Multiplying Fractions: The Complete Guide — Mashup Math (2024)

Multiplying Fractions: The Complete Guide — Mashup Math (1)



by Anthony Persico

Multiplying Fractions: The Complete Guide — Mashup Math (2)

Learning how to multiply fractions, whether it be fraction times fraction or multiplying fractions by whole numbers, is an important skill that every math student must learn at some point.

This complete guide to multiplying fractions will provide a step-by-step tutorial on how to multiply fractions and includes several examples, an animated video mini-lesson, and a free worksheet and answer key.

Let’s get started!

Before we explore how to multiply fractions, let’s do a super quick review of basic multiplication:

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What do you notice about the relationship between figures A, B, and C?

In figure D, why is 2 x (1/2) equal to 1 ?

To help you understand Figure D above, let’s start by learning about the rules for multiplying fractions:

Rule: Whenever multiplying fractions together, multiply the numerators together, then multiply the denominators together.

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The rules for multiplying fractions are as simple as that, and applying the rule to variety of different problems is just as easy. Let’s go ahead and apply this rule in a few examples.


Example 1 (Multiplying Fractions by Fractions):

What is (3/4) x (1/2) ?

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Start by applying the rule and multiplying the numerators together and then the denominators together as follows:

Notice that the fraction (3/8) can not be simplified (since 8 and 3 do not have a common divisor)

Answer: (3/4) x (1/2) = 3/8

Example 2 (Multiplying Fractions by Whole Numbers):

What is 2 x (1/2) ?

This problem should look familiar because it’s from Figure D above.

Now that you understand how to use the multiplying fractions rule, you can solve this problem where you have to multiply fractions and whole numbers.

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You will still use the rule to find the answer, but there is one extra step involved.

Since you are multiplying fractions by whole numbers, you will need to convert the whole number into a fraction.

In this case, you can rewrite the whole number 2 as (2/1) as follows:

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Then apply the rule and solve as follows:

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Answer: 2 x (1/2) = 1

Example 3 (Multiplying Fractions and Simplifying Fractions):

What is (5/6) x (3/4) ?

This will be our final example.

This time, you will have to multiply fractions and then simplify your answer.

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Start by applying the rule as follows:

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Wait! There’s still one more step.

15/24 can simplified because 15 and 24 are both divisible by 3 (which is the GCF of 15 and 24). So you can simplify the fraction by dividing BOTH the numerator and the denominator by 3 as follows:

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And that’s all there is to it!

Answer: (5/6) x (3/4) = (5/8)

Still confused? Check out the animated video lesson below:

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

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Are you looking for some extra practice multiplying fractions? Click the links below to download your free worksheets and answer key:

CLICK HERE TO DOWNLOAD YOUR FREE WORKSHEET

Tags: Multiplying Fractions, Multiplying Fractions and Whole Numbers, Multiplying Fractions Practice, Multiplying Fractions Examples, Simplifying Fractions

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Have thoughts? Share your thoughts in the comments section below!

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By Anthony Persico

Anthony is the content crafter and head educator for YouTube'sMashUp Math. You can often find me happily developing animated math lessons to share on my YouTube channel. Or spending way too much time at the gym or playing on my phone.

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Multiplying Fractions: The Complete Guide — Mashup Math (2024)

FAQs

How do you multiply fractions guide? ›

The correct procedure for multiplying fractions is: find a common denominator, multiply the numerators, multiply the denominators, and simplify if necessary. Add the numerators and add the denominators.

How do you multiply fractions Grade 7? ›

First, multiply the numerators. Then, multiply the denominators of both the fractions to obtain the resultant fraction. Then, we need to simplify the obtained fraction to get the final answer. This can be understood by a simple example → 2/6 × 4/7 = (2 × 4)/(6 × 7) = 8/42 = 4/21.

What is the formula to multiply two fractions? ›

You multiply the numerators (the top numbers) together, and then multiply the denominators (the bottom numbers) together. After putting the two results together as a new fraction, you may need to simplify the fraction in order to express it in its lowest terms.

What grade do kids multiply fractions? ›

For fourth grade, most state standards stop here (of course, check your own standards just to be sure!). For fifth grade, however, they need to understand another type of fraction multiplication problem.

Do 5th graders know multiplication? ›

Multiplication facts are fundamental to many math topics

Multiplication facts need to be embedded by third grade and are also central to 4th grade and 5th grades.

How do you multiply mixed fractions in math? ›

To multiply two mixed numbers, follow these steps:
  • Change each mixed number to an improper fraction.
  • Multiply the numerators.
  • Multiply the denominators.
  • Simplify, if needed. You may want to write your answer as a mixed number.

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