### Answers − Percentage Change

#### 1. The original price is 500 and the new price is 700.

#### Find the percentage increase

(a) the increase amount is 700 − 500 = 200 |

(b) the percentage as a fraction is ^{200}/_{500} = ^{2}/_{5} |

(c) 100 ÷ 5 = 20 (where 5 is the demoninator of the fraction) |

(d) ^{2}/_{5} × ^{20}/_{20} = ^{40}/_{100} = 40% |

So 40% increase in price |

#### 2. The original price is 470 and the new price is 564.

#### Find the percentage increase

(a) the increase amount is 564 − 470 = 94 |

(b) the percentage as a fraction is ^{94}/_{470} = ^{1}/_{5} |

(c) 100 ÷ 5 = 20 (where 5 is the demoninator of the fraction) |

(d) ^{1}/_{5} × ^{20}/_{20} = ^{20}/_{100} = 20% |

So 20% increase in price |

#### 3. The original price is 50 and the new price is 40.

#### Find the percentage decrease

(a) the decrease amount is 50 − 40 = 10 |

(b) the percentage as a fraction is ^{10}/_{50} = ^{1}/_{5} |

(c) 100 ÷ 5 = 20 (where 5 is the demoninator of the fraction) |

(d) ^{1}/_{5} × ^{20}/_{20} = ^{20}/_{100} = 20% |

So 20% decrease in value. |

#### 4. The original price is 1100 and the new price is 990.

#### Find the percentage decrease

(a) the decrease amount is 1100 − 990 = 110 |

(b) the percentage as a fraction is ^{110}/_{1100} = ^{1}/_{10} |

(c) 100 ÷ 10 = 10 (where 10 is the demoninator of the fraction) |

(d) ^{1}/_{10} × ^{10}/_{10} = ^{10}/_{100} = 10% |

So 10% decrease in value. |

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