# Video: AQA GCSE Mathematics Higher Tier Pack 1 β’ Paper 3 β’ Question 21

AQA GCSE Mathematics Higher Tier Pack 1 β’ Paper 3 β’ Question 21

02:23

### Video Transcript

π to π equals three to eight and six π equals 11π. Work out π to π in its simplest form.

Weβll just bring down π to π, but we need to recognize what the ratio of π to π would be. If six times π equals 11 times π, whatβs the ratio between π and π? Itβs 11 to six. We know that six times π equals 11 times π. If we divide both sides of this equation by π, weβll get six π over π equals 11.

From there, we divide both sides of the equation by six. On the left, we have π over π and on the right 11 divided by six or, written as fraction, eleven sixths. The ratio of π to π equals 11 to six. Letβs look closer at these two ratios.

In one of them, our π-value is eight, and in the other, our π-value is 11. We want these two values to be the same. In our π-to-π relationship, we can multiply both sides by 11, which will result in the relationship being 33 to 88. In our second relationship, weβll multiply both values by eight. 11 times eight equals 88, and six times eight equals 48. The relationship of π to π could be said to be 88 to 48.

Now that we have equal π-values, we can say π to π to π equals 33 to 88 to 48. And that means π to π equals 33 to 48. Weβre looking for the relationship of π to π in its simplest form. Both 33 and 48 are divisible by three. 33 divided by three equals 11, and 48 divided by three equals 16. The relationship of π to π in its simplest form equals 11 to 16.