Video: AQA GCSE Mathematics Higher Tier Pack 3 • Paper 3 • Question 2

Circle the fraction which is equivalent to 43.75%. [A] 3/8 [B] 7/16 [C] 1/4 [D] 3/7.

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Video Transcript

Circle the fraction which is equivalent to 43.75 percent. The options are three-eighths, seven sixteenths, one-quarter, or three-sevenths.

To answer this question, we need to convert all of the numbers to a common form. And in this case, it’s going to be easiest to convert them all to decimals. Let’s begin with 43.75 percent. Percent literally means out of 100. So 43.75 percent means 43.75 out of 100. We can express this as a fraction; it’s 43.75 over 100.

Now remember, we want to compare this to the other numbers, all of which are fractions. But, it isn’t going to be easy to do this as some of the fractions have denominators which are not factors of 100. So this is why we’re going to convert them all to decimals. Remember that the horizontal line between the numerator and denominator in a fraction means divide. So this means 43.75 divided by 100 which is 0.4375.

We do have a calculator to help with this but in a non-calculator exam, we could just remember that the decimal point would stay fixed and all of the digits move two places to the right when dividing by 100. So we’ve worked out what 43.75 percent is equal to as a decimal. Let’s look back at the other fractions.

We can eliminate some of the possibilities straightaway. Perhaps, you know that one-quarter is equal to 0.25 as a decimal or 25 percent. So one-quarter is not equivalent to 43.75 percent. You may also know that the fraction three-eighths is equivalent to 0.375 as a decimal. So we can also eliminate three-eighths. But, if you didn’t know this, you could work it out by dividing three by eight on your calculator.

Let’s look at the final two possibilities for which you probably don’t know the decimal equivalents of by heart. To work these out, we need to divide each numerator by the denominator. So that’s seven divided by 16 and three divided by seven. Seven divided by 16 is 0.4375. And three divided by seven is 0.428571 recurring. The dots over the first and last digits after the decimal point indicates that all six digits recur. So of the four options, the only fraction which is equivalent to 0.4375, and therefore 43.75 percent, is seven sixteenths.

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