LESSON: Ordering Fractions

READ: Order Fractions Using Lowest Common Denominator

Order Fractions Using Lowest Common Denominator

We just learned how to compare fractions with different denominators. Sometimes, we need to write fractions in order from least to greatest or from greatest to least. If we have fractions with common denominators, this becomes very simple.

Example

Write in order from least to greatest. $\frac{4}{9},\frac{2}{9},\frac{8}{9},\frac{3}{9},\frac{6}{9}$

Since all of these fractions are written in ninths, the common denominator, we can use the numerators and arrange them in order from the smallest numerator to the largest numerator.

Our answer is $\frac{2}{9},\frac{3}{9},\frac{4}{9},\frac{6}{9},\frac{8}{9}$ .

How do we order fractions that do not have a common denominator?To do this, we will need to rewrite the fractions using a common denominator. This is the best way to know how to order the fractions.

Example

$\frac{2}{3},\frac{1}{4},\frac{1}{2}, \frac{5}{6}$

If we wanted to write these fractions in order from least to greatest, we would need to rewrite them so that they have a common denominator.

We can use the lowest common denominator (LCD) for 3, 4, 2 and 6. That number would be 12.

Next, we rewrite each fraction in terms of twelfths.

$\frac{2}{3}=\frac{8}{12}\\ \frac{1}{4}=\frac{3}{12}\\ \frac{1}{2}=\frac{6}{12}\\ \frac{5}{6}=\frac{10}{12}$

Our answer is $\frac{3}{12},\frac{6}{12},\frac{8}{12},\frac{10}{12}=\frac{1}{4},\frac{1}{2},\frac{2}{3},\frac{5}{6}$ .