Ratios and proportions

A ratio $a : b$ compares two amounts. Like fractions, ratios can be simplified by dividing both parts by the same number.

Sharing in a ratio

1. Add the parts of the ratio to find the total number of parts.
2. Divide the amount by the total parts to find one part.
3. Multiply one part by each number in the ratio.

For example, sharing 60 in the ratio $2 : 3$ gives 5 parts of 12 each, so the shares are 24 and 36.

Solving a proportion

If $a : b = c : x$, the cross products are equal, so $a \cdot x = b \cdot c$ and $x = \frac{bc}{a}$.