Comparing Fractions

Methods

There are four general methods to determine whether two fractions are equal or not:

Converting to decimals
Using common denominators
Cross-multiplication
Using common numerators

Decimals

We can convert fractions into decimals by dividing the denominator into the numerator. You then compare each decimal to see if they are equal and if they aren't, which one is greater.

Common Denominators

When two fractions have the same denominator, you can determine whether or not they are equal or if one is larger by looking at the numerators. For example we can tell that 6/8 is larger than 5/8 because they're both described as having the same type of parts but the first fraction has 6 pieces and the second has five.

If fractions don't have the same denominator than you can find any one, it doesn't have to be that lowest common one. A common denominator can be found by multiplying both denominators of the two fractions.

IMAGE-Beckmann, S. (2022). Mathematics for elementary and middle school teachers: With activities (6th ed.). Pearson Education, Inc.

Cross Multiplying

Once you find the common denominator of two fractions, as seen to the left you just need to compare 3 x 6 and 4 x 5. To cross multiply fractions you multiply the numerators of the fractions by the opposite denominator.

Common Numerators

When looking at two fractions that have the same numerator we can conclude that the larger fraction is the one with the smaller denominator as the parts are larger. Fraction bars are a great way to show this visually in the classroom. Fractions do not always have the same numerators so what happens in that case? Looking at the image to the left you can see that after finding a common numerator and after comparing denominator you can see which fraction is larger.

Classroom Material

This would make a great classroom poster for students to refer back to when working in the classroom.

Boucher, Donna. “Comparing Fractions Poster.” Math Coach’s Corner, 5 Feb. 2024, www.mathcoachscorner.com/2012/12/comparing-fractions/.

Unit Example

Education.com has a tremendous amount of units, lessons, games and worksheets that keep students interested in learning. This worksheet is showing third graders that fractions are everywhere!

“Food Math: Worksheet.” Worksheet | Education.Com, 2025, www.education.com/worksheet/article/food-math/.

Working with fractions has taught me that mistakes will be made and making sure your work is written down is extremely important. I think it's also a good idea going forward working with students to teach all methods and allow them a chance to get comfortable with all concepts.

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