# Multiplying Fractions And Whole Numbers

Multiplying Fractions And Whole Numbers – Welcome to this free lesson guide where you’ll learn a simple two-step process for multiplying fractions by whole numbers AND multiplying whole numbers by fractions.

This complete guide to multiplying fractions by whole numbers includes several examples, an animated video mini-lesson, and a free worksheet and answer key.

## Multiplying Fractions And Whole Numbers

Before we explain how to multiply fractions, let’s do a super quick review of how to multiply a fraction by a fraction (understanding how to apply the rule below will make multiplying fractions and whole numbers much easier!)

## Th Grade Math: Multiplying Fractions

Rule for Multiplying Fractions: Whenever you multiply fractions, multiply the numerators together and then multiply the denominators as follows…

Note that the fraction (3/8) cannot be simplified (since 8 and 3 have no common divisor)

Now that you are familiar with the rule for multiplying a fraction by a fraction, you can use it to more easily multiply a fraction by a whole number.

Now, since you are multiplying a fraction by a fraction, you can apply the rule and solve like this…

#### Divide Whole Numbers By Fractions

Wait! What if the answer could be simplified? Let’s deal with the situation in the following example…

Since the greatest common factor (GCF) of 45 and 10 is 5, you can simplify by dividing the numerator and denominator by 5 so…

### Multiplying Whole Numbers By Mixed Numbers

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This article was co-authored by Mario Banuelos, PhD, and writer Jessica Gibson. Mario Banuelos is an assistant professor of mathematics at California State University, Fresno. With more than eight years of teaching experience, Mario specializes in mathematical biology, optimization, statistical models for genome evolution, and data science. Mario received his bachelor’s degree in mathematics from California State University, Fresno, and his Ph.D. in Applied Mathematics from the University of California, Merced. Mario taught in high school and college.

It’s easy to multiply fractions with mixed fractions or whole numbers. Start by converting mixed fractions or whole numbers to improper fractions. Then multiply the numerators of the two improper fractions. Multiply the denominators and simplify the result.

This article was co-authored by Mario Banuelos, PhD, and writer Jessica Gibson. Mario Banuelos is an assistant professor of mathematics at California State University, Fresno. With more than eight years of teaching experience, Mario specializes in mathematical biology, optimization, statistical models for genome evolution, and data science. Mario received his bachelor’s degree in mathematics from California State University, Fresno, and his Ph.D. in Applied Mathematics from the University of California, Merced. Mario taught in high school and college. This article has been viewed 2,131,809 times.

## Multiplying Fractions And Whole Numbers (video)

To multiply a fraction by a whole number, first write the whole number as a fraction by adding 1 to it. For example, say you’re trying to solve 5 x 8/10. You can start by rewriting 5 as a fraction. Now the equation looks like 5/1 x 8/10. Then you must multiply the numerators, or top numbers, of the fractions together. In our example, 5 and 8 are the numerators, so multiply 5 by 8 to get 40. Now do the same thing with the denominators, or bottom numbers, of the fractions. One and 10 are denominators, so multiply 1 by 10 to get 10. The new fraction is 40/10. If you can’t simplify the new fraction, you’re done and this is your answer. If you can, simplify the fraction to its lowest terms. In our example, we ended up with 40/10, which can be simplified by dividing the numerator and denominator by 10, giving you 4/1. So 5 x 8/10 = 4/1, or 4. To learn how to multiply a normal fraction by a whole number, scroll down! Maybe it was fifth grade when you last thought about multiplying fractions. But if you’re trying to halve a recipe or calculate the new price of a sale sweater with fractions, you may have to dig into the back of your memory to find out how to do it. Let’s refresh ourselves:

Each fraction has an upper and lower number, separated by a short horizontal line. In a proper fraction, the smaller number – called the numerator – will always be on top, while the larger number – the denominator – will be on the bottom. The numerator tells us how many units of the whole we have, and the denominator tells us how many units make up the whole. So in the fraction 1/2, 1 is the numerator and 2 is the denominator – there are two total units, but this fraction tells us that we only have one of those units.

Unlike adding or subtracting fractions, you can multiply fractions with different denominators. For example, it is no problem to multiply 3/4 x 2/5.

The third step is to simplify or reduce the fraction, because there is a better way to read the fraction.

#### Multiplying Fractions And Whole Numbers Using Models Boom Cards

To do this, we find the largest number by which we can divide the numerator and denominator to reduce the fraction. In this case, the largest number that is divisible by both is 2, so the reduced answer to this multiplication problem is 3/10.

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