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

1.	Change any fractions necessary so that all the fractions have a common denominator.
2.	Compare the numerators of the fractions found in Step One. The larger the numerator, the larger the fraction.
3.	Convert the fractions back into the form they were given in the question.

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

1.	Convert any mixed numbers into improper fractions.
2.	Change any fractions necessary so that all the fractions have a common denominator.
3.	Compare the numerators of the fractions found in Step Two. The larger the numerator, the larger the fraction.
4.	Convert the fractions back into the form they were given in the question. Note: Read carefully whether the question asks for your answer as an improper fraction or mixed number.

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.