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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.

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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 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.
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 + 1/4When 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.But we’ll also need to multiply the numerator by 2:

one over two times two over two equals two over four

Since 1/2 and 2/4 are equivalent, we can use 2/4 in place of 1/2 in our original addition problem:2/4 + 1/4 = 3/4Johnny and Lyndon have 3/4 of a cake between the two of them.We can follow the same process to subtract fractions: multiply one of the fractions by a fractional form of 1, so that both fractions have the same denominator. Then you can proceed with the subtraction.

Testing for Equivalency

There’s a surefire way to test two fractions for equivalency that doesn’t involve sliced circles.If we cross multiply two fractions, or multiply the numerator of each fraction by the other’s denominator, and the resulting products are equal, then the fractions are equivalent.Let’s use our previous example of 6/8 and 3/4:

cross multiplying six eighths and three fourths

As indicated by the colors, we’ll multiply the numerator of each fraction by the denominator of the other fraction.

cross multiplying four fifths and eight ninths

Just like we did before, we’ll multiply the red numbers together and then multiply the blue numbers together:

four times 9 equals 36 and 8 times 5 equals 40

The products aren’t equal, so these fractions aren’t equivalent.

Lesson Summary

Let’s review.

  • The numerator is the part of a fraction above the dividing bar.
  • The denominator is the part of a fraction below the dividing bar.

  • Equivalent fractions have different numerators and denominators, but the same value.
  • If you multiply or divide any fraction by a fractional form of 1 (i.e.: 2/2, 3/3, 4/4), the new fraction will be equivalent to the original fraction.

  • Equivalent fractions are used when adding or subtracting fractions with different denominators.
  • You can check if two fractions are equivalent by cross multiplying, which entails multiplying the numerator of each fraction by the denominator of the other fraction.

Key Terms

Fractions in Pizza: Halves vs.</p>
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</table>
<p><b>Numerator</b> – the top number in a fraction<b>Denominator</b> – the bottom number in a fraction<b>Equivalent fractions</b> – two fractions which have the same value (ex. 1/2 and 3/6)<b>Cross multiplication</b> – multiplying the numerator of each fraction by the other’s denominator</p>
<h2>Learning Outcomes</h2>
<p>After this video, check to see if you can:</p>
<ul>
<li>Define equivalent fractions</li>
<li>Identify equivalent fractions using multiplication and division</li>
<li>Solve addition and subtraction problems using equivalent fractions</li>
<li>Determine if two fractions are equivalent using cross multiplication</li>
</ul>
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