**Multiply Whole Number By Fraction** – Welcome to this free tutorial 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.

## Multiply Whole Number By Fraction

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

## Multiplying Fractions (w/ 15 Step By Step Examples!)

Rule of Multiplying Fractions: Whenever you multiply fractions together, multiply the numerators together, then multiply the divisors together as…

Note that the fraction (3/8) cannot be prime (because 8 and 3 have no common divisor).

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

Now, since you’ve multiplied the fraction by the fraction, you can solve by applying the rule like this…

### Ways To Multiply Fractions With Whole Numbers

Hang on ! What if the answer was simple? Let us illustrate the situation with 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.

Watch the video lesson below to learn more about multiplying fractions and for more free practice problems:

Need more practice multiplying fractions by whole numbers? Click the links below to download your free worksheets and answer key:

#### Year 5 Multiply Mixed Numbers By Integers Lesson

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This article was co-authored by Mario Banuelos, PhD, and staff writer Jessica Gibson. Mario Banuelos is an assistant professor of mathematics at California State University, Fresno. With over eight years of teaching experience, Mario specializes in computational biology, optimization, statistical models for genome evolution and data science. Mario has a BA in Mathematics from California State University, Fresno, and a Ph.D. in applied mathematics from the University of California, Merced. Mario taught high school and college.

Multiplying fractions by mixed fractions or whole numbers is easy. Begin by converting your mixed fractions or whole numbers to improper fractions. Then multiply the numbers of the two improper fractions. Simplify the output by multiplying labels.

This article was co-authored by Mario Banuelos, PhD, and staff writer Jessica Gibson. Mario Banuelos is an assistant professor of mathematics at California State University, Fresno. With over eight years of teaching experience, Mario specializes in computational biology, optimization, statistical models for genome evolution and data science. Mario has a BA in Mathematics from California State University, Fresno, and a Ph.D. in applied mathematics from the University of California, Merced. Mario taught high school and college. This article has been viewed 2,132,295 times.

## Multiply Fraction By Whole Number Worksheet

To multiply a fraction by a whole number, write the whole number as a fraction by first placing 1. For example, say you are 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. Next, you need to multiply the fractional numbers or the higher numbers together. In our example, 5 and 8 are numbers, so multiply 5 by 8 and you get 40. Now do the same with fractions or numbers below. One and 10 are denominators, so multiplying 1 by 10 gives you 10. The new fraction is 40/10. If you can’t simplify the new fraction, you’re done and this is your answer. Simplify the fraction to its lowest terms if you can. 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. Scroll down to learn how to multiply a common fraction by a whole number! The last time you thought about multiplying fractions was probably fifth grade. But if you’re trying to cut a recipe in half or calculate the new price of a sale sweater with fractions, you might have to dig into the back of your memory to figure out how to do it. Let’s refresh:

In each section there is an upper number and a lower number separated by a short horizontal line. In an exact fraction, the smallest number – called the numerator – will always be on top, the largest number – the denominator – will be on the bottom. The numerator tells us how many units we have in total and the spade tells us how many units there are in total. So, the fraction 1/2, 1 is the numerator and 2 is the denominator – there are two parts in total, but this fraction tells us that we only have one of those parts.

When adding or subtracting fractions, you can multiply different fractions by different parts. For example, multiplying 3/4 x 2/5 is not a problem.

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

## Decomposing Fractions To Multiply

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

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