Video: AQA GCSE Mathematics Foundation Tier Pack 1 • Paper 1 • Question 13

Recall that 5 miles is approximately equal to 8 kilometres. Use this approximation to convert 22.5 miles to kilometres.

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Video Transcript

Recall that five miles is approximately equal to eight kilometres. Use this approximation to convert 22.5 miles to kilometres.

Let’s consider two methods. We have the ratio five miles to eight kilometres. Using this, we can find out how many kilometres are in 20 miles. We know that five times four equals 20. Five miles times four equals 20 miles. And then we multiply eight kilometres by four. Eight times four equals 32. 20 miles equals 32 kilometres by this approximation.

We found how far 20 miles would be, but we still need another two and a half miles. How can we get from five to two and a half? Well, two and a half is half of five. If we divide five by two, we get two and a half, which means two and a half miles will equal eight divided by two kilometres, four kilometres. 20 plus two and a half miles equals 22 and a half miles, 22.5. And that will be equal to 32 plus four kilometres, 36. Using the given approximation, we can say that 22.5 miles is approximately 36 kilometres.

Let’s look at another method. We could use the bus stop method to divide 22.5 by five. Five goes into two zero times. Five goes into 22 four times. Four times five is 20. So there’s two remaining. Bring up the decimal. Five goes into 25 five times. This tells us that, in 22.5, there are four and a half groups of five. Five times 4.5 equals 22.5. And that means five miles times four and a half equals 22 and a half miles.

We know that five miles is the equivalent of eight kilometres by this approximation. If we multiply five by four and a half to find 22 and a half, we would then multiply eight by four and a half to find the number of kilometres. Eight times four and a half equals 36. Eight times four equals 32, and eight times one-half equals four. Adding those together, and we get 36. The second method confirms that 22.5 miles, using this approximation, is 36 kilometres.

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