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# Fractions

## Multiplication

Imagine for a moment that you have some leftover pie. This bit is 5/12 of the original pie. Now we want just 2/5 of the leftovers for a yummy snack. To work out how much pie we get we need to find out what 2/5 of 5/12 is, we need to multiply the fractions.

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2/5 × 5/12 = (2×5)/(5×12) = 10/60 = 2/12 = 1/6

To multiply two fractions we simply multiply their numerators and multiply their denominators, reducing the answer if possible:

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The answer is called the product of the two fractions.

### Example

Click on the question marks to see an example of multiplication of fractions shown step-by-step.

Now study a few more examples of multiplying two fractions.

 × × = = = ×

### Exercise

Now practise solving a few exercises on your own. Remember to reduce the answer if possible.

 Working space Answer × × = = = ×

Imagine that you have several pies with the same amount leftover from each. We can calculate the amount of pie left by multiplying the amount remaining by the number of pies.

3 × = =

3 × 5/12 = 3/1 × 5/12 = 15/12 = 5/4

To multiply an integer by a fraction, first write the integer as a fraction and then multiply as usual.

### Example

Click on the question marks below to see the example worked out step-by-step.

or simply

### Exercise

Practice with some of these exercises:

## Multiplication of signed fractions

Just as for all operations, the same basic methods apply to signed fractions. The only extra complication is that we must remember to deal with the sign. Decide the sign first before you multiply so you don't forget.

Signs of numbers after multiplication

×

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### Exercise

Now try some exercises. Remember to reduce the fractions if possible.

 Working space Answer × = =