Dividing Fractions by Whole Numbers

Mathematical Approach

 

1)      Treat the whole number as a fraction. In other words write the whole number over a denominator 1. For example if we have the whole number 2, we rewrite as (2/1). Note that when we divide fractions by whole numbers, the divisor is the whole number while the dividend is the fraction.

2)      Multiply the dividend by the reciprocal of the divisor.

Let us take a look at the previous examples mentioned above. We have (6/11) ÷2. Now we will utilize the rules given in the mathematical approach. We rewrite (6/11) ÷2 as (6/11) ÷ (2/1). Now multiply (6/11) by the reciprocal of (2/1). Hence, we have (6/11) × (1/2). This equals (6/22) which reduces to (3/11).

 

Try this example:

(8/15) ÷4

 

Answer: (8/15) ÷4=(8/15) ÷(4/1)=(8/15)×(1/4)=(8/60)=(2/15).

 

Now let us take a conceptual approach. 

 

Sharing Divisions (Conceptual Approach)

Let us start with sharing divisions. Moreover, let us examine sharing divisions that divide evenly. For example, suppose our dividend is (6/11) and our divisor is 2. Hence, this is (6/11) ÷ 2. This can be visualized as two people sharing (6/11) of a pizza pie evenly. We wish to determine how much of that pizza pie does each person receive.  Therefore, (6/11) ÷2 yields to (3/7) because each person receives 3 slices. Suppose our dividend of (6/11) is divided by 3. This can be visualized as 3 people sharing a pizza evenly. We wish to determine how much of that pizza pie each person receives. Therefore, (6/11) ÷3 yields to (2/11).