Module 1 · Numbers and Operations
Chapter 3: Fractions and Decimals
Math Foundations
7 topics
What this chapter covers
The 7 topics below make up Fractions and Decimals on the Digital SAT. Click any topic to open its notes, examples and practice test.
1Proper Fractions
2Improper Fractions
3Mixed Numbers
4Converting Fractions to Decimals
5Recurring Decimals
6Comparing Fractions
7Operations on Fractions
Study material & tests
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Notes, worked examples and hint-guided practice for every topic.
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🎯 Topic tests
8 auto-graded questions per topic, pulled from the question bank.
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📝 Chapter test
25 fresh mixed-difficulty questions, timed, with full solutions.
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Formula Reference Sheet
This chapter
Fractions
| Proper fraction | numerator < denominator (value < 1) |
|---|---|
| Improper fraction | numerator ≥ denominator (value ≥ 1) |
| Mixed → improper | a b/c = (a·c + b)/c |
| Add/subtract | rewrite with a common denominator |
| Multiply | (a/b)(c/d) = ac/bd |
| Divide | (a/b) ÷ (c/d) = (a/b)(d/c) |
Decimals
| Fraction → decimal | divide numerator by denominator |
|---|---|
| Terminating | denominator (lowest terms) has only factors 2 and 5 |
| Recurring | any other denominator → repeating block |
| Compare fractions | cross-multiply or use a common denominator |
Digital SAT reference
Area & Circumference
| Circle area | A = πr² |
|---|---|
| Circle circumference | C = 2πr |
| Rectangle | A = ℓw |
| Triangle | A = ½ b h |
Volume
| Rectangular box | V = ℓwh |
|---|---|
| Cylinder | V = πr²h |
| Sphere | V = 4⁄3 πr³ |
| Cone | V = 1⁄3 πr²h |
| Pyramid | V = 1⁄3 ℓwh |
Right triangles
| Pythagorean theorem | a² + b² = c² |
|---|---|
| 30°–60°–90° | sides x : x√3 : 2x |
| 45°–45°–90° | sides s : s : s√2 |
Constants
| Degrees in a circle | 360° |
|---|---|
| Radians in a circle | 2π |
| Angles of a triangle | sum = 180° |
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