Using Arrays to Multiply Fractions | Free Printable

In this article, I will show the procedures of using arrays to multiply fractions. Do you have visual learners? How about learners that love to draw and color?

Every child learns in a different way, yet many times when we think about teaching upper-grade math we only present a concept one way.

It is so easy to teach our children how to solve an expression using a formula, and then move on. But for our artistic and visual learners, we may not be meeting their needs.

Allowing children to explore, draw and color can help children develop a math sense that may not happen while just solving a problem. Using arrays to multiply fractions is a very good way to learn the multiplication of factors.

Today, we will be looking at how you can help your visual learners understand multiplying fractions by teaching our kiddos to draw arrays.

How to Multiply Fractions Using Arrays

Our children will be able to learn using arrays to multiply factors very easily and interactively with the help of this activity. This approach is quite successful.

This method should assist your young champ in learning basic math operations and laying a solid calculating foundation.

a girl standing with a problem of multiply fractions

Step 1: Build the Array

Our first step is to build the array and to do this we must look to our denominators. My first denominator is 1/3, so I know that I need a rectangle with 3 parts. To represent this, I will make the height of my rectangle 3.

representation of one third with a rectangular box

The next denominator is 4, so my width becomes 4.

representation of one fourth with a rectangular box

You can see that I have created a rectangle that is a 3 by 4. You may also notice that the area of this rectangle is 12. And if you are familiar with multiplying fractions, you know that the answer to 1/3 x 1/4 is 1/12.

The area of a rectangle will help our children know what the denominator will be in the answer. And it is a wonderful way for them to understand and see what is happening when we multiply fractions.

Step 2: Color Boxes

Now it is time for a little coloring. We start by coloring in 1/3.

representation of one third

Then we grab a different color and color in 1/4. (Instead of coloring you can use a pencil and create stripes and dots, etc.)

representation of one fourth

Step 3: Get the Product

Finally, we get to solve….. To figure out what the numerator is, we find all the parts of the rectangle that have been colored in with both colors.

In this example, we only have one part of the rectangle that has both green and red. My numerator is one!!! Next, we figure out our denominator. Just like with any fraction, our denominator is how many parts we have to have to make a whole.

In our example, we can see that it takes 12 parts to make the whole rectangle. Therefore, the denominator is 12. The answer to 1/3 x 1/4 = 1/12

representation of multiplying fractions using arrays

What Happens If We have a Two in the Numerator?

I’m glad you asked. Let’s look at the expression 2/3 x 1/2. We will go through the exact steps that we did before.

  1. Create a rectangle that is a 3 by 2.
  2. Now we will color in 2/3 of the rectangle in one color.
  3. Next, we color in 1/2 in a different color.
  4. Once again, we count up how many parts have both colors… this example, our numerator will be 2.
  5. Finally, we finish up figuring out how many parts are in the rectangle… this example our denominator is 6.

So 2/3 x 1/2 = 2/6 or 1/3!!!!

representation of multiplying fractions using arrays whe 2 in the numerator

Practice Time

Once you teach your students how to multiply fractions using arrays, it is always time for a little practice. Prep – Work

I love printables that require little to now prep-work, and these fit the bill.

  1. Simply print them off.
  2. Then gather up pencils and colored pencils and you are ready to go.

Three Levels

The first practice sheets start off simple. The first one focuses on multiplying fractions that only have numerators with the number one. Also on the first two sheets, the rectangle has already been drawn for them.

This allows them to focus on just coloring in the correct parts, and not having to draw. As we move on, the second sheet now has numerators greater than one. The array is once again provided for them. Finally, on the third practice sheet, students get to put it all together.

They will be multiplying fractions with numerators that have just the number one, and some have numbers greater than one. The catch is that on this printable, the students now get to draw their own array!!!

three levels of multiplying fractions

Download Free Printable PDF

Download the following PDF and play with your kiddo with joy.

Math is so much fun when children are building, drawing, and exploring. Enjoy this time of exploring mutliplying fractions with arrays!! If you have any kind of questions or suggestions, feel free to write them down in the comment box.

I hope these activities help you and your children too.

You’ve Got This!

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