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Mathematics · pattern A, Numeric fields

Simplify a ratio and divide a total by it.

Enter two ratio parts and a total to see the simplified ratio, each share and the value of one part — the step that makes the division obvious.

Inputs

The formula used

share = total × part ÷ sum of parts

Divide the total by the sum of the parts to get one unit, then multiply. This method scales to any number of parts without modification.

First share

180.0000

Second share
300.0000
Value of one part
60.0000
Simplified ratio
3 : 5
Shares as percentages
37.50% and 62.50%
Ratio as a decimal
0.60000
Difference between the shares
120.0000

A ratio is not a fraction of the whole.

A ratio of 3 : 5 means three parts to five, so the first share is three eighths of the total rather than three fifths. Reading the first number as a fraction of the whole is the standard error, and finding the value of one part first is what prevents it.

Questions about ratio

Ratio or proportion?
A ratio compares two quantities; a proportion states that two ratios are equal and is solved by cross-multiplication.
How do three-part ratios work?
Identically: divide by the sum of all three parts, then multiply by each. The method does not care how many parts there are.
Should ratios always be simplified?
Usually, though recipes and mixes often need the actual quantities rather than the reduced form.

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A calculator handles the arithmetic. It cannot teach you the method.

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Arithmetic runs in double-precision floating point, so results beyond about fifteen significant figures are not exact. Where a question wants an exact fraction or surd, keep the exact form rather than a decimal.