SAT Math: Ratios and Proportions
38+ practice questions in Praczo
The concept, explained
- 1
A ratio compares two quantities: a:b or a/b. A proportion states two ratios are equal: a/b = c/d.
- 2
To solve a proportion, cross-multiply: if a/b = c/d, then ad = bc.
- 3
Scale problems use proportions: if a map uses 1 inch = 50 miles, then 3 inches = 150 miles.
- 4
Part-to-whole ratios: if the ratio of boys to girls is 3:5, boys make up 3/(3+5) = 3/8 of the total.
- 5
When a ratio changes, set up a new proportion rather than assuming values scale linearly in unexpected ways.
- ✗ Treating a part-to-part ratio as part-to-whole: a 3:5 ratio does NOT mean boys are 3/5 of the group — they are 3/8.
- ✗ Setting up the proportion with mismatched units: always ensure the same unit is in the same position on both sides.
SAT-style practice
A recipe uses 2 cups of flour for every 3 cups of oats. How many cups of flour are needed if 12 cups of oats are used?
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