SAT Math · Study & Practice
Fractions and Decimals
Fractions and decimals are two ways of writing the same parts-of-a-whole idea, and the SAT expects you to move fluently between them. This chapter covers proper and improper fractions, mixed numbers, decimal conversions, recurring decimals, comparing fractions and the four operations. Read each topic, try the problems with the hint ladder, then take the 8-question topic test.
Topics
1
Proper Fractions
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2
Improper Fractions
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3
Mixed Numbers
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4
Converting Fractions to Decimals
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5
Recurring Decimals
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6
Comparing Fractions
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7
Operations on Fractions
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Chapter test
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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