qcalculate

Ratio Calculator

Simplify a ratio, share an amount in a ratio, find the missing number in a proportion, or use the rule of three for direct and inverse proportion, with every step shown.

Ratio (2 to 4 numbers)

Numbers can be whole, decimal (2.5) or fractions (3/4).

Simplest form

2 : 3

12 : 18 simplifies to 2 : 3. As 1 : n it is 1 : 1.5.

Show me how

All steps as text

    Tip: press ← and → to move between steps, or click any step.

    How to simplify a ratio

    1. If any term has decimals, multiply every term by 10, 100 or 1,000 to make them whole. With fractions, multiply by their lowest common denominator.
    2. Find the greatest common divisor (GCD) of the terms.
    3. Divide every term by the GCD. For example, 12 : 18 has GCD 6, so it simplifies to 2 : 3.

    To write a ratio as 1 : n, divide every term by the first: 2 : 3 is 1 : 1.5.

    How to share an amount in a ratio

    Add the terms to count the parts, divide the amount by the number of parts to get one part, then multiply each term by one part. To share 120 in the ratio 2 : 3 : 5: there are 10 parts, one part is 12, so the shares are 24, 36 and 60.

    Proportions and the rule of three

    In a proportion a : b = c : d, the products across are equal: a × d = b × c. So in 3 : 4 = 9 : x, 3 × x = 36 and x = 12.

    The rule of three answers questions like “if 5 kg cost 20, what do 8 kg cost?”. In direct proportion, find what 1 gives (20 ÷ 5 = 4), then multiply (8 × 4 = 32). In inverse proportion, such as “4 workers take 6 days; how long do 3 workers take?”, the product stays the same: 4 × 6 = 24, and 24 ÷ 3 = 8 days.

    Questions

    Can a ratio have decimals or fractions?

    Yes, but it is usually simplified to whole numbers. 1.5 : 2.25 becomes 150 : 225 after multiplying by 100, which simplifies to 2 : 3.

    Is a ratio the same as a fraction?

    A two-part ratio a : b compares the parts with each other, while a fraction compares a part with the whole. In 2 : 3, the first part is 2/5 of the whole, not 2/3.

    How do I know if a problem is direct or inverse proportion?

    Ask what happens when one amount doubles. If the other doubles too (twice the kilos, twice the price), it is direct. If the other halves (twice the workers, half the time), it is inverse.