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.
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:
|Result||✅ Equal / Proportion||Not equal / Not a proportion|
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How to Solve a Proportion
Step 1. Write the ratios as fractions.
Step 2. Cross-multiply if x marks the spot.
Step 3. Divide.
A proportion is an equation that lets us know two ratios are equal to each other.
x marks the spot!
Do we have to cross-multiply when the unknown variable is in the top?
While we can never go wrong with using cross-multiplication to solve proportions, if the unknown variable is in the top, we can just multiply both sides of the equation by its bottom.