RATIOS &
PROPORTIONS
A ratio compares two quantities in a chosen order. A proportion states that two ratios are equal, so the same multiplicative relationship is preserved as the quantities scale.
Comparing in a Fixed Order
The same ratio can be written in several forms. In every form, the order of the two quantities matters:
“For every 2 of the first quantity, there are 3 of the second.”
Unit Rate
A unit rate rewrites a ratio so the second quantity is 1. That makes comparisons such as price per item much easier.
Scale Drawings
A map scale such as 1 inch to 100 miles uses a constant ratio so distances can change size while proportional relationships are preserved.
The Ratio Machine
3 × 2 = 6
Cross Products
For a proportion with nonzero denominators, multiplying both sides by those denominators clears the fractions. This gives equal cross products. “Butterfly” is sometimes used as a mnemonic for remembering the diagonal pairs, but the equality comes from ordinary multiplication.
Reference & Check
Which of the following is an example of a Unit Rate?
Connect Forward
Equivalent ratios and unit rates connect scaling to fraction operations, percentages, and later algebraic proportions.