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Integers exercise 1 apscert class 7

Multiplication of integers :

To multiply the integers having different signs put the negative sign before the product.For any two integers a and b
(–a) × b = – (a × b) = a × (–b)

Example:Find the values of

(i) (− 6) × 5 = − 30
(ii) (−15) × 2=− 30
(iii) (−12) × 8 =− 96
(iv) (−10) × 6=− 60

The product of two negative integers is always a positive integer.
(–a) × (–b)= a × b

Example:Find the values of

(i) (− 8) × (−7)=56 (ii) (−15) × (−6) =56 (iii) (−12) × (−2) =56 (iv) (−10) × (−9)=90

1. If the signs of two integers are same then the product is positive integer.
2. If the signs of two integers are different then the product is negative integer.

EXAMPLES

Example 1: A sump is full of water, when the motor started pumping the level of water decreasing 2 inches per minute then what is the level of water from the ground level after 20 minutes?

Solution:

The change in level of water per minute = −2 inches (decreasing 2 inches)
The level of water after 20 minutes = 20 × (−2) = −40 inches
So, the level of water in sump is 40 inches depth from the ground level.

Do you know?
1 inch = 2.74cm

Example 2 : An elevator begins from 20m above the ground. It descends into a mine shaft at the rate of 6m per minute. what will be its position after 15 minutes?

Solution :

Since the elevator is going down, so the distance covered by it will be represented by a negative integer.
Change in position of the elevator in one minute = −6m
Change in position of the elevator in 15 minutes = 15 × (−6) = −90m
So, the final position of the elevator = 20 + (−90) = − 70m
∴The elevator is at 70m below the ground level.

Example 3 : In a test, (+5) marks are given for every correct answer and (−3) marks are given for every incorrect answer. Lakshmi gets 45 correct and 15 incorrect answers. What is her score?

Solution :

Marks given for one correct answer = 5
Marks obtained for 45 correct answers = 45 × 5 = 225
Marks given for one incorrect answer = −3
Marks obtained for 15 incorrect answers = 15 × (−3) = −45
∴ Lakshmi’s score = 225 + (−45) = 180.

EXERCISE-1

i) 5 × 7 =35   ii) (−9) × (6) =−54
iii) (9) × (−4) =−36   iv) (8) × (−7)=−56
v) (−124) × (−1)=124   vi) (−12) × (−7) =84
vii) (−63) × 7 =−441  viii) 7 × (−15)=−105
i) 2 × (−5) = −10 is greater than 3 × (−4)=−12

ii) (−6) × (−7)= 42 is greater than (−8) × 5=−40

iii)(−3) × (−21) =63 is greater than (−6) × 10=−60

iv) 6 × (−16)=−96 is greater than 9 × (−11)=−99

v) (−8) × (−5)=40 is greater than (−9) × (−4)=36
i) A negative integer
6 and -96;    -8 and 5;

ii) A positive integer
-9 and -4 ;    8 and 6 ;

iii) Zero
0 and 8;    -7 and 0 ;    0 and 0
Since the frog is slipping down into well, so the distance covered by it will be represented by a negative integer.
Change in position of the frog in one minute = −3m
Change in position of the frog in 5 minutes = 5 × (−3) = −15m
∴The position of frog after 5 minutes in the well = − 15m
The change in level of water per a week = −5 inches (decreasing 5 inches)
The level of water after 6 weeks = 6 × (−5) = −30 inches
So, the change in the level of the water over a period of 6 weeks is 30 inches.
Profit on one note book = ₹ 5
Profit on 1500 books = 1500 × ₹5 = ₹7500
Loss on one pen = − ₹3
loss on 1500 pens = 1500 × (− ₹3) = − ₹4500
total=₹7500 + (−₹4500) =₹3000
∴He got the profit of ₹3000.
Profit on a bag of white cement = ₹8
Profit on 2000 bags of white cement = 2000 × ₹8 = ₹16000
Loss on a bag of grey cement = − ₹6
loss on 3000 bags of grey cement = 3000 × (− ₹6) = − ₹18000
total=₹16000 + (−₹18000) = − ₹2000
∴He got the loss of ₹2000.
i) (−4) × 5 = −20    ii)(−7) × 5 = −35

iii) (−6) × (−8) = 48    iv) (−5) × (−9) = 45

v) (−6) × 7 = − 42    vi) 8 × (−1) = −8
< Review Exercise Exercise 2 >

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