Comparing fractions

​You can compare two fractions to see which one is greater.

Comparing fractions with like denominators

When two fractions have the same denominator, the fraction with the greater numerator is the greater fraction.
Let's try it with 2/4 and 3/4 . Since 2<3, then 2/4 < 3/4 . You can look at the models to see why.

​In both models, the whole is broken into fourths. But 2/4 has only 2 parts shaded, and 3/4 has 3 parts shaded. So, 2/4 is less than 3/4 .

​Comparing fractions with like numerators

When two fractions have the same numerator, the fraction with the smaller denominator is the greater fraction.
Let's try it with 1/4 and 1/10 . Since 4<10, then 1/4 > 1/10 . You can look at the models to see why.

​In both models, one part of the whole is shaded. But since fourths are larger than tenths, 1/4 is greater than 1/10 .
Let's try it with 3/4 and 3/5 , too.

​Both models have three parts shaded. But since fourths are larger than fifths, 3/4 is greater than 3/5 .

​Comparing fractions using a benchmark

You can use a reference number called a benchmark to compare fractions.
As an example, let's compare 3/5 and 3/8 using 1/2 as a benchmark. Compare each fraction to 1/2 .

​3/5 is greater than the benchmark, and 3/8 is less than the benchmark. So, 3/5 is greater than 3/8 .

​Comparing fractions by making equivalent fractions

To compare fractions with unlike denominators and numerators, use equivalent fractions! You can rename the fractions to have the same denominator.
Let's try it with 3/4 and 5/6 . First, rename the fractions using a common denominator.

​Now, compare 9/12 and 10/12 . They have the same denominator, so compare the numerators. Since 9<10, then 9/12 < 10/12 .