How to Split an Amount in a Given Ratio

Splits a total in the ratio a : b. The two shares are total × a ÷ (a + b) and total × b ÷ (a + b).

Explanation

Proportional distribution cuts a total into shares that follow a given ratio. Divide the total by the sum of the ratio terms, then multiply by each term.

A = S \times \dfrac{a}{a + b} \qquad B = S \times \dfrac{b}{a + b}

$S$ is the total to be shared
$a$ and $b$ are the two terms of the ratio
$A$ and $B$ are the resulting shares

The sum $a + b$ counts the equal parts the total is cut into, so $\dfrac{a}{a + b}$ is the fraction of the total that goes to the first share.

Example

Split a total of 1200 in the ratio 2 : 3. The terms add to $2 + 3 = 5$ , so $A = 1200 \times \dfrac{2}{5} = 480$ and $B = 1200 \times \dfrac{3}{5} = 720$ .

Notes

Do not multiply the total by 2 and 3 directly. The multipliers are the fractions $\dfrac{2}{5}$ and $\dfrac{3}{5}$ , not the bare ratio terms.

Scaling a ratio leaves it unchanged. The ratios 2 : 3, 4 : 6 and 20 : 30 all divide a total in exactly the same way, so use whichever numbers are easiest to read.

The shares always add back up to the total: $480 + 720 = 1200$ . If yours do not, something has gone wrong.

If both terms are 0 their sum is 0, there are no parts to hand out, and the split is undefined.