**Solving Proportions**

By definition, ratios must be the same in order for them to be proportionate. Using the process of cross-multiplication we are able to prove if any given set of fractions are proportionate. In solving proportions, you use the same process. In these problems, you are trying to find the value which makes the fractions proportionate.

__Example 1:__

3/n and 5/15

Step 1: Set-up cross multiplication | 3*15 = 5*n |

Step 2: Solve for the variable. | 45 = 5*n |

/5 /5 | |

Divide both sides by 5 | |

9 = n | |

Solution: value of n is 9 |

__Example 2:__

Find the value of y which makes the fractions proportionate.

y/4 and 4/3 | |

Set-up cross multiplication: | y * 3 = 4 * 4 |

3y = 16 | |

Divide each side by 3 | /3 /3 |

y = 16/3 or 5.33 |

__Example 3:__

n/8 and 13/2

Set-up cross multiplication: | n * 2 = 8 * 13 |

2n = 104 | |

/2 /2 | |

n = 52 |

__Example 4:__

8/ x + 2 and 2/3

set-up cross multiplication: | 8 * 3 = 2* (x+2) |

24 = 2x + 4 | |

-4 -4 | |

20 = 2x | |

/2 /2 | |

Final solution | x = 10. |

You can verify by setting up the proportion:

8/(12) and 2/3

Cross multiply: 8 * 3 ? 12 * 2 --> 24 = 24. Since both sides multiply to 24, both fractions are proportionate.