Adding and Subtracting Mixed Numbers

Contributor: Erika Wargo. Lesson ID: 12800

Can you write your own mixed-numbers problems? If mixed numbers are a problem for you, learn how to deal with those crazy whole numbers and fractions, even improper ones, then write your own problems!


Arithmetic, Fractions and Operations

learning style
personality style
Grade Level
Middle School (6-8)
Lesson Type
Quick Query

Lesson Plan - Get It!


Sarah and Devoin are summer camp counselors. They are making trail mix for all their campers.

They need help figuring out how many pounds of trail mix each of their recipes will make. They also want to find out which of their recipes are better - because one has more chocolate!

Before we start making trail mix, let's review what a mixed number even is in the first place!

A mixed number is a number made of a whole number and a fraction. The value of a mixed number will always be greater than one.

Now we are ready to make trail mix!

Sarah's recipe is pretty simple. She will need 4 1/5 pounds of peanuts and 3 2/3 pounds of chocolate chips.

  • How many pounds of trail mix will Sarah's recipe make?

We know that we need to add the two ingredients to find the total amount of trail mix.

  • But how do we add mixed numbers?

Just like regular fractions, you can only add or subtract with common denominators.

Notice in this problem the fractions DO NOT have common denominators:

equation 1

We will have to find common denominators before we can add.

If you need to review finding common denominators and adding fractions, visit our lesson found under Additional Resources in the right-hand sidebar.

When adding or subtracting mixed numbers with this strategy, the whole number does not change. You will just multiply the top and the bottom of each fraction by a number that will give you common denominators:

equation 2

Next, you will add the fractions with the like denominators. Then, you will add the whole numbers together:

equation 3

Once you have an answer, double check if the fraction is not an improper fraction or needs to be simplified:

equation 4

So Sarah's recipe will make 7 13/15 pounds of trail mix in total.


Now, let's look at Devoin's recipe. His recipe calls for 5 3/4 pounds of chocolate chips.

  • How many more pounds of chocolate are in Devoin's trail mix than in Sarah's?

For this problem, we will subtract 5 3/4 and 3 2/3 to find the difference in chocolate chips.

We will solve this subtraction problem the same way as the addition problem - making sure the fractions share common denominators!

equation 5

After you find common denominators, you will first subtract the fractions and then the whole numbers.

Devoin's trail mix has 2 1/12 more pounds of chocolate chips than Sarah's recipe.

Good job! Next let's look at another strategy to solve mixed number problems!

In total, Devoin and Sarah made 11 1/3 pounds of trail mix. The campers ate 9 5/6 pounds of the trail mix.

  • How much is leftover?

We are going to start this problem the same way.

equation 5

  • Do you notice anything different?
  • Anything that will make this problem difficult?

You cannot subtract 2/6 - 5/6 . You will have to regroup!

equation 7

You will borrow one whole from the 11 and add it back into the fraction. 1 whole is equal to 6/6 which will now make the improper fraction 8/6.

Now, you can subtract 8/6 - 5/6.

Notice the fraction in the answer is not in simplest form.

Reduced, the answer is 1 ½.

Sarah and Devoin have 1 ½ pounds of trail mix leftover.

We will make our own trail mix in the Go! section. But first, click NEXT to practice adding and subtracting mixed numbers in the Got It? section.

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