10.04 Area of rectangles using fractions

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Let's review how to find the area of a rectangle using an array.

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We can use this idea of finding the area of a rectangular array to find the area of rectangles with fractional side lengths.

For example, if a rectangle has side lengths of $2$2 whole units by $3$3 whole units, we can represent it as an array like this:

If instead the rectangle has side lengths of $2$2 thirds by $3$3 fourths, we can still represent it as a $2$2 by $3$3 array - but rather than each small region of the array being one whole square unit, these regions measure $1$1 third by $1$1 fourth:

We can find the area of one small region by multiplying the fractions. Here, the area of one small region is $\frac{1}{3}\times\frac{1}{4}=\frac{1}{12}$13​×14​=112​ square unit.

We can also find how many of these regions are in the whole rectangle in the same way as before: there are $2$2 rows and $3$3 columns, so there are $2\times3=6$2×3=6 regions in total.

Putting this together, the rectangle is made of $6$6 regions that are each $\frac{1}{12}$112​ of a square unit. So the rectangle has an area of $\frac{6}{12}$612​ of a square unit (which is the same as $\frac{1}{2}$12​ of a square unit).

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