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Video: Solving Word Problem Involving Percentages

Tim Burnham

In a family, 21 out of 25 members are female. What percentage of the family are female?


Video Transcript

In a family, twenty-one out of twenty-five members are female. What percentage of the family are female?

Well this question is all about proportion. And we’ve got two common ways of representing proportion. The idea of a fraction represents a proportion, and the idea of a percentage also represents a proportion.

Now in our question, it tells us that twenty-one out of the twenty-five members of the family are female. So the fraction that would be female is twenty-one out of twenty-five, or twenty-one over twenty-five.

So we’ve got to find the equivalent proportion as a percentage. In other word, percentage could be broken down into per and cent. Per means out of, and cent means a hundred. So percentages are a number out of a hundred. So if I can find an equivalent fraction to twenty-one twenty-fifths, where the denominator is a hundred rather than twenty-five, then my numerator will simply be the percentage.

And in this case, that’s relatively easy to do. If I multiply twenty-five by four, I get a hundred. So to create an equivalent fraction, I have to multiply the numerator by four as well. And four times twenty-one is eighty-four. So twenty-one over twenty-five is equivalent to eighty-four over a hundred.

And since percentages are the amount per hundred, we’ve got an answer straightaway, that eighty-four out of a hundred. So the percentage is eighty-four percent.