Put fractions in order

Key Notes :

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.

A circle split into fourths with two of the fourths shaded. Another circle split into fourths with three of the fourths shaded. Under the circles is the inequality two fourths is less than three fourths.

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.

A circle split into fourths with one of the fourths shaded. This circle is labeled "one fourth". Another circle split into tenths with one of the tenths shaded. This circle is labeled "one tenth". Under the circles is the inequality one fourth is greater than one tenth.

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.

A circle split into fourths with three of the fourths shaded. This circle is labeled "three fourths". Another circle split into fifths with three of the fifths shaded. This circle is labeled "three fifths". Under the circles is the inequality three fourths is greater than three fifths.

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.

A fraction tape diagram of three fifths above a tape diagram of one half. These two diagrams are labeled with the inequality three fifths is greater than one half.
A tape diagram of three eighths above a tape diagram of one half. These two diagrams are labeled with the inequality three eighths is less than one half.

3/5 is greater than the benchmark, and 3/8 is less than the benchmark. So, 35 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.

Learn with an example

🙂Put these fractions in order from largest to smallest.

  • 6/11
  • 6/8
  • 6/9

These shapes show the fractions from largest to smallest:

Each shape has 6 parts shaded. Notice that each shape has smaller parts than the previous shape. The total shaded part of each shape is smaller than in the previous shape.

The fractions in order from largest to smallest are:

  • 6/8
  • 6/9
  • 6/11

🙂 Put these fractions in order from smallest to largest.

  • 4/10
  • 2/10
  • 3/10
  • 9/10

These shapes show the fractions from smallest to largest:

Each shape has 10 parts. Notice how each shape has more parts shaded than the previous shape.

The fractions in order from smallest to largest are:

  • 2/10
  • 3/10
  • 4/10
  • 9/10

🙂 Put these fractions in order from smallest to largest.

  • 6/11
  • 6/10
  • 6/7
  • 6/8

These shapes show the fractions from smallest to largest:

Each shape has 6 parts shaded. Notice that each shape has larger parts than the previous shape. The total shaded part of each shape is larger than in the previous shape.

The fractions in order from smallest to largest are:

  • 6/11
  • 6/10
  • 6/8
  • 6/7

Let’s try some problems!