ML Aggarwal Class 7 Solutions for ICSE Maths Chapter 1 Integers Check Your Progress
Question 1.
Evaluate the following:
(i) (-7) × (-9) × (-11)
(ii) (-5) × 7 × (-6) × (-8)
(iii) (-1024) ÷ 32
(iv) (-216) ÷ (-12)
Solution:
(i) (-7) × (-9) × (-11) = (63) × (-11) = -693
(ii) (-5) × 7 × (-6) × (-8) = -35 × (48) = -1680
(iii) (-1024) ÷ 32
= \(\frac { -1024 }{ 32 }\)
= -32
(iv) (-216) ÷ (-12)
= \(\frac { -216 }{ -12 }\)
= +18
= 18
Question 2.
What will be the sign of the product if we multiply 39 negative integers and 98 positive integers?
Solution:
39 is odd and 98 is even.
Product of 39 negative integers and 98 positive integers will be negative.
Question 3.
Use the sign >, < or = in the box to make the following statements true:
(i) (-15) + 38 ……… 27 + (-50)
(ii) (-13) × 0 × (-5) …….. (-7) × (-6) × 14
(iii) (-18) ÷ (-3) …….. (-10) + (-15) + 31
(iv) (-5) × (-7) × (-10) …….. (-1400) ÷ (-4)
Solution:
(i) (-15) + 38 ……. 27 + (-50)
LHS = -15 + 38 = 23
RHS = 27 – 50 = -23
(23) > (-23)
(ii) (-13) × 0 × (-5) ……. (-7) × (-6) × 14
LHS = -13 × 0 × (-5) = 0
and (-7) × (-6) × 14
RHS = 42 × 14 = 588
0 < 588
(iii) (-18) ÷ (-3) ……. (-10) + (-15) + 31
-18
LHS = -18 ÷ -3 = 6
RHS = (-10)+ (-15) + 31 = -25 + 31 = 6
6 = 6
(iv) (-5) × (-7) × (-10) ……… (-1400) ÷ (-4)
LHS = (-5) × (-7) × (-10) = 35 × (-10) = -350
RHS = (-1400) ÷ (-4) = -350
-350 < 350
Question 4.
Is {(-45) ÷ (-15)} ÷ (-3) = (-45) ÷ [(-15) ÷ (-3)]?
Solution:
(-45) ÷ (-15) ÷ (-3)
LHS = \(\frac { -45 }{ -15 }\) ÷ (-3) = 3 ÷ -3 = -1
and RHS = -45 ÷ (\(\frac { -15 }{ -3 }\))
= -45 ÷ 5
= -9
(-1) ≠ -9
No, not equal.
Question 5.
A cement company earns a profit of ₹ 8 per bag of white cement sold and a loss of ₹ 5 per bag of grey cement sold.
(i) The company sells 3000 bags of white cement and 5000 bags of grey cement in a month. What is its profit or loss?
(ii) What is the number of white cement bags it must sell to have neither profit nor loss, if the number of grey cement bags sold is 6400?
Solution:
Profit on one white cement bag = ₹ 8
and loss on one bag grey cement bag = ₹ 5
(i) On the sale of 3000 bags of white cement and 5000 bags of grey cement bags.
Sale = 3000 × 8 – 5000 × 5 = ₹ 24000 – ₹ 25000 = – ₹ 1000
There will be a loss of ₹ 1000
(ii) Loss on 6400 bags of grey cement = ₹ 6400 × 5 = 32000
In order to get a gain of ₹ 32000
The white cement bags be sold = \(\frac { 32000 }{ 8 }\) = 4000 bags
Question 6.
Simplify the following:
(i) (-7) + (-6) ÷ 2 – {(-5) × (-4) – (3 – 5)}
(ii) 11 – [7 – (5 – 3 (9 – \(\bar { 3-6 }\))}].
Solution:
(i) (-7) + (-6) ÷ 2 – {(-5) × (-4) – (3 – 5)}
= (-7) + (-6) ÷ 2 – [+20 – (-2)]
= (-7) + (-6) ÷ 2 – (20 + 2)
= (-7) + \(\frac { -6 }{ 2 }\) – 22
= (-7) + (-3) – 22
= -7 – 3 – 22
= -32
(ii) 11 – [7 – (5 – 3 (9 – \(\bar { 3-6 }\))}]
= 11 – [7 – {5 – 3 (9 – 3 + 6)}]
= 11 – [7 – {5 – 3 × 12}]
= 11 – [7 – {5 – 36}]
= 11 – [7 – {-31}]
= 11 – [7 + 31]
= 11 – 38
= -27