Simplifying Compound Fractions

Instructor: Emily Hume

Emily is a Reading Specialist and Literacy coach in a public elementary school with a Master's Degree in Elementary Education.

Have you ever simplified a fraction? Simplifying compound fractions may sound complicated, but it really isn't if you follow a few simple steps. In this lesson, you will learn how to simplify compound fractions.

What is a Compound Fraction?

Have you ever had to share something? Maybe you've shared candy or a chocolate bar with a friend or sibling. How did you make it fair? You probably had to use fractions!

Let's say your mom is feeling generous and buys you and your brother 3 candy bars to share! Using fractions, it's easy to split them and make sure everyone's happy. Here's how you do it:

Chocolate Bar Mixed Number
Chocolate Bar Mixed Number

What fraction of the candy bars did you each get? You got a whole candy bar, plus half of another one. You got 1 1/2 and so did your brother!

A number followed by a fraction is called a compound fraction or a mixed number. That's right - two names for the exact same thing, but don't let it confuse you. Take a look at the Compound Fraction/Mixed Number image.

Compound Fraction also known as Mixed Number
Compound fraction and mixed number

Whole Numbers, Fractions and Mixed Numbers

A whole number is exactly as its name says: it is whole or complete. In our image, the 7 is the whole number. A fraction indicates part of a whole. In our image, the fraction 3/4, indicates that we have 3 parts out of the total number of parts, which is 4. And a compound fraction or mixed number contains both a whole number and a fraction - 7 3/4.

Now that we have all of this information, we are ready to simplify our compound fraction.

Simplifying the Compound Fraction

We are going to simplify our compound fraction of 1 1/2 candy bars. To do this, you will need to complete the following steps:

1) Multiply the denominator, or bottom number of the fraction, by the whole number. In this case, this would mean you multiply

2 x 1 = 2.

2) Then, take that answer (2) and add it to the numerator, or top number of the fraction (in this case, 1). So,

2 + 1 = 3.

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