ACT Math · Study Guide
Pre-Algebra
Review percentages, ratios, and proportions (high-frequency ACT topics) and practice translating word problems into solvable equations.
About 45 minutes to master
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What you'll learn
- Convert between fractions, decimals, and percentages in problem contexts
- Set up and solve proportion equations (cross-multiplication)
- Calculate percent increase and percent decrease
- Translate ratio word problems into algebraic expressions
- Review the week's material and identify remaining gaps
Key concepts
A ratio compares two quantities (e.g., 3:5); a proportion states that two ratios are equal (3/5 = 6/10). To solve a proportion, cross-multiply: if a/b = c/d, then ad = bc. Percent change is calculated as (new − old) / old × 100. The ACT frequently wraps these concepts in word problems: 'If 40% of students are male and there are 240 males, how many students total?' translates to 0.40 × total = 240, so total = 600. Being fluent with these translations is worth several easy points.
Pro tips
- Percent increase of 25% means multiplying by 1.25; percent decrease of 25% means multiplying by 0.75.
- For ratio problems, assign a variable to the ratio unit: if the ratio is 3:5, let the parts be 3x and 5x.
- Use this day to revisit any concepts from Days 1-6 that felt shaky. Strong foundations prevent mistakes later.
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