# Fractions - Multiplication and Division

### Concept

- Fractions can be multiplied and divided just like whole numbers.

### Theory

#### Multiplying fractions

Multiplication is simply addition done as many times as the number you need to multiply with. So if 2 x 4 = 2 + 2 +2 + 2, the same rules apply to fractions too.

1/2 x 4 = 1/2 + 1/2 + 1/2 + 1/2 = 2.

But what about if you have to multiply 1/3 x 12. That’s a lot of circles to draw. And what about multiplying 1/3 x 4/5.

A simple rule to multiply fractions:

- Multiply the numerators = new numerator
- Multiply the denominators = new denominator
- numerator / denominator = result.

In pictures ![[/concepts/attachments/fraction-multiplications.png]]

Sometimes you may not have a denominator - for example when you are multiplying by a whole number. But wait, you do - the denominator is 1. Because 4 is the same as 4/1.

#### Dividing fractions

To understand division you have to understand the concept of a reciprocal. The reciprocal of a/b is b/a. Flip the numerator and denominator and you have the reciprocal.

Let’s now use this concept to perform the following fraction division problem.

1/3 divided by 2 => 1/3 multiplied by 1/2 (reciprocal of 2/1) => 1/6 (answer)

So to divide fractions, you convert it to a multiplication problem and use the steps to multiply as before.

### Common Misconceptions

- When multiplying a fraction, say 3/4 times 2, the learner might multiply both numerator and denominator by 2.
- Not remembering that 2 is the same as 2/1.