Comparing Fractions

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To compare fractions with the same denominators we look at their numerators. The one with the larger numerator is the one with the larger fraction.

Example:

Compare the two fractions and

Solution:

is larger than because the denominators are the same but the numerator is larger.

To compare fractions with different denominators, we can use cross product (or cross multiplication).

The first cross-product is the product of the first numerator and the second denominator.

The second cross-product is the product of the second numerator and the first denominator.

Then, compare the cross products using the following rules:

Example:

Compare and

Solution:

First, get the first cross product by multiplying the first numerator and the second denominator.

4 × 10 = 40 (First cross product)

Next, get the second cross product by multiplying the second numerator and the first denominator.

3 × 7 = 21 (Second cross product)

Since the first cross product is larger, the first fraction is larger.

Example:

Compare and

Solution:

First, get the first cross product by multiplying the first numerator and the second denominator.

5 × 9 = 45 (First cross product)

Next, get the second cross product by multiplying the second numerator and the first denominator.

8 × 6 = 48 (Second cross product)

The second cross product is larger, so the second fraction is larger.

The following video shows how to compare fractions using cross multiplication.

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