Compare Unlike Fractions

How to Compare Fractions using cross multiplication?

The idea behind cross multiplication is to turn both fractions into whole numbers that are easy to compare, while still maintaining the relationship between them. The following diagram shows an example of comparing fractions using cross multiplication. Scroll down the page for more examples and solutions of comparing fractions using cross multiplication.

Step 1: Set up the Fractions
Write the two fractions next to each other with a blank space in between where you’ll put your comparison symbol (>, <, or =).
Example: Compare \(\frac{3}{5}\) and \(\frac{4}{7}\)

\(\frac{3}{5} ? \frac{4}{7}\)

Step 2: Multiply Upwards
Multiply the denominator of the second fraction by the numerator of the first fraction. Write the result above the first fraction.
In our example, you multiply 7×3.

Step 3: Complete the “Cross”
Multiply the denominator of the first fraction by the numerator of the second fraction. Write this result above the second fraction.
In our example, you multiply 5×4.

Step 4: Compare the Products
You now have two new numbers. The number on the left corresponds to the first fraction, and the number on the right corresponds to the second fraction. Compare these two numbers to determine which fraction is larger.

Using our example:
The first product is 7×3=21.
The second product is 5×4=20.

Since 21 is greater than 20, the first fraction is greater.

Videos

Comparing Fractions

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Comparing Fractions

How to Compare Fractions using cross multiplication?

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Math Tricks: Comparing Fractions

In this math video we look at an easy way to compare fractions when the denominators are different. (Cross Multiplication)

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