Finding Area of Rectangles with Fractional Sides

Lesson Plan - Get It!

Audio:

If you guessed to find the area of the rectangular window, you are correct!

However, this is not just a regular rectangle window. The window has measurements that are mixed numbers. In other words, the measurements include a whole number and a fraction.

Let's sketch a picture of the window and label the measurements of the sides:

To find the area of a rectangle, you will need to multiply the length by the width. This is more complicated when there are fractional measurements.

To make finding the area easier, we will break the rectangle into smaller rectangles. This is called tiling.

First, we need to decompose the mixed numbers.

3 ¼ feet can be decomposed into the whole number 3 and the fraction ¼. These two numbers will make up the lengths of our new rectangles:

Next, decompose 1 ½ and label the new widths of the rectangles:

There are now four rectangles, and it will be easier to find the area of each smaller rectangle.

Let's start with the top left rectangle:

Move to the bottom left:

Remember that when you multiply a fraction by a whole number, you must put the whole number over 1.

Now, find the area of the top right rectangle:

Remember, to multiply fractions, you simply multiply across the top and across the bottom.

Find the area of the last rectangle:

The last step is to add all four areas together to find the area of the whole rectangle:

Remember that when you add fractions, there must be common denominators.

Great! Now we know the area of the whole rectangle is 4 ⁷/₈ feet squared!

You will need 4 ⁷/₈ square feet of glass to fix the broken window!

• Ready to practice on your own?

Visit the Got It? section to find the area of rectangles with fractions as the sides!