# Dividing Fractions

## How can you divide fractions?

Dividing fractions is explained with several examples. When dividing a fraction by a fraction you can multiply it by the reciprocal. Exchange the division sign for a multiplication sign and flip the numerator and the denominator of the second fraction.
Three examples are discussed
- Dividing a fraction by a cardinal number
- Dividing a fraction by a fraction
- Dividing a mixed fraction by a fraction

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### Exercise 1:

Number of questions:

Time per question:

In this exercise you get all kinds of divisions.
Look at the examples if you don't know the answer.

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### Example 1

#### Dividing a fraction by a cardinal number.

67 ÷ 3.

Divisions can be solved in two ways. Dividing the numerator by the numerator and the denominator by the denominator or multiplying by the reciprocal. In this case division is easier than multiplication with the reciprocal.
We first change the cardinal number into a fraction.

3 = 31.

We then get the following sum:

67 ÷ 31 =

Divide numerator by numerator and denominator by denominator:
6 ÷ 3 = 2 and 7 ÷ 1 = 7

67 ÷ 31 = 27

### Example 2

#### Dividing a fraction by a fraction

12 ÷ 34= We solve this sum by multiplying by the reciprocal.

We need to flip 34. That becomes 43.

The sum now becomes:

12 x 43=

1 x 4 = 4 and 2 x 3 = 6

12 x 43=46.

We can also simplify this answer. We then get:

46=23.

### Example 3

#### Dividing a mixed fraction by a fraction

212 ÷ 14=

We also solve this sum with the rule: Dividing by a fraction is multiplying by the reciprocal. First 212 needs to be written as a fraction.

That's: 212 =52 Now we can solve the sum just like in example 2.

52 x 41=202

We need to simplify 202. That becomes 101 and that's the same as 10