What this calculates
This does two jobs. Simplify reduces a ratio such as 12 : 18 to its lowest terms, and also gives it as a single decimal and as each part's share of the whole. Find the missing term solves a proportion a : b = c : x for x — the way you scale a recipe, a map or a screen size. Each step of the working is shown.
The formula
Lowest terms
a : b = (a ÷ g) : (b ÷ g), where g = gcd(a, b)Missing term
a : b = c : x, so x = b × c ÷ aEach part's share
first share = a ÷ (a + b) × 100%g is the greatest common divisor — the largest whole number both terms divide by. When a term has decimals, both are first multiplied by the same power of ten to make them whole.
Worked example
To find the missing term in 2 : 3 = 10 : x, cross-multiply: x = 3 × 10 ÷ 2 = 15. A 16 : 9 screen 1,920 pixels wide is 9 × 1,920 ÷ 16 = 1,080 pixels high.
When to use it, and the mistakes to avoid
Use it to reduce a ratio for homework, to split money or ingredients in a fixed ratio, to scale a recipe or a drawing, and to work out a screen or photo size from its aspect ratio.
The mistakes that cost the most:
- Stopping before lowest terms. 12 : 18 halves to 6 : 9, but both still divide by 3 — the simplest form is 2 : 3.
- Swapping the order. 2 : 3 and 3 : 2 are different ratios. Keep the terms in the order the question gives them.
- Cross-multiplying the wrong pair. In a : b = c : x, x is b × c ÷ a — not a × c ÷ b. Check it: both sides must reduce to the same ratio.
- Reading a ratio as a fraction. A 2 : 3 split gives the first part 2/5 of the whole, not 2/3.
- Mixing units. Put both terms in the same unit first — 50 cm : 2 m is 50 : 200, or 1 : 4.
FAQ
How do you simplify a ratio?
Divide both terms by their greatest common divisor - the largest number that divides both exactly. For 12 : 18 that is 6, so 12 : 18 simplifies to 2 : 3. When the terms share no divisor but 1, the ratio is already in lowest terms, like 16 : 9.
How do you simplify a ratio with decimals?
Multiply both terms by the same power of ten until they are whole numbers, then reduce. 1.5 : 2.5 times 10 is 15 : 25, and dividing both by 5 gives 3 : 5.
How do you find the missing term in a proportion?
Cross-multiply and divide. In a : b = c : x, the missing term is x = b × c ÷ a. For 2 : 3 = 10 : x, x = 3 × 10 ÷ 2 = 15.
What is the difference between a ratio and a fraction?
A ratio compares two parts with each other; a fraction compares a part with the whole. In a ratio of 2 : 3 there are 5 parts in all, so the first part is 2/5 of the whole - 40% - and the second is 3/5, or 60%.
How do I work out a screen size from an aspect ratio?
Treat it as a proportion. A 16 : 9 screen that is 1,920 pixels wide is 16 : 9 = 1,920 : x high, so x = 9 × 1,920 ÷ 16 = 1,080 pixels.
Why can't a term of a ratio be zero?
A ratio compares two amounts, and a zero amount has nothing to compare. Finding a missing term would also mean dividing by the first term, and dividing by zero has no answer, so the calculator asks for amounts above zero.