Percents, Ratios, and Proportions
Key translations, formulas, and shortcuts for PSAT percent, ratio, and proportion word problems.
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Questions Covered in This Set
12 cards to master
What does "percent" literally mean, and how do you convert 37% to a decimal?
"Percent" means "per hundred." 37% = 37/100 = 0.37 — move the decimal two places left.
Translate: "of", "is", "what number", "percent"
"of" = ×, "is/was/equals" = =, "what number" = x, "percent" = /100
Set up and solve: 18 is what percent of 45?
18 = (x/100)(45) → 1800 = 45x → x = 40, so 40%
Percent change formula
percent change = (new − old)/old × 100%. The denominator is always the ORIGINAL value.
What multiplier represents a 20% increase? A 20% decrease?
Increase: × 1.20. Decrease: × 0.80.
A $200 jacket is marked down 30%, then 10% more. Final price and total discount?
200 × 0.70 × 0.90 = $126; total discount = (200−126)/200 = 37%, not 40% — successive percents multiply.
If a price after a 25% increase is $75, what was the original?
1.25x = 75 → x = $60 (reverse the multiplier by dividing).
What does a ratio of 3:5 actually mean, and what is the k trick?
The quantities are 3k and 5k for some positive k. Find k from the total or a given value, then compute each part.
A class of 32 students has a boy-to-girl ratio of 3:5. How many girls?
Parts: 3+5 = 8, so 8k = 32, k = 4. Girls = 5k = 20.
Part-to-part vs. part-to-whole ratio
3:5 boys to girls is part-to-part; 3:8 boys to all students is part-to-whole. Misreading this is the most common ratio error.
Solve: 3 cups of flour makes 24 cookies. Flour for 60 cookies?
3/24 = x/60 → 24x = 180 → x = 7.5 cups (or unit rate 0.125 cups/cookie × 60).
How do you convert 45 km/hr to m/s?
Multiply by fractions equal to 1 so units cancel: 45 × (1000 m/1 km) × (1 hr/3600 s) = 12.5 m/s.
