Percent Word Problems
SAT Math — Complete Mastery Guide
The Three Fundamental Percent Relationships
Every percent problem on the SAT boils down to three quantities: Part, Percent, and Whole. Master these three formulas and you can solve any basic percent problem.
Finding the Part
Part = Percent × Whole
"What is 15% of 80?"
Part = 0.15 · 80 = 12
Finding the Percent
Percent = (Part ÷ Whole) · 100%
"12 is what percent of 80?"
Percent = (12 ÷ 80) · 100% = 15%
Finding the Whole
Whole = Part ÷ (Percent ÷ 100)
"12 is 15% of what number?"
Whole = 12 ÷ 0.15 = 80
💡 SAT Tip — Translating Words to Math:
• "of" means multiply (·)
• "is" means equals (=)
• "what" means variable (x)
• "what percent" means x/100
Example: "What percent of 80 is 20?" → (x/100) · 80 = 20 → x = 25
• "of" means multiply (·)
• "is" means equals (=)
• "what" means variable (x)
• "what percent" means x/100
Example: "What percent of 80 is 20?" → (x/100) · 80 = 20 → x = 25
Percent ↔ Decimal Conversion
To convert a percent to a decimal, divide by 100 (move the decimal point two places left). This is critical for all calculations.
| Percent | Decimal | Fraction |
|---|---|---|
| 50% | 0.50 | 1/2 |
| 25% | 0.25 | 1/4 |
| 20% | 0.20 | 1/5 |
| 10% | 0.10 | 1/10 |
| 33.3̄% | 0.333... | 1/3 |
| 7% | 0.07 | 7/100 |
| 0.5% | 0.005 | 1/200 |
| 150% | 1.50 | 3/2 |
🧠 No-Calculator Section Tip:
Memorize these fraction equivalents for fast mental math:
• 25% = 1/4 • 50% = 1/2
• 20% = 1/5 • 10% = 1/10
• 33⅓% = 1/3 • 12.5% = 1/8
• 75% = 3/4 • 40% = 2/5
SAT Shortcut for 15% of 80:
10% of 80 = 8
5% of 80 = 4 (half of 10%)
15% of 80 = 8 + 4 = 12 ✓
Memorize these fraction equivalents for fast mental math:
• 25% = 1/4 • 50% = 1/2
• 20% = 1/5 • 10% = 1/10
• 33⅓% = 1/3 • 12.5% = 1/8
• 75% = 3/4 • 40% = 2/5
SAT Shortcut for 15% of 80:
10% of 80 = 8
5% of 80 = 4 (half of 10%)
15% of 80 = 8 + 4 = 12 ✓