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Last modified on July 18th, 2024

To convert a percent to a fraction, we remove the ‘%’ sign, divide by 100, and then simplify the resulting fraction.

Let us convert 75% to a fraction.

**Removing the ‘%’ Sign and Dividing by 100**

75% = ${\dfrac{75}{100}}$

**Simplifying **

${\dfrac{75\div 25}{100\div 25}}$ = ${\dfrac{3}{4}}$

Thus, 75% = ${\dfrac{3}{4}}$

Here are some more percent-to-fraction conversions.

20% = ${\dfrac{20}{100}}$ = ${\dfrac{20\div 20}{100\div 20}}$ = ${\dfrac{1}{5}}$

40% = ${\dfrac{40}{100}}$ = ${\dfrac{40\div 20}{100\div 20}}$ = ${\dfrac{2}{5}}$

60% = ${\dfrac{60}{100}}$ = ${\dfrac{60\div 20}{100\div 20}}$ = ${\dfrac{3}{5}}$

80% = ${\dfrac{80}{100}}$ = ${\dfrac{80\div 20}{100\div 20}}$ = ${\dfrac{4}{5}}$

To convert mixed numbers, we first convert them to improper fractions, remove the % sign, and divide by 100.

Let us now convert ${1\dfrac{2}{5}}$ %

**Converting the Mixed Number to an Improper Fraction**

${1\dfrac{2}{5}}$ % = ${\dfrac{\left( 1\times 5\right) +2}{5}}$ % = ${\dfrac{7}{5}}$ %

**Removing the ‘%’ Sign and Dividing by 100**

${\dfrac{\dfrac{7}{5}}{100}}$

= ${\dfrac{7}{5}\times \dfrac{1}{100}}$

= ${\dfrac{7}{500}}$, which can not be simplified or reduced further.

Thus, ${1\dfrac{2}{5}}$ % = ${\dfrac{7}{500}}

To convert any decimal number, we first remove the %sign, divide by 100, and then multiply both numerator and denominator by 10.

Let us now convert 12.5% to fractional form.

**Removing the ‘%’ Sign and Dividing by 100**

${\dfrac{12\cdot 5}{100}}$

**Multiplying the Numerator and Denominator by 10 or Powers of 10 **

Here, we multiply both the numerator and the denominator by 10 for each digit after the decimal point.

Since there is 1 decimal digit in 12.5

On multiplying the numerator and the denominator by 10,

${\dfrac{12\cdot 5\times 10}{100\times 10}}$

= ${\dfrac{125}{1000}}$

= ${\dfrac{125\div 125}{1000\div 125}}$

= ${\dfrac{1}{8}}$

Here is a percent-to-fraction conversion table for your use.

Percent | Fraction |
---|---|

1% | ${\dfrac{1}{100}}$ |

2% | ${\dfrac{1}{50}}$ |

4% | ${\dfrac{1}{25}}$ |

5% | ${\dfrac{1}{20}}$ |

10% | ${\dfrac{1}{10}}$ |

12% | ${\dfrac{3}{25}}$ |

12.5% | ${\dfrac{1}{8}}$ |

20% | ${\dfrac{1}{5}}$ |

25% | ${\dfrac{1}{4}}$ |

30% | ${\dfrac{3}{10}}$ |

40% | ${\dfrac{2}{5}}$ |

50% | ${\dfrac{1}{2}}$ |

60% | ${\dfrac{3}{5}}$ |

70% | ${\dfrac{7}{10}}$ |

75% | ${\dfrac{3}{4}}$ |

80% | ${\dfrac{4}{5}}$ |

90% | ${\dfrac{9}{10}}$ |

100% | ${1}$ |

**Convert ${12\dfrac{1}{2}}$ % to fraction.**

Solution:

${12\dfrac{1}{2}}$ %

= ${\dfrac{\left( 12\times 2\right) +1}{2}}$ %

= ${\dfrac{25}{2}}$ %

= ${\dfrac{\dfrac{25}{2}}{100}}$

= ${\dfrac{25}{2}\times \dfrac{1}{100}}$

= ${\dfrac{1}{8}}$

Thus, ${12\dfrac{1}{2}}$ % = ${\dfrac{1}{8}}$

**Convert 68% to fraction.**

Solution:

Here, 68% = ${\dfrac{68}{100}}$ = ${\dfrac{68\div 4}{100\div 4}}$ = ${\dfrac{17}{25}}$

Last modified on July 18th, 2024