Comparing and ordering fractions greater than 1

In a nutshell

To compare or order fractions greater than 1, the fractions must have a common denominator.  Mixed numbers should be changed to improper fractions to make comparison easier.

Comparing improper fractions

Procedure

Example 1

Which is larger $$\frac{11}{10}$$ or $$\frac{6}{5}$$?

Change the fraction with the smaller denominator so both fractions have a common denominator:

$$\frac{6\times2}{5\times2}=\frac{12}{10}$$​​

Compare the numerators of the two fractions:

$$12 > 11$$​ therefore $$\frac{12}{10}>\frac{11}{10}$$​

Convert the fraction ($$\frac{12}{10}$$) back into the form given in the question.

$$\frac{6}{5}>\frac{11}{10}$$​ so $$\underline{\frac{6}{5}}$$ is the larger fraction.

Comparing mixed numbers

procedure

Example 2

Which is larger $$2\frac{2}{3}$$ or $$2\frac{5}{6}$$? Give your answer as a mixed number.

Convert the mixed numbers into improper fractions:

$$2\frac{2}{3}= \frac{8}{3}$$​​

$$2\frac{5}{6}=\frac{17}{6}$$​​

Change the fraction with the smaller denominator so both fractions have a common denominator:

$$\frac{8\times2}{3\times2} = \frac{16}{6}$$​​

Compare the numerators of the two fractions:

$$17 > 16$$​ therefore $$\frac{17}{6} > \frac{16}{6}$$​

Change the fraction back into a mixed number in the form given in the question.

$$2\frac{5}{6}>2\frac{2}{3}$$​ so $$\underline{2\frac{5}{6}}$$ is the larger fraction.

Note: Read the question carefully to check whether it asks for the larger or smaller fraction.