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This ratio calculator allows you to divide a value by a ratio. The Divide Ratio Calculator is designed for those who are learning ratios and allows division by a simple format ratio (i.e. 2:7), if you are already confident in calculating ratio division or looking to calculate more complete ratio division (i.e. 975 ÷ 4:7:19:23:7) then we suggest you use this Ratio Division Calculator. This ratio calculator includes a step by step breakdown of the ratio calculations along with a simple ratio division formula that helps you to calculate ratio division manually. This ratio calculator is a good calculator for checking your ratio calculations when completing math homework and math coursework.

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Ratio Division Formula | |
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R_{r} = R_{n} × M : R_{d} × M | |

Ratio Division Values | |

R_{n} = | Ratio Numerator |

R_{d} = | Ratio Denominator |

R_{s} = R_{n} + R_{d}R _{s} = + R _{s} = | Ratio Sum |

a = | Amount to Divide |

M = a ÷ R_{s}M = ÷ M = | Multiplier |

Ratio Division Calculation | |

R_{r} = R_{n} × M : R_{d} × M | |

R_{r} = × : × | |

R_{r} = : |

Please note that the formula for each ratio calculation along with detailed calculations for the full ratio division process is shown further below this page. As you enter the specific factors of each divide ratio calculation, the Divide Ratio Calculator will automatically calculate the results and update the formula elements with each element of the divide ratio calculation. You can then email or print this divide ratio calculation as required for later use.

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Dividing ratios is quite a simple math calculation once you are familiar with the approach. The step by step guide below details how to divide ratios, these steps are also shown in the calculations within the "Divide Ratio Calculator" so that you can manual calculate the ratio values and then compare your ratio division workings with those produced by the calculator. This is useful for checking your math homework and coursework to ensure you are calculating the division of ratios correctly. Lets look at the steps involved in ratio division calculation, we will then cover each step in detail with a practical example and clear ratio division formula that you can use for manual math calculation:

- Using pen and paper, write down the amount (a) that you wish to divide and the ratio (R)
- Add the value of the ratio numerator to the denominator, we will then refer to the sum of the ratio as the "Ratio Sum".
- Divide the amount you wish to divide by the Ratio Sum. We will refer to this number as the "Multiplier"
- Multiply the ratio numerator by the "multiplier"
- Multiply the ratio denominator by the "multiplier"
- Write the multiplied ratio in ratio form using the multiplied numerator and denominator

Congratulations, you have now divided a ratio. We will now repeat the steps above using an example and provide a formula for you to use for dividing ratios, we also use this ratio division formula in the calculator and results so you can compare your manual calculations.

In our ratio division example, we use simple numbers to make it easy to understand how the division and multiplication occurs within each calculation. Let's say we wish to divide 200 by the ration 3:7

- 200 3:7 (we write down the amount and ratio)
- 3 + 7 = 10 (We then add the ratio numerator to the denominator to calculate the "Ratio Sum")
- 200 ÷ 10 = 20 (Now we divide the amount by the Ratio Sum to calculate the "Multiplier")
- 3 × 20 = 60 (then we multiply the ratio numerator by the "multiplier")
- 7 × 20 = 140( and our final calculation is to multiply the ratio denominator by the "multiplier")
- 60:140 (we know write our ratio division calculation as our final answer)

The above steps can be written using the following ratio division formula:

R_{r} = R_{n} × M : R_{d} × M

where:

- R
_{r}: Divided Ratio result - R
_{n}: Ratio Numerator - R
_{d}: Ratio Denominator - R
_{s}: Ratio Sum (R_{n}+ R_{d}) - M : Multiplier