What is the difference between a ratio and a fraction?

A ratio compares two parts to each other; a fraction compares one part to the whole. A 2:3 mix means 2 parts in every 5, which is the fraction 2/5.

How do I scale a ratio up?

Multiply both sides by the same number. A 2:3 ratio needing 10 units of the first part becomes 10:15 — the relationship holds as long as both sides move together.

Why express a ratio as 1 to n?

It makes two ratios directly comparable. 16:24 and 21:31 are hard to rank by eye, but 1:1.5 against 1:1.48 settles it immediately.

Math

Ratio Calculator

Enter two quantities to see the ratio reduced, split as percentages and expressed as 1 to n.

The formula

simplified = a ÷ gcd(a, b) : b ÷ gcd(a, b)

share of a = a ÷ (a + b) × 100

Worked example

A 16 : 24 mix

gcd(16, 24) = 8
16 ÷ 8 = 2 and 24 ÷ 8 = 3, so 2 : 3
16 ÷ 40 = 40% and 24 ÷ 40 = 60%

Where this goes wrong

Mixing part-to-part with part-to-whole

A 2:3 ratio means five parts in total, so the first share is two fifths — 40%, not 50% and not 66%. Reading a ratio as if the second number were the total is the single commonest ratio error, and it shows up wherever mixes and splits are written down.

Questions

What is the difference between a ratio and a fraction?: A ratio compares two parts to each other; a fraction compares one part to the whole. A 2:3 mix means 2 parts in every 5, which is the fraction 2/5.
How do I scale a ratio up?: Multiply both sides by the same number. A 2:3 ratio needing 10 units of the first part becomes 10:15 — the relationship holds as long as both sides move together.
Why express a ratio as 1 to n?: It makes two ratios directly comparable. 16:24 and 21:31 are hard to rank by eye, but 1:1.5 against 1:1.48 settles it immediately.