# Introductory Percentages

Percentages are used in:

**bank savings, loans and credit cards****discounts and profits of store transactions****population increase and decrease**

It is helpful to remember that:

**"Per" means "divide" and "Cent" means "100"****To change a fraction to a decimal, divide using a calculator.****To change a decimal to a percent, multiply by 100.**

LEARN THESE OFF BY HEART | ||

FRACTION | DECIMAL | PERCENTAGE |

^{1}⁄_{2} | 0.5 | 50% |

^{1}⁄_{4} | 0.25 | 25% |

^{3}⁄_{4} | 0.75 | 75% |

^{1}⁄_{10} | 0.1 | 10% |

^{1}⁄_{5} | 0.2 | 20% |

^{3}⁄_{10} | 0.3 | 30% |

^{2}⁄_{5} | 0.4 | 40% |

^{3}⁄_{5} | 0.6 | 60% |

^{7}⁄_{10} | 0.7 | 70% |

^{4}⁄_{5} | 0.8 | 80% |

^{9}⁄_{10} | 0.9 | 90% |

1 | 1 | 100% |

## Example One - Changing a Fraction to a Percentage

Change ^{3}⁄_{8} to a percentage.

**Answer:**
^{3}⁄_{8} = 0.375 *(Use a calculator to divide.)*
^{3}⁄_{8} × 100 = 37.5%

0.375 × 100 = 37.5%

## Example Two - Changing a Percentage to a Decimal

Change 245% to a decimal.

**Answer:**

245% = 2.45 *(Divide by 100 or move the decimal point 2 places to the left.)*

## Example Three - Changing a Percentage to a Proper Fraction

Change 96% to a fraction.

**Answer:**

96% = ^{96}⁄_{100} = ^{24}⁄_{25} *(Simplify the fraction by dividing the numerator and the denominator by 4.)*

## Example Four - Changing a Percentage to a Mixed Number

Change 235% to a fraction.

**Answer:**

235%

= ^{235}⁄_{100}

= ^{47}⁄_{20} *(Simplify the fraction by dividing the numerator and the denominator by 5.)*

= 2 ^{7}⁄_{20}

## Questions

**Q1.** Change ^{7}⁄_{8} to a decimal and a percentage.
**Q2.** Change 24% to a decimal.
**Q3.** Change 48% to a fraction.

**Answers**
**A1.** 0.875
**A2.** 0.24
**A3.** ^{12}⁄_{25}

## Example Five - Finding Percent Change

**Divide the amount of change by the original amount.**

The International Whaling Commission estimates that Humpback Whale numbers have increased **from 50 000 to 55000** in 2009-2011.
What percent increase is this?

**Answer:**

Amount of increase = 55000 – 50000 = 5000 whales

Percent increase = | Amount of increase | × 100 |

Original Amount |

= | 5000 | × 100 |

50000 |

= 10% increase

## Did You Know That...?

This painting entitled "Red Vineyards" by Dutch painter, Vincent van Gogh, was the only painting he sold in his lifetime. It sold in 1890 for about $1500 and is now worth millions.

## Example Six - Finding the Original Amount

A **discount of 20%** for a soccer jersey was given at a sports store. This **discount is $13.00**. What was the original price before the discount?
*(Hint: Turn the fraction upside down and multiply.)*

**Answer:**

The original price is always 100%.

Original price = | 100 | × 43 |

20 |

= $65

## Questions

**Q1.** The introduction of the **Cane Toad** to Australia was a curse. It is poisonous, kills native wildlife, is a prolific breeder and has no predators.
From 1990 to 2010, the estimated area it inhabits has increased from 120 000 to 150 000 square kilometres. What percent increase is this?

**Q2.** The habitat of the **African Mountain Gorilla**, now an endangered animal, is being destroyed to mine Coltan, the **Rare Earth Metal** ore needed for
mobile 'phone technology. The population was estimated at 480 gorillas in 2010. This is a 25% decrease since 2003. What is the **original population** in 2003?

**Answers**
**A1.** 25% increase
**A2.** Current population is 75%; Original population was ^{100}⁄_{75} × 480 = 640 gorillas