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Comparing Fractions




 
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How to Compare Fractions With The Same Denominators?


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.

How to Compare Fractions With Different Denominators?


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:

  • If the cross-products are equal, the fractions are equivalent.
  • If the first cross product is larger, the first fraction is larger.
  • If the second cross product is larger, the second fraction is larger.

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.



 

Rotate to landscape screen format on a mobile phone or small tablet to use the Mathway widget, a free math problem solver that answers your questions with step-by-step explanations.


You can use the free Mathway calculator and problem solver below to practice Algebra or other math topics. Try the given examples, or type in your own problem and check your answer with the step-by-step explanations.


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