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Cross Multiplication: Definition & Examples

Instructor: Joseph Vigil
In this lesson, you'll review some fraction terminology. Then, you'll learn what cross multiplication is and how it's useful. Afterward, you can test your new knowledge with a brief quiz.

Parts of a Fraction

Before we begin our story, let's name the parts of a fraction. A fraction always has a division bar and two numbers--one above the division bar and one below it.

The number above the division bar is the numerator, and the number below the division bar is the denominator.

So in the fraction 1/2, 1 would be the numerator, and 2 would be the denominator.

One way to remember what goes where in a fraction is to note that denominator and down both start with d, so the denominator goes down in a fraction.

Comparing Fractions

Michael and Lena have each inherited part of a family fortune. Michael stands to inherit 1/4 of the fortune, while Lena will get 2/5. Who's getting the larger portion?

We can compare fractions by cross multiplying, which means multiplying the numerator of each fraction by the other's denominator.

cross multiplying one fourth and two fifths

When we find the products from cross-multiplication, we'll want to place them next to their respective numerators. In this example, when we multiply 1 * 5, we get a product of 5. Since 1 is the numerator in this case, I'll put a 5 near the 1 in the first fraction.

a 5 near one fourth

Next, we'll need to multiply 2 * 4, which gives us a product of 8. Since 2 is the numerator we're multiplying by, I'll place the 8 by the 2 in the second fraction.

an 8 near two fifths

After we cross multiply, whichever fraction has the larger number by it is the larger fraction. Since the 8 is by 2/5, that fraction is larger than 1/4.

It seems Lena has been in the family's good graces!

Let's compare another pair of fractions: 7/15 and 12/24.

cross multiplying seven fifteenths and twelve twenty fourths

First, we'll multiply 7 * 24, which gives us a product of 168. Let's put 168 by the 7 in the first fraction, since that's the numerator we just multiplied by.

168 near seven fifteenths

Now, we'll multiply 12 * 15, which gives us a product of 180. So we'll put 180 by the 12 in the second fraction, since it's the numerator we just multiplied by.

180 near twelve twenty fourths

Since 180 is greater than 168, and it's next to 12/24, that's the larger fraction.

Equivalent Fractions

In the time it took Jose to finish 6/8 of his homework, his brother Roberto finished 3/4 of his. Who completed more of his homework in that time?

Well, let's cross multiply.

cross multiplying six eighths and three fourths

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