Multiplying Mixed Numbers by Mixed Numbers | 6 Free Worksheets

These multiplying mixed numbers by mixed numbers worksheets will help to visualize and understand place value and number systems. 5th and 6th-grade students will learn basic multiplication methods with mixed numbers and can improve their basic math skills with our free printable multiplying mixed numbers by mixed numbers worksheets.

Multiplying Mixed Numbers by Mixed Numbers: Basic Idea

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.

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.

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.

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.

3 Fun Ways of Multiplying Mixed Numbers by Mixed Numbers

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 of Arrays to Multiply Mixed Numbers by Mixed Numbers

The first example will describe the use of arrays for multiplying mixed fractions by mixed fractions.

To do the multiplication, 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.

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

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

• 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.

• 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.

• 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 place the proper fraction beside it and show the final result.

Now, solve the following multiplication problem using arrays after understanding the above discussion.

Apply Area Models to Multiply Mixed Numbers by Mixed Numbers

In this method, we will multiply mixed numbers by mixed numbers using the area model. 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.

• 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.

• 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.

• 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.

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

Now, solve the following multiplication problem using area model after understanding the above discussion.

Simple Word Problem on Multiplying Mixed Numbers by Mixed Numbers

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.

Now, solve the following word problems on multiplying mixed numbers by mixed numbers.