Finding Area of Rectangles with Fractional Sides

Contributor: Ashley Nail. Lesson ID: 13408

Finding the area of a rectangle is easy! But what about a rectangle with measurements in fractions? Learn how to decompose mixed numbers, multiply fractions, and find area.

categories

Arithmetic, Geometry, Geometry

subject
Math
learning style
Kinesthetic, Visual
personality style
Lion, Otter, Beaver, Golden Retriever
Grade Level
Intermediate (3-5)
Lesson Type
Quick Query

Lesson Plan - Get It!

Audio:

Imagine you and your friends are playing baseball. You hit a home run! But you don't get to celebrate for very long - you broke the glass in your neighbor's window!

broken window

You now need to replace the glass in this window. Let's figure out how much glass you will need to buy in order to fix the window.

You take exact measurements of the rectangular window.

One side is 3 ¼ feet and the other is 1 ½ feet.

  • How can you figure out the exact amount of glass you will need to replace the window?

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:

diagram 1

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:

diagram 2

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

diagram 3

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:

diagram 4

Move to the bottom left:

diagram 5

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:

diagram 6

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

Find the area of the last rectangle:

diagram 7

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.

diagram 8

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!

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