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the ratio of $a$ to $b,$where $b$ is a non-zero number.

$Fractionba Colon Notationa:b $

The ratio $a:b$ means that for every $a$ units of one quantity, there are $b$ units of another quantity. Ratios can be part-to-part or part-to-whole.

Part-To-Part | Part-To-Whole | |
---|---|---|

Explanation | Describes how two different groups are related | Describes the relationship between a specific group to a whole |

Example $1$ | The number of sophomores to freshmen on the basketball team is $7:15.$ | The number of sophomores to all basketball team members is $7:22.$ |

Example $2$ | The number of mangoes to jackfruits the vendor has is $10:20.$ | The number of mangoes to all fruits the vendor has is $10:42.$ |

$Tearrik’s Ratio1527 Zain’s Ratio2545 $

These ratios can be simplified by finding the greatest common factor of their numerator and denominator. That factor can then be used to rewrite each ratio. Fraction Form | Greatest Common Factor | Rewrite | Simplify | |
---|---|---|---|---|

Tearrik | $1527 $ | $GCF(27,15)=3$ | $5⋅3 9⋅3 $ | $59 $ |

Zain | $2545 $ | $GCF(45,25)=5$ | $5⋅5 9⋅5 $ | $59 $ |

These ratios are equivalent because both simplify to $59 .$ Equivalent ratios can be created by multiplying or dividing the numerator and denominator of a ratio by the same number.