Welcome to Mathnasium’s Math Tricks series. Today we are comparing fractions to the benchmark number, one half.

When comparing fractions, it can be difficult to determine whether they represent values that are greater than or less than one another. It might be helpful to identify whether they are greater than or less than one half. To do so, we find how many parts make one half of each whole, and then we compare the number of parts to the half.

Follow the example below to arrange the fractions in order.

Example: Arrange the numbers from smallest to largest:

   Step 1: Determine the smallest number and largest number.

Since the fractions are proper fractions, they are all greater than 0 and less than 1.

Smallest: 0

Largest: 1

   Step 2: Group the remaining numbers as less than half, greater than half, or equal to half.

715 is less than half.

916 is greater than half.

   Answer: The numbers arranged in order are 

Now, with this strategy, you are ready to compare fractions using the benchmark of one-half. Click here for more practice problems, then check your answers here.

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