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What are Equivalent Fractions? - Definition & Examples

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  • 0:00 The Parts Of A Fraction
  • 0:30 Multiplication
  • 1:55 Division
  • 2:30 Addition And Subtraction
  • 3:35 Testing For Equivalency
  • 4:25 Lesson Summary
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Lesson Transcript
Instructor: Joseph Vigil
In this lesson, you'll review some fraction terminology and then learn what equivalent fractions are. Afterward, you can test your new knowledge with a brief quiz.

The Parts of a Fraction

It will benefit us to review some fraction terminology before we define equivalent fractions.

When we write a fraction, there's always a number above the dividing bar and a number below the dividing bar. The upper number in a fraction is called the numerator. The lower number is called the denominator. So in the fraction 1/2, 1 would be the numerator, and 2 would be the denominator.

fraction with numerator and denominator labeled

An easy trick to remember which part goes where is that denominator and down both start with the letter 'd,' so the denominator is always the number that's down in a fraction.

Multiplication

Your sly friend has made two pizzas. He said that he cut one pizza into two big slices, and you can have one of them. He's cut the other pizza into six slices and said you can have three of them. You have to decide which would give you more pizza.

Well, three slices are more than one, but let's take a closer look...

Let's consider the fractions of the two pizzas: 1/2 and 3/6. Look at the numerators in both fractions. To get from 1 to 3, we multiply by 3. We do the same thing with the denominators: we multiply 2 by 3 to get 6.

In essence, what we've done is multiply 1/2 by 3/3, and 3/3 is just a fractional form of 1. When we multiply any number by 1, we're not changing its value. So we could multiply 1/2 by any fractional form of 1.

one half times four fourths equals four eighths

one half times five fifths equals five tenths

one half times six sixths equals twelve

And on and on...

Since we're really multiplying by 1 in each case, we're not changing the value of the original fraction; we're just creating another fraction with the same value. These are called equivalent fractions. 1/2 and 3/6 may look different, but they have the same value.

Let's look at our original example, 1/2 and 3/6, graphically:

These fractions cover the same area, so they are equivalent fractions.
one half of one circle and three sixths of another circle

Although 1/2 and 3/6 are different in the way they're written, they cover the same portion of the circles. This is because they're equivalent fractions with the same value!

No matter which pizza you chose, you'd get the same amount of pizza. Each of the three slices would just be smaller than the one big slice.

Division

We can also use division to create equivalent fractions. Just like multiplying a number by 1 doesn't change it's value, the same is true if we divide by 1. So we could take a fraction like 6/8 and divide it by a fractional form of 1, such as 2/2:

six eighths divided by 2 over 2 equals 3 fourths

Let's use the circles again to see their equivalency:

The different fractions cover the same portion of the circles.
pie charts of three fourths and six eighths

Although 6/8 and 3/4 are different in the way they're written, they cover the same portion of the above circles. This is because they're equivalent fractions with the same value!

Addition and Subtraction

Equivalent fractions are an important tool when adding or subtracting fractions with different denominators. Let's look at an example:

Johnny bought one half of a cake. He didn't know that while he was out, his wife, Lyndon, bought one fourth of a cake. When they got home, how much cake did they have altogether?

We're adding fractions here:

1/2 + 1/4

When we're adding fractions, they must have the same denominator, but in this case, they have different denominators (2 and 4). However, we can make their denominators equal by changing the denominator in 1/2.

Remember that we can form equivalent fractions by multiplying the numerator and denominator by the same number. If we multiply the denominator in 1/2 by 2, we'll have a new denominator of 4, and the fractions will have the same denominator.

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