Video: Solving Word Problems by Dividing a Fraction by a Whole Number

A parking lot that is 1/4 of an acre is to be divided into 9 equally sized areas. Determine the size of each area.

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Video Transcript

A parking lot that is one-quarter of an acre is to be divided into nine equally sized areas. Determine the size of each area.

So the total size of this parking lot is one- quarter of an acre, and we’re dividing it into nine equal parts. The calculation we need to perform then is one-quarter divided by nine. We’re, therefore, being asked to find the result of a fraction divided by an integer. Let’s think about how we do this.

First, we can express the integer nine as a fraction. It’s equal to nine over one. We have a standard rule for dividing by a fraction; it is that to divide by a fraction, we multiply by its reciprocal. The reciprocal is the fraction formed when we swap the places of the numerator and denominator around.

The reciprocal of nine over one is one over nine. So the calculation becomes one-quarter multiplied by one-ninth. Multiplying fractions together is much more straightforward. We multiply the numerators together, and we multiply the denominators, giving one multiplied by one over four multiplied by nine.

There is no canceling to be done, as none of the numbers in the numerator have common factors with numbers in the denominator. One multiplied by one is one, and four multiplied by nine is 36. Therefore, the size of each area of the parking lot is one over 36 or one thirty-sixth of an acre.

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