Ratio, proportion & variation

A ratio tells us how many parts of one quantity correspond to each part of another. To work with ratios, write them as a fraction and treat the two quantities as proportional: if $a:b=c:d$, then $\frac{a}{b}=\frac{c}{d}$, so $a\cdot d=b\cdot c$. When a total amount is given, first split the total into the same number of parts as the ratio, then multiply each part by the appropriate factor. This method lets you find any missing piece—whether it’s the amount of a ingredient, the number of objects, or a share of money—by setting up a simple equation and solving for the unknown.