Page 20 - Math_Genius_V1.0_C7_Flipbook

D:\Surender Prajapati\CBSE_ICSE_Book_New\CBSE\Grade-7\Math_Genius-7\Open_File\01_Chapter\01_Chapter
\ 15-Nov-2024 Surender Prajapati Proof-6 Reader’s Sign _______________________ Date __________

Division of Integers

We know that division is the inverse operation of multiplication.
For example, for whole numbers 6 and 7, 6 × 7 = 42.
So, 42 ÷ 7 = 6 and 42 ÷ 6 = 7
\ Each multiplication fact has two division facts. The same rule is true for integers also.
For example: (a) (–8) × 7 = –56

So, (–56) ÷ 7 = –8 and (–56) ÷ (–8) = 7
(b) (–4) × (–3) = 12
So, 12 ÷ (–4) = (–3) and 12 ÷ (–3) = (–4)
Let us see how to divide integers.
Division of Integers with the Same Sign

If the dividend and divisor are of the same sign, we divide In chapter 18 of Brahma-
them as whole numbers and write the quotient with a positive sphuṭa-siddhanta, Brahmagupta
(+) sign or without any sign. also describes the rules of
For example: (a) (–12) ÷ (–4) = (12 ÷ 4) = 3 division of integers.
(b) 18 ÷ 3 = 6 • A positive divided by a positive

Division of Integers with Different Signs is positive.
• A negative divided by a negative
If dividend and divisor are of different signs, we divide them is positive.
as whole numbers and write the quotient with a minus (–) sign.
• A positive divided by a negative
For example: (a) (–32) ÷ 4 = – (32 ÷ 4) = –8 is negative.

(b) (30) ÷ (–6) = – (30 ÷ 6) = –5 • A negative divided by a positive
From the above we can conclude that: is negative.
• If both dividend and divisor are either positive or negative,
then the quotient is positive.
• If both dividend and divisor have opposite signs, then the quotient is negative. • (+) ÷ (+) = +
• (–) ÷ (–) = +
Example 7: Divide the following. • (+) ÷ (–) = (–)
(a) 24 by 6 (b) 15 by (–3) (c) (–48) by 8 (d) • (–) ÷ (+) = (–)
(–72) by (–9)
Solution: (a) 24 by 6 = 24 ÷ 6 = 4 (b) 15 by (–3) = 15 ÷ (–3) = –(15 ÷ 3) = –5

(c) (–48) by 8 = (–48) ÷ 8 = –(48 ÷ 8) = –6 (d) (–72) by (–9) = (–72) ÷ (–9) = 72 ÷ 9 = 8
Properties of Division of Integers

Closure Property Let us observe the following examples:
(a) 10 ÷ 2 = 5 (5 is an integer)
(b) –8 ÷ 4 = –2 (–2 is an integer)
2
(c) 2 ÷ 3 = (it is a fraction, not an integer.)
3
If a and b are any two integers, then a ÷ b is not always an integer.
Thus, integers are not closed under division.

Mathematics-7 18