Subtraction Involving Mixed Numbers

The great thing about subtracting fractions (Specifically Subtraction Involving Mixed Numbers) is that we have the opportunity to cut up the “wholes” into the number of pieces we need! Fractions can be tough because students see the numbers and don’t always think about the value of the fraction. I like to focus on the denominator and cut up all sorts of things to show that the denominator not only tells us how many parts the whole is cut into, but it also helps tell us the size of the pieces. The larger the denominator, the more pieces you have… and the smaller the piece!

Introduction to Adding and Subtracting with Mixed Numbers

I like to start by talking about sharing. Many times I pose the following scenario to the class:

If you have 1 cookie and you share it with another person, you need to cut it into 2 pieces and you each get ½. But what if you had to share the same cookie with 4 people? What about 5? Or the whole class? How big would your piece be?

See? The more pieces, the smaller the piece!

But the beauty of fractions and subtraction, is that you can divide up items into any number of pieces that you want. You are not restricted by only cutting things in half or into tenths. You can cut it up into the parts that you need in order to subtract

Using Pizza to Teach Adding and Subtracting Fractions

We often use pizza as a food to share and represent fractions. Another circle food that is easy to get and fun to cut are tortillas. So I brought in tortillas to my class and had some pizza cutters (you can even use scissors!). The students could cut up their tortillas and share away!

I noticed that it was hard to subtract fractions on paper, but as soon as they started to see fractions are parts and pieces to share, then they could subtract and understand how much they had left. When it was just numbers, they often forgot that they had to cut up a whole tortilla in order to subtract.

Teaching Addition and Subtraction with Mixed Numbers Using Rice Krispie Treats

Another great way to show subtraction is to use Rice Krispie Treats (it’s also yummy and often allergy friendly!). I have also used cupcake tins and ice cube trays because they are already divided into equal parts. Buying the cupcake tin liners and having fraction scenarios or drawings of circles helps out too, because then they can build a whole with any number for the denominator.

Set up for Subtraction Involving Mixed Numbers Activity

Set up stations with supplies for multiple students. The supplies can be reused
Tortillas (small corn, taco-sized work well) 4-6 for each student
Scissors
9×12 construction paper
4-6 twelve-count or six-count Cupcake tins and a stack of cupcake liners.
Subtraction involving mixed numbers worksheet for every student.
Plastic cups or items to draw circles

Launch the Subtracting Mixed Numbers Activity

Give every one 2 whole tortillas and say: How would you cut these if you had to give away ¼ of a tortilla?

Let them work together and observe. Then ask if they could eat or give away 2/4, or ¾.

What about 1 and ¼?

Now this part gets interesting. Some students cut up the second tortilla; others realize that they can give away 1 whole without cutting it and ¼ of the other. Then other students see that they had to cut them all up into fourths and give away 5 pieces. It’s a great visual to see them work through the possibilities. Have them share the different ways they cut it up and distribute their pieces. You can have them share with partners, small groups or the whole class.

Write an Equation involving Adding and Subtracting Mixed Numbers

Write the equation for each tortilla scenario. Also found on the worksheet.

2 – 1 ¼ = ¾

1 ¼ is the same as 5/4

1= 4/4

4/4 + ¼ = 5/4

You can show this with the tortillas now that they are cut.

2 – 5/4 = ¾

If 1 whole has 4 pieces = 4/4

2 tortillas has 8 pieces = 8/4

8/4 – 5/4 = ¾

Mixed Numbers as Improper Fractions

To help show how to see mixed numbers as improper fractions you can model other denominators too.

You can hold up a tortilla and say “If this whole tortilla is cut into halves, how many halves are there?” 1 whole = 2/2

Then say “If I have 2 whole tortillas and I cut them both into halves, how many halves do I have?” 2 wholes = 2/2 + 2/2 or 4 halves = 4/2

Student Questions About Addition and Subtraction with Mixed Numbers

Use this opportunity for questions and examples about how to convert a mixed number into improper fractions. Remind students that the denominator tells us how many pieces are in a whole. So if you had to model 1 and ⅓ – students know there is 3/3 + ⅓ or 4/3.

Model the subtraction together.

Have the students draw and shade how they cut their tortillas too. Explain that they shade the amount they are giving away and the non-shaded parts are what they have left.

Now introduce the activity. Students will model and show subtraction at various stations:

Station 1 :

Tortillas- halves, fourths, and eighths. Students will have word problems and scenarios about serving tortillas to friends. They will have to cut the tortillas and give away fractions.

Station 2:

Cupcake tins and liners – halves, sixths, twelfths. Students will be given equations and have to take cupcake liners, place them into tins, and model the subtraction.

Station 3:

9×12 construction paper – thirds, sixths, and ninths. Students will have to cut their own construction paper into 3 equal parts. They will be given equations to model with their paper. They will also have to determine how to cut their thirds to make ninths for one problem.

Student Grouping for the Activity

The students will have to follow the instructions on the worksheet, model the subtraction problems, and answer the questions about subtraction involving mixed numbers.

Separate the students into groups at each station. Depending on the size of your class, each station can have enough supplies for 2-3 groups of students. Aim to have 1-3 students working with the materials. They may not have to all cut the pieces, but should each be able to model the problem. Tell them that they will present 1 subtraction problem with a visual model and explain their work to the class at the end of the activity.

Students can use cups to make circles to help them sketch their models on blank paper to use during their presentation to the class.

Subtraction Involving Mixed Numbers Reflection

Walk around and ask the students questions about the size of the pieces or the number of pieces. You can also ask if there is more than one way to show the subtraction.

Stop the station work with enough time for students to share and make presentations for each station. You can assign a problem to each student or group, or you can let them choose a model to draw and demonstrate at the end of class.

Each student or group can show and present their models as well as explain what they did to show subtraction. Each presentation only needs to be 1-2 minutes long and then you can begin a discussion.

Ask Questions Like:

Which station has the smallest pieces?
Did you ever have an answer with 1-half when the subtraction problem had a different fraction in it?
Do you always have to cut it up into pieces?
How many pieces is a whole tortilla if you are subtracting eighths?
How many cupcake liners are equal to half of the tin?
Model the following equation: 3 ¼ – ¾
What is the equation for the following model?

Extensions with Adding and Subtracting Mixed Numbers

Students can make their own pizza, quesadillas, brownies, or Rice Krispie treats and take photos or make a video to show subtraction involving mixed numbers. They must model it and write the equation.
Pizza restaurant – create a menu for serving slices from a whole pizza. Students can “sell” pizza by the slice. They should have different size slices.

For example: Have pizzas cut into 4th, 8ths, and 16ths. If they have 5 pizzas sliced into 1/4s, 4 pizzas cut into 8ths, and 3 pizzas cut into 16ths, and they sell 20 slices of each size, how many slices do they have left of each?

Pizza by the slice!

Choose a size:

- Large slice = ¼ , fourths
- Medium slice = ⅛ , eighths,
- Small slice = 1/16 sixteenths

Students can show subtraction of mixed numbers using measuring cups. Pour 2 and ½ cups of water or lemonade into a pitcher. If you pour out ¾ of a cup, how much water is left?
Explore online fraction strips: https://toytheater.com/fraction-strips/

FREE Subtraction Involving Mixed Numbers Worksheets and Resources

These are all PDF Files. They will open and print easily. The Student Edition Files are labeled SE and the Teacher Editions Files are labeled TE. Click the links below to download the different resources.

5-7 Assignment SE – Subtraction Involving Mixed Numbers (PDF)
5-7 Assignment TE – Subtraction Involving Mixed Numbers (Members Only)
5-7 Bell Work SE – Subtraction Involving Mixed Numbers (PDF)
5-7 Bell Work TE – Subtraction Involving Mixed Numbers (Members Only)
5-7 Exit Quiz SE – Subtraction Involving Mixed Numbers (PDF)
5-7 Exit Quiz TE – Subtraction Involving Mixed Numbers (Members Only)
5-7 Guided Notes SE – Subtraction Involving Mixed Numbers (PDF)
5-7 Guided Notes TE – Subtraction Involving Mixed Numbers (Members Only)
5-7 Interactive Notebook – Subtraction Involving Mixed Numbers (Members Only)
5-7 Lesson Plan – Subtraction Involving Mixed Numbers (PDF)
5-7 Online Activities – Subtraction Involving Mixed Numbers (PDF)
5-7 Slide Show – Subtraction Involving Mixed Numbers (PDF)

Subtraction Involving Mixed Numbers Worksheets and Resources

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5-7 Assignment SE – Subtraction Involving Mixed Numbers (Doc – Members Only)
5-7 Assignment TE – Subtraction Involving Mixed Numbers (Doc – Members Only)
5-7 Bell Work SE – Subtraction Involving Mixed Numbers (Doc – Members Only)
5-7 Bell Work TE – Subtraction Involving Mixed Numbers (Doc – Members Only)
5-7 Exit Quiz SE – Subtraction Involving Mixed Numbers (Doc – Members Only)
5-7 Exit Quiz TE – Subtraction Involving Mixed Numbers (Doc – Members Only)
5-7 Guided Notes SE – Subtraction Involving Mixed Numbers (Doc – Members Only)
5-7 Guided Notes TE – Subtraction Involving Mixed Numbers (Doc – Members Only)
5-7 Interactive Notebook – Subtraction Involving Mixed Numbers (Doc – Members Only)
5-7 Lesson Plan – Subtraction Involving Mixed Numbers (Doc – Members Only)
5-7 Online Activities – Subtraction Involving Mixed Numbers (Doc – Members Only)
5-7 Slide Show – Subtraction Involving Mixed Numbers (PPT – Members Only)