# 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.*