In this lesson, we will see how to add mixed numbers with unlike denominators, it’s easy. We have prepared some examples and exercises.
Content:
Before getting into this topic, remember that a proper fraction is a fraction where the numerator is less than the denominator. Also, a mixed number is the sum of a whole number and a proper fraction.
1) Add 51/2 + 41/3
We start by adding the whole numbers (5+4) and the fractions (1/2 + 1/3) separately. To add the fractions, we rewrite them as equivalent fractions with the LCD (least common denominator), 6.
Then, we add the sum of the fractions (5/6) to the sum of the whole numbers (9).
That’s it, the final answer is 95/6.
Steps for adding mixed numbers with unlike denominators
To add mixed numbers of mixed fractions with unlike denominators, follow these steps:
- Add the whole numbers.
- Add the fractions, don’t forget to convert them to equivalent fractions with the LCD (least common denominator).
- Add the sum of the fractions to the sum of the whole numbers.
2) Add 73/4 + 21/6
First, we add the whole numbers (7+2) and the fractions separately (3/4 + 1/6). To find the sum of the fractions, we rewrite them as equivalent fractions with the LCD, 12.
Then, we add the sum of the fractions (11/12) to the sum of the whole numbers (9).
The resulting mixed number is 911/12.
3) Find the sum 72/3 + 63/4
We start by adding the whole numbers (7+6) and the fractions separately (2/5 + 3/4). For adding the fractions, we need to rewrite them as equivalent fractions with the LCD, 20.
The sum of the fractions is an improper fraction (17/12), and since we don’t want an improper fraction in the answer, we need to convert this improper fraction to a mixed number.
Next, we add the sum of the fractions (15/12) to the sum of the whole numbers (14). First, we add the whole numbers (14+1) and then we keep the fraction 5/12.
The final answer is 145/12.
Videos
In this video, we will see how to add mixed numbers with unlike denominators step by step.
In the following video, we will see how to add mixed numbers with unlike denominators quickly.
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.
- OpenStax (2020). Prealgebra 2e (pp. 374-375). Rice University.