Page 36 - BUSINESS MATHEMATICS MODULE 1 (WHOLE)_revised 10.20.2020

WALKTHROUGH

D. DIVISION
Division is the operation of separating something into parts or the process of being

separated. In mathematics, it is splitting a large number into a smaller quantity of numbers. It
is the inverse operation of multiplication.

Some common symbols for division can be a slash, a line, or the division sign (÷), as in:
6
6 ⁄ or 3 or 6 ÷ 3
3

It is read as six divided by three.
Moreover, a division can also be expressed as 3|6 which is read as three divides six.

In the division equation, a number to be divided is called the dividend, a number by
which another number is to be divided is called the divisor, and the result is called the

quotient.

⏞ ÷ ⏞ = ⏞

Division operation is neither Commutative nor Associative.
Consider the integers 6 and 3.

We see that: 6 ÷ 4 = 2
4 2
4 ÷ 6 = or
6 3
Therefore, 7 ÷ 4 ≠ 4 ÷ 7

In general, for any two integers a and b

a ÷ b ≠ b ÷ a
Therefore, we conclude that the Division is not Commutative for integers.

Consider the integers 8, 4 and 2

8 ÷ (4 ÷ 2) = 8 ÷ 2 = 4

(8 ÷ 4) ÷ 2 = 2 ÷ 2 = 1
Therefore, 8 ÷ (4 ÷ 2) ≠ (8 ÷ 4) ÷ 2

In general, for any three integers a, b and c

a ÷ (b ÷ c) ≠ (a ÷ b) ÷ c.
Therefore, the Division of integers is not Associative.

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