How to Divide an Amount in a Given Ratio (with Money, Time and Mixes)

Splitting a bill by income, sharing profit between partners, dividing a work shift or mixing two liquids in a set proportion are all the same problem: dividing a total in a given ratio. One method, the parts method, solves all of them.

The parts method

Add the terms of the ratio to get the total number of parts.
Divide the amount by the number of parts to find the value of one part.
Multiply each ratio term by the value of one part.
Check that the results add up to the original amount.

Example 1: two people

Share $1,200 in the ratio 5 : 3.

Total parts: 5 + 3 = 8
One part: 1,200 ÷ 8 = $150
Shares: 5 × 150 = $750 and 3 × 150 = $450
Check: 750 + 450 = 1,200 ✓

Example 2: three people

Three partners invested $20,000, $30,000 and $50,000 and agree to split $18,000 of profit in proportion to their investment. The ratio is 20 : 30 : 50, which simplifies to 2 : 3 : 5. There are 10 parts, each worth $1,800, so the shares are $3,600, $5,400 and $9,000.

Example 3: time

A 9-hour project is split between design and building in the ratio 1 : 2. There are 3 parts of 3 hours each: 3 hours of design and 6 hours of building.

Example 4: a mix

You need 5 liters of a cleaning solution mixed 1 : 4 concentrate to water. There are 5 parts of 1 liter each, so use 1 liter of concentrate and 4 liters of water. Watch the wording: "1 : 4" usually means 1 part to 4 parts (5 parts in total), while "1 in 5" means 1 part out of 5 total. For this mix they happen to be the same, but "1 in 4" would be 1 part concentrate and 3 parts water.

When the amounts don't divide evenly

Sharing $100 in the ratio 1 : 2 gives $33.33… and $66.66…. With money you have to round, and rounding both shares can leave a cent missing or extra. A fair approach:

Round each share down to the cent.
Give any leftover cents, one at a time, to the shares with the largest dropped fractions.

For $100 at 1 : 2, the shares become $33.33 and $66.67. The ratio calculator shows the exact values so you can decide how to round.

Working backward from one share

If you know one person's share and the ratio, you can find the total. Two siblings share an inheritance in the ratio 3 : 5, and the smaller share is $24,000. One part is 24,000 ÷ 3 = $8,000, so the larger share is $40,000 and the total is $64,000.

Common mistakes

Dividing by a single term instead of the total number of parts.
Mixing up the order: in "share in the ratio 2 : 3 between Ana and Ben," Ana gets 2 parts.
Using an unsimplified ratio inconsistently: 20 : 30 : 50 and 2 : 3 : 5 give the same answer, as long as you use the same ratio throughout.

Shares as percentages

Each share's percentage is its term divided by the total parts. In 2 : 3 : 5, the shares are 20%, 30% and 50%. Percentages are useful when the total changes month to month, such as splitting utility bills.

To reduce a ratio before dividing, see how to simplify ratios. For problems where you compare two ratios, try the proportion calculator.