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Multiplying Mixed Numbers by Mixed Numbers | Free Worksheet


Multiplication is a fun thing to do. As we all know, multiplication is the advanced form of addition. It’s much easier to do multiplication than big addition problems.

When the term mixed numbers is used with multiplication, almost all the students will not have the same fun as with simple multiplication. Take no worry. Show some spirit.

Because in the following section, we will cover some interesting ways of multiplying mixed numbers by mixed numbers. Let’s Start.

Multiplying Mixed Numbers by Mixed Numbers: Basic Idea

When we are talking about mixed numbers, the names of their components come first. Basically, a mixed number is formed by two things, a whole number and a proper fraction.

Explaining Mixed Number

At this point, there may be a question inside you all. When is the term mixed numbers used? Or when do we need to work with mixed numbers?

A mixed number or mixed fraction is related to an improper fraction. When the denominator of a fraction is smaller than the numerator, it is called an improper fraction.

We cannot directly add, multiply, subtract, or divide a mixed number from another. For that, you have to convert it into an improper fraction.

Showing the Process to Convert Mixed Number to A Improper Fraction

Now comes the multiplication part. As you are thinking, the multiplication of mixed numbers by mixed numbers is not that difficult. To do the multiplication, you have to follow some simple steps.

  • Convert both mixed numbers into improper fractions.
  • Divide the numerators and denominators of both fractions by their common factors.
  • After completing the division process, do as usual multiplication of fractions.
  • If the final result is again an improper fraction then, rewrite it as a mixed number.

Full Details of Multiplying mixed numbers by mixed numbers

3 Fun Ways of Multiplying Mixed Numbers by Mixed Numbers

Thank you all for your patience up until now. We are now marching toward our main procedure. In the following section, you will find three fun ways of multiplying mixed numbers by mixed numbers for understanding.

Also, at the end of the article, you will find our free printable worksheets to practice more. Then, why lag behind? Let’s start our journey.

Use Arrays

The first example will describe the use of arrays for multiplying mixed fractions by mixed fractions. How are we gonna do that?

Just follow the simple steps given below.

  • First of all, after getting the problem, make a square and divide it into 4 fields.
  • Then, distribute the whole number and the proper fraction around the square like in the following image.

Using Area Model to Multiply Mixed Numbers by Mixed Numbers

  • Now, it’s time for multiplication. See the direction of the arrows in the below-given image.
  • Follow the arrows to multiply the numbers.

Showing the Direction of Multiplication

  • After multiplications, place the result in their respective fields.

Writing Result of Each Multiplication

  • Then, take each of the multiplication results and then, add them to get the final result.
  • Here, notice how the addition is done.
  • If any of the multiplication results are whole numbers then add them directly, or keep it the same if there is one whole number.

Adding All the Multiplication Result

  • Then, add all the fractions by making their denominators the same. Notice, if the resultant fraction becomes an improper fraction or not.
  • If it is a proper fraction then no need to proceed further, you have got your result.
  • But if the resultant fraction is an improper one, then again turn it into a mixed number.

Showing Final Result of Using Arrays for Multiplying mixed numbers by mixed numbers

  • After converting into the mixed number, you will find one whole number and a proper fraction.
  • Add the newly found whole number to the previous whole number from the addition result and place the proper fraction beside it.

Tada! Take a breath of relief, and you are done.

Apply Area Models

Another fun way to multiply mixed numbers by mixed numbers is the area model. The term may be new to you.

In this procedure, you need to do the multiplication with the help of an area model. Let’s look at the following steps for more details.

  • Firstly, after getting the mixed numbers, draw a square and make horizontal and vertical lines that are more than one from each whole number of the mixed fractions.
  • For example, if you have 3 and 5 as the two whole numbers then, you have to make 4 horizontal spaces and 6 vertical spaces or vice versa in the square.

Apply Area Model for Multiplying mixed numbers by mixed numbers

  • It’s time for multiplication. Multiply the following arrow direction and color the consecutive area.
  • First, we are going to color the area represented by the multiplication of the whole number by the whole number. For our example it is 2 x 3 so, we will color a total of 6 fields.

Multiplying Whole Number by Whole Number and Coloring the Specific Region

  • Then, start to multiply the whole numbers with each of the fractions. Multiply the fraction that is 2 by 3 and multiply the fraction with 3 by 2.
  • As we are multiplying 1/2 by 3, we will color three fields in the same row each equal to 1/2  in the respective fields.
  • Again the second multiplication is 2/3 by 2 so, we will color four fields each equal to 1/3.

Multiplying Whole Numbers by Fractions and Coloring the Specific Region

  • Here comes the difficult part, the multiplication between two fractions.
  • Multiply 1/2 by 2/3 and as the result is 1/3, color the same amount of fields.

Multiplying Fraction by Fraction and Coloring the Specific Region

  • After all the multiplication, add all the resultants like the following image and therefore get the final result.

Adding All the Multiplication Result ans Showing Final Result

Simple Word Problem

All the previous two examples contain direct mixed number problems. But this time we want to provide you with multiplying mixed numbers by mixed numbers word problems. See the following image. Read the question attentively. Find the mixed numbers and do the multiplication as per the previous two methods. Show the result and earn your victory treat.

Demonstrating Way of Multiplying Mixed Numbers by Mixed Numbers through Word Problems

Download Free Printable PDF

In the above discussion, I have discussed some fun ways of multiplying mixed numbers by mixed numbers. These examples will help your students enhance their skills regarding these types of multiplication of mixed numbers problems.

The free missing multiplying mixed numbers by mixed numbers pdf is available for download below. You can download this practice sheet by clicking on the download button and printing it from your device.


Please feel free to give any feedback regarding this article. Also, if your little one is having trouble doing these activities, let us know in the comment section.



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