Integers exercise 2 apscert class 7
Division of Integers :
Division is the inverse operation of multiplication.
example:take two non- zero integers 6 × 4 = 24.
So, 24 ÷ 4 = 6 and 24 ÷ 6 = 4
We can say for each multiplication statement there are two division statements.
Do you know?
Division by zero is not defined
Division of two integers follows the same rules of multiplication.
If the signs are same then the quotient is positive.
If the signs are different then the quotient is negative.
Example:Fill the following table
| S.No. | Integer 1 ÷ Integer 2 | Quotient |
|---|---|---|
| 1 | (+25) ÷ (+5) | 5 |
| 2 | 42 ÷ (− 6) | − 7 |
| 3 | (−75) ÷ 15 | − 5 |
| 4 | (−27) ÷ (−3) | 9 |
EXAMPLES
Example 4 : A borewell machine drills down 72 feet per hour from surface of the earth. If the water is at 360 feet down from surface of earth, after how many hours it will touch the water layer?
Solution :Depth of drilling in one hour = −72 feet
Depth of water layer from surface of earth = −360feet
Number of hours required = −360 ÷ (−72) = 5
Hence, the borewell machine will touch water layer at 5 hours of drilling.
Example 5 : In a test, (+4) marks are given for every correct answer and (−2) marks are given for every incorrect answer. Sai answered all the questions and scored 26 marks from 8 correct answers. How many incorrect answers had Sai attempted?
Solution :Marks given for one correct answer = 4
So, marks given for 8 correct answers = 4 × 8 = 32
Sai score = 26
Marks obtained for incorrect answers = 26 − 32 = −6
Marks given for one incorrect answer = (−2)
∴ Number of incorrect answers = (−6) ÷ (−2) = 3
Example 6 : Shop keeper Yaseen earns a profit of ₹20 per bag of Sonamasoori rice sold and loss of ₹12 per bag of Hamsa rice. In one week he gets neither profit nor loss, if he solds 1440 Sonamasoori rice bags. How many Hamsa rice bags did he sell?
Solution :In the given problem there is neither profit or loss.
So, Profit earned + loss incurred = 0
Profit earned = − loss incurred
Profit earned by selling one Sonamasoori rice bag = ₹20
Profit earned by selling 1440 Sonamasoori rice bag = 1440 × ₹20 = ₹28800
Loss incurred by selling one Hamsa rice bag = ₹12 which we denoted by −₹12
Loss incurred by selling on Hamsa rice bags = −₹28800
Total number of Hamsa rice bags sold = (−₹28800) ÷ (−₹12) = 2400 bags
EXERCISE-2
iii) (−51) ÷ 17 =−3 iv) 38 ÷ (−19)=−2
v) (−80) ÷ 20 =−4 vi) (−150) ÷ (−25)=6
vii) (−600) ÷ 60=−10 viii) (−54) ÷ 9=−6
ix) 130 ÷ 65=2 x) (−315) ÷ (−315)=1
one number = −15
other number = (−165) ÷ (−15)=11
1 month loss =(−₹1,32,000)÷6= −₹22000
∴ The company got ₹22000 average loss of each month.
temperature decrease rate per hour = −2°C
temperature decreased to 8°C below zero = −8°C
So,total change in temperature = −8°C−10°C=−18°C
number of hours taken for this change = (−18°C) ÷ (−2°C) = 9 hours
∴At the time of 9pm the temperature is −8°C.
Total time from 12 noon to mid-night= 12 hours
Temperature decreased in 12 hours = 12 × (−2°C) =(−24°C)
So, temperature at mid-night= 10°C −24°C = −14°C
So, Profit earned + loss incurred = 0
Profit earned = − loss incurred
Profit earned by selling one kg of tomato = ₹7
Profit earned by selling 68 kgs of tomato= 68 × ₹7 = ₹476
Loss incurred by selling one kg of brinjal = ₹4 which we denoted by −₹4
Loss incurred by selling on brinjal= −₹476
Total kgs of brinjal sold = (−₹476) ÷ (−₹4) =119 kgs
So, marks given for 10 correct answers = 3× 10 = 30
Sona score = +20
Marks obtained for incorrect answers = 20 − 30 = −10
Marks given for one incorrect answer = (−1)
(i) Number of incorrect answers = (−10) ÷ (−1) = 10
(ii) Total questions given in test = correct answers + incorrect answers = 10+10=20
ii.(8,−2) because 8÷ (−2) = − 4
iii.(−8,2) because (−8)÷ 2 = − 4
iv.(16,−4) because 16÷ (−4) = − 4
v.(−20,5) because (−20)÷ 5 = − 4
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