Proportions

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Proportions Calculator

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INTRO

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A ratio is a comparison of two quantities, and a proportion is an equation that lets us know two ratios are equal to each other.

So when we solve a proportion, we’re really just solving an equation, and we find that it’s easiest to do this when the ratios are written as fractions.

The top and bottom of each side of the equation form the 4 corners of an x, which means we can cross-multiply to solve for the unknown.

\frac{2}{3}

=

\frac{4}{x}

2 \times x

=

4 \times 3

2 x

=

12

\frac{2 x}{2}

=

\frac{1 2}{2}

x

=

6

Remember, we can only cross-multiply when we have two ratios or fractions that are equal to each other - x marks the spot!

We can also use cross-multiplication to double check that two ratios are equivalent and form a proportion:

	$\frac{2}{3} ? \frac{4}{6}$	$\frac{2}{5} ? \frac{1}{3}$
Cross-Multiply	$\frac{2}{3}$ $=$ $\frac{4}{6}$ $2 \times 6$ $=$ $4 \times 3$ $12$ $=$ $12$	$\frac{2}{5}$ $=$ $\frac{1}{3}$ $2 \times 5$ $=$ $1 \times 3$ $10$ $\neq =$ $3$
Result	✅ Equal / Proportion	Not equal / Not a proportion

Check out our

Calculator

or explore our

Lesson

and

Practice

sections to learn more about solving proportions problems.

You can also use the Quick Links menu on the left to jump to a section of your choice.

You can also use the Quick Links dropdown above to jump to a section of your choice.

KEY STEPS

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How to Solve a Proportion

Step 1. Write the ratios as fractions.

If the ratios are already in fraction format, continue to Step 2.

a : b = c : d ⟹ \frac{a}{b} = \frac{c}{d}

a to b is equal to c to d ⟹ \frac{a}{b} = \frac{c}{d}

Step 2. Cross-multiply if x marks the spot.

The top and bottom of each side of the equation form the 4 corners of an x.

This means we can multiply across the diagonals, and the products are equal.

\frac{a}{b}

=

\frac{c}{d}

a \times d

=

c \times b

Step 3. Divide.

If solving for an unknown, divide both sides of the equation by the number it’s being multiplied by.

LESSON

— Solving Proportions

PRACTICE

— Solving Proportions

CONCLUSION

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