Division of Integers

Division of Integers

We have already seen that each multiplication statement has two division statements in whole numbers. Can we try the same for integers also; let us play with this number converter machine and see how division works.

Number Converter

From the above table, we infer that the division of two integers with the same sign is a positive integer.

Division of two integers with opposite signs gives a negative integer.

Try these

(i) (−32)÷ 4 = – 8

(ii) (−50)÷ 50 = –1

(iii) 30 ÷ 15 = 2

(iv) −200 ÷10 = –20

(v) −48 ÷ 6 = –8

Example 1.25

Divide: (i) (−85) by 5 (ii) (–250) by (–25) (iii) 120 by (–6) (iv) 182 by (–2)

Solution

(i) (−85) ÷ 5 = −17

(ii) (−250)÷ (−25)= +10

(iii) 120 ÷ (–6) = −20

(iv) 182 ÷ (–2) = −91

Example 1.26

In a competitive exam 4 marks are given for every correct answer and (-2) marks are given for every incorrect answer, kalaivizhi attended the exam and answered all the questions and scored 20 marks only even though she got 10 correct answers. How many questions did she answer incorrectly?

Solution

Marks given for one correct answer = 4

Marks given for 10 correct answers = 10 × 4

= 40

Kalaivizhi’s final score = 20

Marks reduced for incorrect answers = 40 − 20

= 20

Therefore, number of questions answered incorrectly = 20 ÷ 2 = 10

Example 1.27

A shopkeeper earns a profit of ₹ 5 by selling one notebook and incurs a loss of ₹ 2 per pen while selling of his old stock. In a particular day he earns neither profit nor loss. If he sold 20 notebooks, how many pens did he sell?

Solution

Since neither profit nor loss

Profit + Loss = 0

(ie) profit = − Loss

 Profit earned from 1 notebook = ₹ 5

Profit earned from 20 notebooks = 20 ×₹5

 = ₹ 100

 Loss incurred by selling pens = ₹ 100 Loss

 = −100

Loss for 1 pen = ₹ 2

 loss = −2

Total number of pens sold = (−100)÷ (−2)

 = 50 pens.

Activity

 Students may be divided into two groups and do the activity using "In-out box". This box takes any number as input and apply the rule to the given number and gives the answer. One group will carry out the role of finding output applying the corresponding rule. One is done in each rule for your reference.