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Video: Expressing a Given Percentage as a Fraction in Its Simplest Form

Tim Burnham

Convert 32% into a fraction giving your answer in simplest form.

02:23

Video Transcript

Convert thirty-two percent into a fraction, giving your answer in its simplest form.

Now percentages and fractions are both ways of expressing the idea of a proportion. For example, if you imagine a nice chocolate cake, you might like to think what share of that cake would I get if we shared it out amongst our friends. Will I get the whole cake, so that’s one hundred percent of the cake, or just half the cake, fifty percent of the cake? Maybe only a quarter of the cake, twenty-five percent, or maybe only an eighth of the cake, or twelve and half percent.

So you can see that there are percentages and fractions which represent the same proportion, and that’s what we’ve gotta find here, the fraction which represents the same proportion as thirty-two percent.

Now the word percent can be split up into two. Per means out of, and cent means a hundred. So when we’re given a fraction like thirty-two percent, we can represent it as a fraction out of a hundred.

So thirty-two percent as a percentage represents the same proportion as thirty-two over a hundred as a fraction. Well that’s done the first part of the question. We’ve got thirty-two percent into its equivalent fraction. Now we’ve got to give our answer in its simplest form, so can we simplify this fraction by doing any cancelling down?

Well thirty-two and a hundred are both divisible by two. Thirty-two divided by two is sixteen and a hundred divided by two is fifty, so thirty-two over a hundred is equivalent to sixteen over fifty. But wait, sixteen and fifty, they’re both divisible by two as well.

So sixteen over fifty was a simpler form than thirty-two over a hundred, but it wasn’t its simplest form because sixteen and fifty have a common factor of two. Sixteen divided by two is eight and fifty divided by two is twenty-five.

Now eight and twenty-five don’t have any common factors bigger than one, so I can’t simplify that fraction any further. So my answer is eight twenty-fifths.