Module 1 · Numbers and Operations
Chapter 4: Ratios and Proportions
Problem-Solving & Data Analysis
7 topics
What this chapter covers
The 7 topics below make up Ratios and Proportions on the Digital SAT. Click any topic to open its notes, examples and practice test.
1Ratios
2Equivalent Ratios
3Proportions
4Direct Variation
5Inverse Variation
6Scale Factors
7Unit Rates
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Formula Reference Sheet
This chapter
Ratios & proportions
| Ratio | a : b (compares two quantities) |
|---|---|
| Proportion | a/b = c/d |
| Cross-multiplication | a/b = c/d ⇒ a·d = b·c |
| Total parts | a : b → split a whole into (a + b) parts |
Variation & rates
| Direct variation | y = kx (y/x constant) |
|---|---|
| Inverse variation | y = k/x (xy constant) |
| Unit rate | quantity ÷ number of units |
| Scale factor | ratio of corresponding lengths |
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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