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## Working with numbers The value of a fraction is unaltered if both numerator and denominator are multiplied by the same number. ### Multiplication of fractions To multiply fractions, multiply the numerators together and multiply the denominators together. Any mixed numbers must be changed into i...

## Working with numbers The value of a fraction is unaltered if both numerator and denominator are multiplied by the same number. ### Multiplication of fractions To multiply fractions, multiply the numerators together and multiply the denominators together. Any mixed numbers must be changed into improper fractions, and factors that are common to the numerator and denominator should be cancelled before multiplication. ### Reciprocals If the product of two numbers is 1, then each number is called the *reciprocal* of the other. We know that 1/3 x 3 = 1 so 1/3 is the reciprocal of 3 and 3 is the reciprocal of 1/3. To find the reciprocal of 3/4 we require the number which when multiplied by 3/4 gives 1. Now 4/3 x 3/4 = 1 so 4/3 is the reciprocal of 3/4. In all cases the reciprocal of a fraction is obtained by turning the fraction upside down. A number can be written as a fraction, for example, 3= 3/1 and 2.5 = 2.5/1 so the reciprocal of 3/1 is 1/3 or 1÷3 and the reciprocal of 2.5/1 is 1/2.5 or 1÷2.5 (=0.4). The reciprocal of a number is 1 divided by that number. ### Division by a fraction Consider 2/5 ÷ 3/7. This can be interpreted as 2/5 x 1 ÷ 3/7. Now 1 ÷ 3/7 is the reciprocal of 3/7, i.e. 7/3. Therefore 2/5 ÷ 3/7 = 2/5 x 7/3 = 14/15. To divide by a fraction we multiply by its reciprocal. ## Exercise 2b Write down the reciprocals of the following numbers. | Number | Reciprocal | | ----------- | ----------- | | 1 | 4 | | 2 1/2 | 2/5 | | 3 2/5 | 5/17 | | 4 | 1/10 | | 5 1/8 | 8/41 | | 6 3/11 | 11/69 | | 7 | 1/100 | | 8 2/9 | 9/74 | | 9 15/4 | 4/51 | | 10 | 0.25 | | 11 | 3.2 | | 12 | 1.6 |