Dividing Fractions

Dividing Fractions Video:

Dividing a WHOLE number by a Fraction

When dividing by fractions it's helpful to remember what division means. If we divide by it's like asking how many groups of cookies would there be.

You can see that 1 cookie divided by (1/3 or 1 divided by 1/3 ) = 3. There are 3 (groups of) thirds.

If all 12 cookies were divided into 1/3 how many thirds would there be?

12 divided by 1/3

Besides a lot of cookie crumbs, you can see that there would be 36 thirds. By dividing the cookies up you end up with way more parts. So 12 divided by 1/3 would equal 36.

Remember that dividing a whole number by a fraction results in a much larger number because you are finding how many fraction parts there are.

Example

Jeremiah had 6 meters of ribbon and needed of a meter to tie around each parcel. How many parcels could he tie?

Solution

The question is asking 'how many 2/3 are there in 6?' We could find this by drawing a line to represent the 6 meters, then dividing it into meter pieces.

Begin by drawing a number line to represent the 6 meters. Then mark off the sections that would represent 2/3 of a meter.

The result is that there are 9 pieces of 2/3 of a meter in 6 meters.

6 divided by 2/3 = 9

If you look at the above example you'll see that because dividing and multiplying are opposite operations, dividing is the same as multiplying by the reciprocal of a number. You can change a division question into a multiplication question by changing the divisor into its reciprocal.

Reciprocals are two numbers that when multiplied together equal 1.

3 and 1/3 are reciprocals because

6 and 1/6 are reciprocals

2/7 and 7/2 are reciprocals.

So another way of looking at dividing by fractions is to change it into a multiplication question by using the reciprocal.

Dividing a Fraction by a Fraction

There are 3 Simple Steps to Divide Fractions:

Step 1. Turn the second fraction (the one you want to divide by) upside down

(this is now a reciprocal).

Step 2. Multiply the first fraction by that reciprocal

Step 3. Simplify the fraction (if needed)

Example:

1/2 ÷ 1/6

Step 1. Turn the second fraction upside down (it becomes a reciprocal):

1/6 becomes 6/1

Step 2. Multiply the first fraction by that reciprocal:

(multiply tops ...)

1/2 × 6/1 = 1 × 6/2 × 1 = 6/2

(... multiply bottoms)

Step 3. Simplify the fraction:

6/2 = 3