Today we will see how to add mixed numbers with unlike denominators. It’s easier than it sounds.
Content:
Before we see the examples, don’t forget that a proper fraction is a fraction where the numerator is less than the denominator. In addition, a mixed number is the sum of a whole number and a proper fraction.
1) Add 31/2 + 52/3 + 91/4:
To find the sum, we start by adding the whole numbers (3 + 5 + 9).
Then, we add the fractions (1/2 + 2/3 + 1/4). Given that these fractions have different denominators, we start by finding the least common multiple of the denominators (2, 3 and 4).
The least common multiple (LCM) of the denominators is 12, so we find equivalent fractions with denominator 12, and finally, we find the sum of the fractions.
Since the resulting fraction is an improper fraction, we convert this fraction to a mixed number.
The final step is adding the sum of the fractions (15/12) to the sum of the whole numbers (17).
The resulting mixed number is 185/12.
Steps for adding 3 mixed numbers
To find the sum of 3 mixed numbers 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.
Video
Let’s look to another example to understand the addition of 3 mixed numbers:
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.