KATE'S MATH LESSONS
  • Home
  • LESSONS
    • Pre-Algebra
    • Algebra 1
    • Geometry
    • Algebra 2
  • About
  • Contact
  • Blog
  • Shop
  • Courses
  • Home
  • LESSONS
    • Pre-Algebra
    • Algebra 1
    • Geometry
    • Algebra 2
  • About
  • Contact
  • Blog
  • Shop
  • Courses

Multiplying Fractions

Accompanying Resources:  Boom Cards (digital task cards),
​Google or Microsoft Activity
Multiplying Fractions Boom Cards - digital activity great for distance learning!
Picture

What Does It Mean to Multiply by a Fraction?

When you multiply a number by a fraction, you are finding part of that number.  For example, if you multiply 6 by 1/2, you are finding 1/2 of 6.
Multiplying a fraction by a whole number.

It gets a little trickier if both numbers are fractions, but the idea is still the same.  Anytime you're multiplying a number by a fraction, you're finding part of that number.  If you're multiplying 1/4 by 1/2, you're finding 1/2 of 1/4.
Multiplying two fractions together.

To figure out what 1/2 of 1/4 is, let's look at a picture of the fraction 1/4. The fraction 1/4 means the whole item has been divided equally into 4 pieces and you have 1 of those pieces:
Picture of 1/4: One out of 4 equal pieces.

To find 1/2 of the fraction shaded above, we need to split it down the middle.  We can do this by drawing a horizontal line halfway across the box.  1/2 of 1/4 is half of the shaded part.
Visual of a fraction of a fraction.

So what is 1/2 of 1/4?  By splitting the box down the middle, we now have 8 equal boxes and want only one of them.  This means the answer is one out of 8 pieces: 1/8.
Kate's Math Lessons
Welcome to Kate's Math Lessons!  
Teachers,make sure to check out the study guides and activities.
Picture
1/2 of 1/4 is 1/8.

Do you see a shortcut that we could have used?  To find the answer without a diagram, we can multiply the numerators together (1 x 1 = 1) and multiply the denominators together (2 x 4 = 8) to get the answer.

​Let's look at one more example to see if this shortcut still applies. Let's say we have 2/3 times 4/5.  This means we want 2/3 of the fraction 4/5.  Let's start with a picture of 4/5.  4/5 means the whole has been divided into 5 equal parts and we have 4 of the 5 equal pieces.
4/5 means you have 4 out of 5 equal pieces.

If we want to find 2/3 of 4/5, that means we need to find 2/3 of the shaded part above.  To do this, we can split the rectangle into 3 equal rows.  To find 2/3, we need 2 out of the 3 rows.
Visual for multiplying two fractions together.

So what is 2/3 of 4/5?  When we split the box into 3 rows, we formed a rectangle that is 5 x 3.  This gives us a total of 15 equal pieces.  We only wanted 2/3 of the shaded part, so we need to count only what's shaded in 2 out of the 3 rows (inside the purple box shown above).  We can see that this gives us 8 equal pieces out of 15 total: 8/15.
Multiplying fractions

Can you see the shortcut?  To find the answer, we can multiply the numerators together (2 x 4 = 8) and multiply the denominators together (3 x 5 = 15).


​How To Multiply Fractions

You do not need to draw a picture every time you multiply two fractions together.  Instead, use the shortcut.  To multiply fractions together, you just multiply straight across.  Multiply the numerators together. Then multiply the denominators together.  Last, simplify your answer if necessary.
How do you multiply fractions? Multiply straight across (multiply the numerators, multiply the denominators). Then simplify if necessary.
How do you multiply fractions?


​15 and 56 do not have any common factors other than 1, so the fraction does not need to be simplified.  Here's an example where the fraction can be simplified:
How to multiply fractions.

There is an another option that may be easier.  Instead of simplifying at the end, you can simplify in the beginning.  If you simplify first, it can be easier to see common factors with the smaller numbers at the beginning.
Alternate rule for multiplying fractions. Simplify first and then multiply.
You can simplify fractions before you multiply if you prefer.

It does not matter if you simplify first or last, you end up with the same answer.  Choose the method that seems easiest to you.

Multiplying Fractions by Whole Numbers

What do you do if only one number is a fraction is the other is a whole number?  Change the whole number into a fraction by using 1 as the denominator.  Dividing by 1 does not change a number, so any whole number can be rewritten with a 1 in the denominator. After you've written the whole number as a fraction, you can follow the steps for multiplying fractions.
Multiplying a whole number by a fraction. Rewrite the whole number as a fraction, then multiply.


​Multiplying by a Mixed Number

One or both of the numbers you're multiplying might be a mixed number.  Before you multiply, first rewrite the mixed number as an improper fraction.  The rest of the steps will be the same.
How do you  multiply a mixed number by a fraction?


​Video

Want to see another example? Check out the short video below.


Practice

Ready to try some problems on your own? Click the START button below to try a practice quiz.

Powered by Interact


Want to learn how to add fractions?
Want to try one of my digital math activities for free?  Click the link to grab the teacher version or student version.

Home

About

Privacy Policy

Lessons

Contact

Copyright © 2015 - 2021 Kate's Math Lessons