Ordering Fractions from Least to Greatest

This video shows examples of how to order fractions. When ordering fractions, you must first look at the denominator. If the denominators of the fractions are the same, then you must order them according to their numerators, with the values increasing left to right.

Ordering Fractions

Ordering Fractions

When ordering fractions you must first look at the denominator. If the denominators of the fractions are the same, then you order them according to the numerators with the value increasing left to right. Let’s look at an example.

You can see all the denominators are the same. We’re going to order these fractions by looking at our numerators. If we’re ordering them from left to right, or from least to greatest, then the smallest number would be our biggest negative number, negative 7/9.

Our next number will be our next negative number, negative 4/9. Next biggest would be our first positive number, 2/9. Finally, 4/9. Now let’s look at some fractions that don’t have the same denominator.

For these factions we could first find the least common denominator so that we could have all the same denominator and then order them by the numerator. The least common denominator, or LCD, for 4, 12, 2, and 6 would be 12.

First, we’re going to convert all these fractions to have the denominator of 12. 3/4, to convert 3/4 to something over 12, we need to multiply 4 times 3 so we’ll do the same to our numerator. 3 times 3 is 9 and 4 times 3 is 12. 3/4 is 9/12.

Negative 7/12 already has our least common denominator of 12, so we’re going to leave it alone. 1/2, 2 would need to be multiplied by 6 to get 12, so we’ll do the same to our numerator, 1 times 6 is 6, 2 times 6 is 12. Negative 5/6, 6 would need to be multiplied by 2 to get 12 so we’ll do the same numerator. 5 times 2 is 10, 6 times 2 is 12, and of course it’s still negative.

Now we can order our fractions based on their numerators from least to greatest, from left to right. Our smallest number is our biggest negative which is negative 10/12. Then our next negative 7/12, then 6/12, and finally 9/12 would be our largest number.

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by Mometrix Test Preparation | Last Updated: August 15, 2019