Proportion

Four numbers a, b, c, d are in proportion if the ratio of the first pair equals the ratio of the second pair. The proportion is written a : b = c : d, \quad\text{or}\quad \frac ab = \frac cd, read "a is to b as c is to d."

The first and fourth terms (a and d) are the extremes; the second and third (b and c) are the means.

A proportion is an equation, so anything you may do to an equation you may do to a proportion. Multiplying both members of \frac ab = \frac cd by bd gives ad = bc:

In any proportion the product of the means equals the product of the extremes.

That gives a quick way to find a missing term.

Example 1. Find x if 3 : x = 7 : 9. The product of the means is 7x and of the extremes 27, so 7x = 27 and x = \frac{27}{7}.

Example 2. Find x if 5 : (x - 3) = 7 : (2x + 6). Then 7(x - 3) = 5(2x + 6), so 7x - 21 = 10x + 30 and x = -17.

When you type a proportion's terms, use parentheses around sums, as in 5 : (x - 3).

Try one: solve 2 : 5 = x : 15.

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Quick check

2 : 5 = x : 15

Exercises

0 of 14 solved

How to type math

Use ^ for powers (a^2), / for fractions ((a+b)/2), sqrt(x) for square roots, and cbrt(x) for cube roots. You can leave out the multiplication sign: 3ab means 3 \cdot a \cdot b. Mixed numbers like 4 1/2 work too. The preview under each box shows how your answer was read.

Find the value of x in each proportion.

\dfrac34 = \dfrac6x

\dfrac47 = \dfrac{16}{x}

\dfrac32 = \dfrac x5

3 : x = 7 : 9

x : 4 = 3 : 6

\dfrac43 = 2 : \dfrac1x

\dfrac23 = \dfrac{\frac1x}{4}

\dfrac{2}{\frac1x} = \dfrac{3\frac13}{4}

\dfrac1x : 2 = 3 : 4\tfrac12

\dfrac ab = \dfrac cx

a : b = c : \dfrac1x

\dfrac{a}{x^2} = \dfrac1x : a^3

4 : 3\tfrac13 = 3 : (x - 3)

5 : (x - 3) = 7 : (2x + 6)