Key Concepts
- Using models to add mixed numbers
- Adding mixed numbers
Introduction
In this chapter, we will learn about adding mixed numbers using models.
Example 1:
You and your friend went to a pizza shop. You ate 1 pizza, and your friend ate 1/2 pizza. It means you and your friend ate 3/2 pizza in total.
3/2 is equal to 1 1/2.
![one and half pizza](https://www.turito.com/learn-internal/wp-content/uploads/2022/09/e27503a6-5826-4ba6-95eb-9761dae6ca73.png)
If you observe the above example, 3/2 is called fraction and 1 1/2 is called mixed number.
Using Models to Adding Mixed Numbers
Example 1:
Mary worked 2 3/4 hours on Monday and 1 1/2 hours on Tuesday. How many hours did she work in all on Monday and Tuesday?
Solution:
Step 1:
Add the fractional parts first.
To do this, we need to rename the fractional parts as equivalent fractions with a like denominator.
![adding mixed numbers](https://www.turito.com/learn-internal/wp-content/uploads/2022/09/image-7361-945x1024.png)
3/4 + 2/4 = 5/4
![1/4](https://www.turito.com/learn-internal/wp-content/uploads/2022/09/89af5f68-b696-4e9c-b914-e93b2d0aad5c-1024x92.png)
Rename 5/4 as 1 1/4.
![Rename 5/4 as 1 1/4](https://www.turito.com/learn-internal/wp-content/uploads/2022/09/image-7359-1024x95.png)
Step 2:
Add the whole number parts.
![Add the whole number parts.](https://www.turito.com/learn-internal/wp-content/uploads/2022/09/image-7360-984x1024.png)
2 + 1 = 3
Then add the sum of the functional parts.
3 + 1 1/4 = 4 1/4
So, 2 3/4 + 1 1/2 = 4 1/4
The total number of hours worked in all on Monday and Tuesday is 4 1/4
Adding Mixed Numbers
Example 1:
Joaquin used two types of flours in a muffin recipe. How much flour did he use in all? Solve it in any way you choose.
![muffins](https://www.turito.com/learn-internal/wp-content/uploads/2022/09/image-7362.png)
Solution:
Step 1:
From the given ingredients, we can understand that Joaquin used 1 1/2 c of whole wheat flour and 4 2/3 c of buckwheat flour.
So, we need to add 1 1/2 and 4 2/3 to find the total flour used.
Write equivalent fractions with a common denominator.
1 1/2 = 1 3/6
4 2/3 = 4 4/6
Step 2:
Add the fractions.
![1/6](https://www.turito.com/learn-internal/wp-content/uploads/2022/09/image-7363-1024x539.png)
Step 3:
Add the whole numbers.
1 1/2 = 1 3/6
![11111](https://www.turito.com/learn-internal/wp-content/uploads/2022/09/f9652b4e-ce22-4969-95e2-b784693a9b16-1024x535.png)
4 2/3 = 4 4/6
![1/6](https://www.turito.com/learn-internal/wp-content/uploads/2022/09/dd667c93-02b8-4c79-b0c0-62f7a591967d-1024x149.png)
___________
5 7/6
Rewrite
7/6 as a mixed number.
5 7/6 = 5 + 1 1/6 = 6 1/6
The total flour used by Joaquin was 6 1/6c.
Example 2:
Arnie has 1 1/2 apple pies with him. Louise has 2 1/3 apple pies with her. They mixed their apple pies together. They are wondering about the total apple pies they have with them. Solve it in any way you choose.
![apple pies](https://www.turito.com/learn-internal/wp-content/uploads/2022/09/image-7366-1024x263.png)
Solution:
Step 1:
Add 1 1/2 and 2 1/3 to find the total apple pies.
Write equivalent fractions with a common denominator.
1 1/2 = 1 3/6
2 1/3 = 2 2/6
Step 2:
Add the fractions.
![1/6](https://www.turito.com/learn-internal/wp-content/uploads/2022/09/5da64b52-fbeb-4317-80e2-ff9de099c887.png)
1 1/2 = 1 3/6
2 1/3 = 2 2/6
_____________
5/6
Step 3:
Add the whole numbers.
1 1/2 = 1 3/6
![111](https://www.turito.com/learn-internal/wp-content/uploads/2022/09/587cb8d7-1c4a-488f-8e8a-1619f44c91c0.png)
2 1/3 = 2 2/6
![1/6](https://www.turito.com/learn-internal/wp-content/uploads/2022/09/98120136-129f-4d6c-b7f0-00bdacca30a0.png)
_____________
3 5/6
The total apple pies are 3 5/6
Exercise
- Use fraction strips and find the sum.
- 2 1/10 + 1 3/5
- 4 3/5 + 3 7/10
- Use fraction strips and find the sum.
- 1 7/8 + 5 1/4
- 3 2/5 +1 9/10
- Lindsey used 1 1/4 gallons of tan paint for the ceiling and 4 3/8 gallons of green paint for the walls of her kitchen. How much paint did Lindsey use in all? Use fraction strips to help.
- Paul said, “I walked 2 1/2 miles on Saturday and 2 3/4 miles on Sunday.” How many miles is that in all?
- Estimate and then find the sum.
1 7/8 = 1 ?/8
+ 1 1/4 = 1 ?/8
________________
- Estimate and then find the sum.
6 5/12 + 4 5/8
- What is the missing number in the following equation?
3 1/3 + 4/? = 4 2/15
- After a party, there were 1 1/4 quesadillas left on one tray and 2 3/6 quesadillas left on another tray. How many quesadillas were left?
- James wants to send two gifts by mail. One package weighs 2 3/4 pounds. The other package weighs 1 3/6 pounds. What is the total weight of the packages?
- Louise started from one point and reached another point. Use the map to find the distance from the start to the end of the trail.
![exercise](https://www.turito.com/learn-internal/wp-content/uploads/2022/09/1-55.png)
Concept Map
![Concept Map](https://www.turito.com/learn-internal/wp-content/uploads/2022/09/image-7369-1024x410.png)
What have we learned
- Adding mixed numbers using models
- Adding mixed numbers
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