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10.04 Area of rectangles using fractions

Lesson

Are you ready?

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

What is the area of the rectangle?

  1. $\editable{}$ unit squares

Learn

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).

Apply

Question

We are going to find the area of a rectangle which measures $\frac{3}{8}$38 unit by $\frac{2}{5}$25 unit.

  1. Which of these rectangles measures $\frac{3}{8}$38 unit by $\frac{2}{5}$25 unit?

    A

    B

    C

    D
  2. One region of the rectangle is shaded:

    What is the area of this region?

    $\frac{\editable{}}{\editable{}}$ unit2

  3. How many of these regions make up the whole rectangle?

  4. What is the total area of the rectangle?

Remember!

The area of a rectangle with fractional side lengths can still be found using an array, where

  • the denominators tell us the size of the small regions
  • the numerators tell us how many regions there are

Outcomes

5.NF.4.b

Find the area of a rectangle with fractional side lengths by tiling it with unit squares of the appropriate unit fraction side lengths, and show that the area is the same as would be found by multiplying the side lengths. Multiply fractional side lengths to find areas of rectangles, and represent fraction products as rectangular areas.

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