(ii) The sum of two integers is always greater than their difference.
(iii) For any two integers a and b, the inequality -a < b is always true.
(iv) The product of two integers is always greater than the sum of the integers.
Solution:
(i) The sum of a positive integer and a negative integer is always a positive integer. (False)
Correct:
As 3 + (-8) = 3 – 8 = -5 which is negative.
(ii) The sum of two integers is always greater than their difference. (False)
Correct:
As 3 + (-4) = -1 but 3 – (-4) = 3 + 4 = 7 and -1 < 7
(iii) For any two integers a and b, the inequality -a < b is always true. (False) Correct: Let a = -5 and b = 2, then -a = -(-5) = 5 and -a> b
(iv) The product of two integers is always greater than the sum of the integers. (False)
Correct:
Let two integers be -2 and 3
Then product = -2 × 3 = -6
and sum = -2 + 3 = 1
But -6 < 1
Their product < Their sum.

Multiple Choice Questions

Choose the correct answer from the given four options (4 to 19):
Question 4.
If the integers 10, -7, 5, 3, -4 and 0 are marked on the number line, then the integer which lies on the extreme left is
(a) 10
(b) 0
(c) -7
(d) -4
Solution:
Numbers (Integers) 10, -7, 5, 3, -4 and 0 are marked on a number line.
The integer on the extreme left will be -7. (c)

Question 5.
On the number line, the value of (-3) × 3 lies on the right hand side of
(a) -10
(b) -6
(c) 0
(d) 9
Solution:
Value of (-3) × 3 = -9 lies on the right side of-10 as (-10) < (-9) (a)

Question 6.
The vqlue of 5 ÷ (-1) does not lie between
(a) 0 and-10
(b) Oand 10
(c) -3 and -10
(d) -7 and 7
Solution:
5 ÷ (-1) = $$\frac { 5 }{ -1 }$$ = -5
-5 does not lie between 0 and 10
As -5 is negative but 0 to 10 are positive integer.
0 and 10 (b)

Question 7.
The next number in the pattern -62, -37, -12, ……. is
(a) 25
(b) 0
(c) 13
(d) -13
Solution:
-62, -37, -12, …….
Next number is 0. (b)

Question 8.
Multiplication of integers satisfies the property of
(a) closure
(b) commutativity
(c) associativity
(d) all of these
Solution:
Multiplication of integers satisfies the property of closure, commutative, associative i.e. all there properties. (d)

Question 9.
Closure property does not hold in integers for
(a) multiplication
(b) division
(d) subtraction
Solution:
Closure property does not hold in the integers for the division. (b)

Question 10.
The number of integers between -20 and -10 are
(a) 8
(b) 9
(c) 10
(d) 11
Solution:
The number of integers between -20 and -10 are 9
(-19, -18, -17, -16, -15, -14, -13, -12, -11) (b)

Question 11.
If the sum of two integers is -10 and one of them is 2, then the other is
(a) 8
(b) -8
(b) 12
(d) -12
Solution:
Sum of two integers = -10
One integers = 2,
then Second integer will be = -10 – (2) = -12 (d)

Question 12.
The integer that must be subtracted from -5 to obtain -12 is
(a) 7
(b) -7
(c) 17
(d) -17
Solution:
The integer will -12 if -5 is subtracted from that -5 – (……) = -12
12 – 5 = 7 (a)

Question 13.
Which of the following is not the additive inverse of a?
(a) -(-a)
(b) -a
(c) a ÷ (-1)
(d) a × (-1)
Solution:
Additive inverse of a is not a i.e. -(-a) (a)

Question 14.
0 ÷ (-10) is equal to
(a) 0
(b) -1
(c) -10
(d) none of these
Sol.
0 ÷ (-10) = $$\frac { 0 }{ -10 }$$ = 0 (a)

Question 15.
(-33) × 102 + (-33) × (-2) is equal to
(a) 3300
(b) -3300
(c) 3432
(d) -3432
Solution:
(-33) × 102 + (-33) × (-2) = (-33) (102 – 2) = -33 × 100 = -3300 (b)

Question 16.
(-25) (6 + 4) is not the same as
(a) -250
(b) (-25) × 10
(c) (-25) × 6 × 4
(d) (-25) × 6 + (-25) × 4
Solution:
(-25) (6 + 4) is not same as (-25) × 6 × 4
6 + 4 = 10 but 6 × 4 = 24 (c)

Question 17.
101 × (-1) + 0 ÷ (-1) is equal to
(a) -101
(b) 101
(c) -102
(d) 102
Solution:
101 × (-1) + 0 ÷ (-1) = -101 + 0 = -101 (a)

Question 18.
If a and b are two integers, then which of the following may not be an integer?
(a) a + b
(b) a – b
(c) a × b
(d) a ÷ b
Solution:
a and b are two integers, then
By closure proper a ÷ b is not an integer. (d)

Question 19.
For a non-zero integer a which is the following is not defined?
(a) a ÷ 0
(b) 0 ÷ a
(c) a = 1
(d) 1 ÷ a
Solution:
a is a non-zero integer, then
a ÷ 0 or $$\frac { a }{ 0 }$$ is not defined. (a)

Value Based Questions

Question 1.
In a competitive exam, 3 marks are given for every correct answer and 1 mark is deducted for every incorrect answer. Raju copied some answers from Reema and answered all the questions, he scored 20 marks though he got 10 correct answers. How many incorrect answers had he attempted? What values are promoted in the question?
Solution:
In competitive exam
3 marks awarded for every correct answer.
1 mark is deducted for an incorrect answer.
Raju copied some answers from Reema.
He scored 20 marks but he got 10 correct answers.
For correct answer, his scores = 10 × 3 = 30
But he scored 20 marks
30 – 20 = 10 marks were deducted
He attempted 10 ÷ 1 = 10 incorrect answers.
A student should not use unfair mean in the exam. It is a bad habit. He should work hard.

Question 2.
In a quiz, ₹ 300 are awarded for every correct answer and a penalty of ₹ 75 is put for every incorrect answer. Madhuri answered 15 questions out of which only 6 answers were correct. How much money is earned by Madhuri in the quiz?
If she distributes the money earned by her to poor children in the neighborhood, what values are being promoted?
Solution:
In a quiz,
₹ 300 are awarded for every correct answer.
₹ 75 is put as the penalty for every incorrect answer.
Madhuri scored 15 questions, but 6 questions were correct answers.
Money earned for correct answer = 6 × 300 = ₹ 1800
She scored incorrect = 15 – 6 = 9
Penalty = ₹ 75 × 9 = ₹ 675
Correct amount she got = ₹ 1800 – ₹ 675 = ₹ 1125
So, she got ₹ 1125

Higher Order Thinking Skills (HOTS)

Question 1.
Write a pair of integers whose product is -12 and there lies seven integers between them.
Solution:
Product of two integers = -12
The pairs can be possible
1 × 12, 2 × 6, 3 × 4
But has 7 integers between them
The pair can be -2 × 6 or -6 × 2
and seven integers between them will be
-1, 0, 1, 2, 3, 4, 5 or -5, -4, -3, -2, -1, 0, 1

Question 2.
A water tank has steps inside it. A monkey is sitting on the first step. The water level is at the ninth step.
(i) He jumps 3 steps down and then jumps back 2 steps up. In how many jumps will he reach the water level?
(ii) After drinking water, he wants to go back. For this, he jumps 5 steps up and then jumps back 3 steps down in every move. In how many jumps will he reach back the top of the tank?
Solution:
In a tank,
Monkey is at first step and water level is at 9th step.
(i) Monkey jumps 3 steps down jumps back 2 steps
So, he jumps 3 – 2 = 1 step in one attempt.
(ii) After drinking water, he jumps up 5 steps and then back 3 steps. So, he covers 2 steps in one jump.
So, 9 – 5 = 4 + 1 = 5 jumps, he will come back at the first step of the tank.

Question 3.
A shopkeeper earns a profit of ₹ 2 by selling a pen and incurs a loss of 50 paise per pencil and loss of 15 paise per eraser while selling pencils and erasers of old stock. On a particular day, he earns a profit of ₹ 10. If he sold 10 pens and the number of pencils and erasers he sold are in the ratio 7 : 10, then find the number of pencils and eraser she sold on that day.
Solution:
By selling a pen, gain is ₹ 2
and by selling a pencils, he loses 50 paise
and an eraser, he loses 15 paise
On one day, he gains = ₹ 10
On that day he sold 10 pens and pencils and erasers in the ratio of 7 : 10
On ten pens, his gain =10 × 2 = ₹ 20
loss on penicls and erasers = ₹ 20 – ₹ 10 = ₹ 10 = 1000 paise
Ratio in pencil and erasers = 7 : 10
Let number of pencils = 7x, then eraser = 10x
7x × 50 + 10x × 15 = 1000
⇒ 350x + 150x = 1000
⇒ 500x = 1000
⇒ x = 2
Number of pencils = 7 × 2 = 14
and number of erasers = 10 × 2 = 20