LESSON: Ordering Fractions

READ: Compare Fractions Using Lowest Common Denominator

Compare Fractions Using Lowest Common Denominator

If you think back to our last lesson on equivalent fractions, you may have noticed that some fractions have different denominators. Remember that when we are talking about the denominator we are talking about the bottom number of the fraction. The numerator refers to the top number of the fraction. Anyway, sometimes we have fractions with different denominators.

Example

$\frac{1}{4}$ and $\frac{2}{3}$

Here we have two different fractions with two different denominators. Remember that the denominator lets us know how many parts one whole has been divided into. Here the first fraction, one-fourth has been divided into four parts. The second fraction, two-thirds has been divided into three parts. In this example, if we wanted to compare the size of these two fractions, we would have two different fractions to compare.

How do we compare fractions?

When we compare two fractions, we want to figure out which fraction is larger and which one is smaller. If we have two fractions with the same denominator, it becomes easier to determine which fraction is greater and which one is less.

Example

$\frac{1}{5} {\underline{\;\;\;\;\;\;\;\;\;}} \frac{3}{5}$

We want to use greater than >, less than < or equal to = to compare these two fractions. This one is easy because our denominators are the same. They have common or like denominators. Think about this in terms of pizza.

If both pizzas were divided into five pieces and one person has one-fifth of the pizza and the other person has three-fifths of the pizza, who has more pizza? The person with three-fifths of the pizza has more pizza. Therefore, we can compare those fractions like this.

$\frac{1}{5} < \frac{3}{5}$

How do we compare fractions that do not have common or like denominators? When we are trying to compare two fractions that do not have like denominators, we need to rewrite them so that they have a common denominator.

Let’s look at the two fractions we had earlier.

$\frac{1}{4} \underline{\;\;\;\;\;\;\;\;} \frac{2}{3}$

We want to compare these fractions, but that is difficult because we have two different denominators. We can rewrite the denominators by finding the least common multiple of each denominator. This least common multiple becomes the lowest common denominator.

First, write out the multiples of 4 and 3.

4, 8, 12

3, 6, 9, 12

I can stop there because twelve is the lowest common denominator of both 4 and 3.

Next, we rewrite the each fraction in terms of twelfths. This means we make an equivalent fraction to one-fourth in terms of twelfths, and we make an equivalent fraction to two-thirds in terms of twelfths.

$\frac{1}{4} = \frac{}{12}$

Remember back to creating equal fractions? We multiplied the numerator and the denominator by the same number to create the equal fraction. Well, half of our work is done for us here. Four times three is twelve. We need to complete our equal fraction by multiplying the numerator by 3 too.

$\frac{1}{4} = \frac{3}{12}$

Now we can work on rewriting two-thirds in terms of twelfths.

$\frac{2}{3} = \frac{8}{12}$

Now that both fractions have been written in terms of twelfths, we can compare them.

$\frac{3}{12} < \frac{8}{12}$

$\frac{1}{4} < \frac{2}{3}$