Today we will see how to multiply mixed numbers. Take a look at the examples below.
Content:
Before getting into it, don’t forget that a proper fraction is a fraction where the numerator (the top number) is less than the denominator (the bottom number). Also, a mixed number is the sum of a whole number and a proper fraction. See the image below.
1) Multiply 31/5 × 23/4:
First, we will convert both mixed numbers to improper fractions.
Then, we simplify and multiply the improper fractions.
The resulting improper fraction is 44/5, which we need to convert back to a mixed number. To do that, we divide 44 by 5. The quotient of that division (8) is the whole number part of the mixed number, while the remainder (4) is the numerator of the fractional part of the mixed number. Finally, we keep the denominator (5) the same.
The final answer is 84/5.
Steps for multiplying mixed numbers
To multiply mixed numbers, just follow these simple steps:
- Convert the mixed numbers to improper fractions.
- Multiply the improper fractions.
- Convert the result to a mixed number or a whole number.
Let’s continue with more examples.
2) Multiply 43/5 × 31/2:
We start by rewriting the mixed numbers as improper fractions.
In this case, it is not possible to simplify. Next, we proceed by multiplying the fractions.
Then, we convert the resulting fraction (161/10) back to a mixed number. So, we divide 161 by 10. The quotient (16) of that division is the whole number part of the mixed number, and the remainder (1) is the numerator of the fractional part of the mixed number. Finally, the denominator (10) stays the same.
The final answer is 161/10.
3) Multiply 62/3 × 41/2:
First, we rewrite both mixed numbers as improper fractions.
Next, we simplify and multiply the improper fractions.
The resulting fraction is 30/1. Don’t forget that we can also see a fraction as a division, and 30 divided by 1 is 30.
The final answer is 30, a whole number.
Video
In the following video, we will see more examples of multiplying mixed numbers.
References
For this lesson, we have used these books:
- Tussy, K., Gustafson, D. y Koenig, D. (2013). Prealgebra (4th ed.; pp. 364-368). Cengage Learning.
- OpenStax (2020). Prealgebra 2e (pp. 317-320). Rice University.