DIVISION FACTS

We have four binary operations in math. They are

Addition, Subtraction, Multiplication and Division

When we use each of the above binary operations, the result may be different.   

It is because of the work done by the binary operation that we have between the two numbers. Knowing the work done by the binary operation is called the fact of that operation.

Let us consider the following example to understand the important fact of division.

Example : 

A person wants to share the money $240 equally to his four sons. How much money will each son receive ?

To get answer for the above question, we will be dividing $240 by 4.

That is, 

240 ÷ 4 or 240/4

To know the result of the above division, we are going to use multiplication.

That is,  

The result of the above division is equal to, "How many times of the denominator is equal to the numerator ?" 

More clearly, how many times 4 goes into 240 ?

60 times of the denominator 4 is equal the numerator 240.

Then, 240 ÷ 4  =  240/4  =  60

Hence, each son will receive $60.

Other Facts of Division :

(i)  Commutative property (does not hold)

(ii)  Associative property (does not hold)

(iii)  Division by zero (not defined)

(iv)  Some other properties of division

Commutative Property

Observe the following examples :

15 ÷ 5  =  15/5  =  3

5 ÷ 15  =  5/15  =  1/3

Therefore, 15 ÷ 5  ≠  5 ÷ 15

From the above example, we observe that division is not commutative. 

Hence, commutative property does not hold for division. 

Associative Property

Observe the following examples :

12 ÷ (6 ÷ 2)  =  12 ÷ 3  =  4

(12 ÷ 6) ÷ 2  =  2 ÷ 2  =  1

Therefore, 12 ÷ (6 ÷ 2)  ≠  (12 ÷ 6) ÷ 2

From the above example, we observe that division is not associative. 

Hence, associative property does not hold for division. 

Division by Zero

Division of any number (except 0) by zero  is meaningless.

Because division by zero is not defined.

That is, 

2/0  =  Undefined

8/0  =  Undefined

Some Other Properties of Division

We know that division is the inverse operation of multiplication.

Positive number / Positive number  =  Positive number

Negative number / Negative number  =  Positive number

Negative number / Positive number  =  Negative number

Positive number / Negative number  =  Negative number

For example, 

250 / 50  =  5

(-144) / (-12)  =  12

(-120) / 20  =  -6

100 / (-25)  =  -4

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