GCSE(F),

Percentages, fractions and decimals can be freely interchanged. A percentage can be written as a fraction (38% is `frac(38)(100)` which simplifies to `frac(19)(50)`). The fraction can also be converted to a decimal number by a division.

To turn a percentage into a:

• fraction: make the percentage the numerator and 100 the denominator;

• decimal: divide by 100.

To turn a decimal into a:

• fraction: multiply numerator and denominator by 10s until the decimal point has been removed;

• percentage: multiply by 100.

To turn a fraction into a:

• decimal: divide the numerator by the denominator;

• percentage: divide the numerator by the denominator and multiply by 100.

Common fractions, percentages and decimals should be known:

Fraction | Decimal | Percentage |
---|---|---|

0 | 0 | 0 |

`frac(1)(10)` | 0.1 | 10% |

`frac(1)(8)` | 0.125 | 12.5% |

`frac(1)(5)` | 0.2 | 20% |

`frac(1)(4)` | 0.25 | 25% |

`frac(1)(3)` | 0.33 (rounded) | 33% (rounded) |

`frac(1)(2)` | 0.5 | 50% |

`frac(3)(4)` | 0.75 | 75% |

`frac(1)(1)` = 1 | 1.0 | 100% |

1. Write `frac(3)(8)` as a percentage.

Answer: 37.5%

`frac(1)(8)` is 12.5%. Three times that is 3 x 12.5 = 37.5%

2. Jon eats `frac(1)(4)` of a bar of chocolate. Sally eats 30% of the same bar. How much of the bar is left? Write the answer as a decimal.

Answer: 0.45

`frac(1)(4)` is 0.25. 30% is equivalent to 0.3. Added together this totals to 0.55. The question asked for the remainder: 1 - 0.55 = 0.45.

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