ML Aggarwal Class 7 Solutions for ICSE Maths Chapter 1 Integers Ex 1.3
Question 1.
Find the following products:
(i) 7 × (-35)
(ii) (-13) × (-15)
(iii) (-12) × (-11) × (-10)
(iv) (-13) × 0 × (-24)
(v) (-1) × (-2) × (-3) × 4
(vi) (-3) × (-6) × (-2) × (-1)
Solution:
(i) 7 × (-35) = -245
{∵ (+) × (-) = -; (-) × (-) = +; (-) × (-) × (-) = -}
(ii) (-13) × (-15) = +195
(iii) (-12) × (-11) × (-10) = 132 × (-10) = -1320
(iv) (-13) × 0 × (-24) = -13 × 0 = 0 × (-24) = 0 (Multiplication by 0, result is always zero)
(v) (-1) × (-2) × (-3) × 4 = (2) (-3) × 4 = -6 × 4 = -24
(vi) (-3) × (-6) × (-2) × (-1) = +(18) × (+2) = 36
Question 2.
Verify the following:
(i) 37 × [6 + (-3)] = 37 × 6 + 37 × (-3)
(ii) (-21) × [(-6) + (-4)] = (-21) × (-6) + (-21) × (-4)
Solution:
(i) 37 × [6 + (-3)] = 37 × 6 + 37 × (-3)
LHS = 37 × [6 – 3] = 37 × 3 = 111
RHS = 37 × 6 + 37 × (-3) = 222 – 111 = 111
LHS = RHS
(ii) (-21) × [(-6) + (-4)] = (-21) × (-6) + (-21) × (-4)
LHS = (-21) × [(-6) + (-4)] = -21 × [-6 – 4] = (-21) × (-10) = +210
RHS = (-21) × (-6) + (-21) × (-4) = 126 + 84 = 210
LHS = RHS
Question 3.
Using suitable properties, evaluate the following:
(i) 8 × 53 × (-125)
(ii) (-8) × (-2) × 3 × (-5)
(iii) (-6) × 2 × (-8) × 5
(iv) 15 × (-25) × (-4) × (-10)
(v) 26 × (-48) + (-48) × (-36)
(vi) 724 × (-56) + (-724) × 44
(vii) (-47) × 102
(viii)(-39) × (-97)
Solution:
(i) 8 × 53 × (-125)
Using associative property
= 8 × (-125) × 53 = -1000 × 53 = -53000
(ii) (-8) × (-2) × 3 × (-5)
Using associative property
= (-2) × (-5) × (-8) × 3
= +10 × (-8) × 3
= -80 × 3
= -240
(iii) (-6) × 2 × (-8) × 5
Using associative property
= 2 × 5 × (-6) × (-8)
= 10 × (+48)
= 480
(iv) 15 × (-25) × (-4) × (-10)
= (-25) × (-4) × (-10) × 15
= 100 × (-150)
= -15000
(v) 26 × (-48) + (-48) × (-36)
Using distributive law of mutliplication
= (-48) [26 + (-36)]
= (-48) × (-10)
= 480
(vi) 724 × (-56) + (-724) × 44
Using distributive law of mutliplication
= 724 × (-56 – 44)
= 724 × 100
= 72400
(vii) (-47) × 102
= (-47) × (100 + 2)
Using distributive law of mutliplication
= (-47) × 100 + (-47 × 2)
= -4700 – 94
= -4794
(viii) (-39) × (-97)
= -39 × (-100 + 3)
= (-39) × (-100) + (-39) (3)
= 3900 – 117
= 3783
Question 4.
Fill in the blanks to make the following true statements:
(i) (-4) × …… = 44
(ii) 7 × …… = -42
(iii) …… × (-13) = 143
(iv) (-5) × …… = 0
Solution:
(i) (-4) × …… = 44
⇒ (-4) × (41) = 44 (∵ 44 ÷ -4 = -11)
(ii) 7 × …… = 42
7 × (-6) = -42 (∵ -42 ÷ 7 = -6)
(iii) ….. × (-13) = 143
(-11) × (-13) = 143 (∵ -143 ÷ -13 = -11)
(iv) (-5) × ….. = 0
(-5) × 0 = 0 (∵ 0 ÷ -5 = 0)
Question 5.
A certain freezing process requires that room temperature be lowered from 32°C at the rate of 5°C every hour. What will be the room temperature 8 hours after the freezing process begins?
Solution:
Original temperature = 32°C
Rate of lowering the temperature = 5°C per hour
After 8 hours, the freezing process begins = 32°C – (5°C × 8) = 32°C – 40°C = -8°C
Question 6.
In a class test containing 10 questions, 5 marks are awarded for every correct answer and 2 marks are deducted for every incorrect answer and 0 for questions not attempted.
(i) Rohit gets four correct and six incorrect answers. What is his score?
(ii) Seema gets 5 correct and 5 incorrect answers. What is her score?
(iii) Ritu attempted 7 questions and gets only 2 correct answers. What is her score?
Solution:
Total number of questions in a test = 10
Award for a correct answer = 5 marks
Deduction for an incorrect answer = 2 marks
Answer for not attempting the question = 0 mark
(i) Rohit award for 4 correct answers and 6 incorrect answers = 54 – 6 × 2 = 20 – 12 = 8 marks
(ii) Seema’s award for 5 correct answers and 5 incorrect answers = 5 × 5 – 5 × 2 = 25 – 10 = 15 marks
(iii) Ritu’s award for attempting 7 questions 3 questions not attempted, 2 correct answers
= (10 – 7) = 3 not attempted = 0 marks and 5 incorrect answers
= 2 × 5 + 3 × 0 – 5 × 2
= 10 + 0 – 10
= 0 marks
Question 7.
(i) Find a pair of integers whose product is -15 and whose difference is 8.
(ii) Find a pair of integers whose product is -36 and whose difference is 15.
Solution:
(i) A pair of integers whose product = -15
and difference = 8
These integers can be -3, 5 as
-3 × 5 = -15
5 – (-3) = 5 + 3 = 8
as -5, 3 is another pair as
3 × (-5) = -15
and 3 – (-5) = 8
(ii) A pair of integer whose product is -36
and differnce = 15
There integers can be -12 and 3
as -12 × 3 = -36
and 3 – (-12) = 3 + 12 = 15
Other pair can be -3, 12 as
-3 + 12 = -36
and 12 – (-3)
= 12 + 3 = 15