Today we will see how to multiply mixed numbers and whole numbers. Let’s walk through the examples step by step.
Content:
Before getting into this topic, don’t forget that a proper fraction is a fraction where the numerator (the top number) is less than the denominator (the bottom number). In addition, a mixed number is the sum of a whole number and a proper fraction. Take a look at the image below.
1) Multiply 31/5 × 2:
We start by rewriting the mixed number (31/5) as an improper fraction. Then, we rewrite the whole number (2) as a fraction by putting 1 as the denominator.
Next, we multiply the fractions.
Finally, we convert the improper fraction 32/5 to a mixed number. To do that, we divide 32 by 5. The quotient of that division (6) is the whole number part of the mixed number, while the remainder (2) is the numerator of the fractional part of the mixed number. Lastly, the denominator (5) stays the same.
The final answer is 62/5.
Steps for multiplying a mixed number by a whole number
For multiplying mixed numbers and whole numbers, follow these simple steps:
- Convert the mixed number and the whole number to improper fractions.
- Multiply those improper fractions.
- Convert the result to a mixed number or a whole number.
Let’s move on to the next example.
2) Multiply 23/8 × 4:
First, we convert the mixed number (23/8) to an improper fraction. Then, we convert the whole number (4) to an improper fraction by putting 1 as the denominator.
We simplify and multiply the fractions.
Next, we rewrite this improper fraction (19/2) as a mixed number. In order to do that, we divide the numerator 19 by the denominator 2. The quotient of that division (9) is the whole number part of the mixed number, while the remainder (1) is the numerator of the fractional part of the mixed number. Finally, we keep the denominator (2) the same.
The final answer is 91/2.
Video
In the following video, we will see more examples of multiplying mixed numbers by whole 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.
- Bittinger, M., Beecher, J. and Johnson, B. (2019). Basic College Mathematics (11th ed.; p. 186). Pearson.