In previous lessons, we have learned how to add proper and improper fractions, but we haven´t covered mixed numbers yet. In this lesson, I will show you how to add mixed numbers with like denominators using several examples.
Content:
Before seeing the examples, just remember that a proper fraction is a fraction where the numerator is less than the denominator. Additionally, a mixed number is the sum of a whole number and a proper fraction, take a look at this example.
1) Add 31/5 + 42/5:
First, we add the whole numbers (3+4), and then we add the fractions (1/5 + 2/5).
Next, we add the sum of the whole numbers (7) with the sum of the fractions (3/5). Don’t forget that a mixed number is the sum of a whole number and a proper fraction. So, we could rewrite the sum of 7 and 3/5 as the mixed number 73/5.
The final answer is 73/5.
In the following image, I am going to add one more step, so you can see why we add the whole numbers and the fractions. The key is to remember that a mixed number is the sum of a whole number and a proper fraction. Therefore, we could rewrite the mixed number 31/5 as the sum 3 + 1/5, and the mixed number 42/5 as the sum 4 + 2/5.
Steps for adding mixed numbers with like denominators
- Add the whole numbers.
- Add the proper fractions.
- Add the sum of to the fractions to the sum of the whole numbers and rewrite this sum as a mixed number.
2) Find the sum 11/6 + 21/6:
We start by adding the whole numbers (1+2), and then we add the proper fractions (1/6 + 1/6).
In this case, the sum of the fractions is 2/6, this is a fraction that we can simplify dividing the numerator and denominator by 2. Lastly, we add the sum of the fractions (1/3) to the sum of the whole numbers (3). Recall that we can rewrite the sum of 3 and 1/3 as the mixed number 31/3.
The resulting mixed number is 31/3, this mixed number is read as three and one-third.
3) Add 54/7 + 46/7:
First, we add the whole numbers (5+4) and next, the fractions (4/7 + 6/7).
As you can see the sum of the fractions is 10/7, an improper fraction that we need to rewrite as the mixed number 13/7.
Now we add 9 + 13/7, so we add the whole numbers first (9+1), and then we add the fractions, however, here we only have one fraction (3/7).
The final answer is 103/7.
Videos
In this video, you will find more examples of adding mixed numbers with the same denominators:
And here, more examples:
References
For this lesson, we have used these books:
- Tussy, K., Gustafson, D. y Koenig, D. (2013). Prealgebra (4th ed.; pp. 374-378). Cengage Learning.
- Aufmann, R. y Lockwood, J. (2014). Basic College Mathematics (10th ed.; pp. 79-81). Cengage Learning.