Percents are a core component of the SAT Math section. This guided path will teach you the foundational skills, the specific strategies for modeling real-world problems, and the crucial shortcuts needed for speed and accuracy in both the calculator and no-calculator sections.
Start with the basics. Practice converting between percents, fractions, and decimals to build a solid foundation.
Convert any fraction to a percentage.
Learn the most important shortcut for percent changes: converting them to decimal multipliers. See how it works with an interactive tool.
Master the fundamental algebraic skill for all word problems: solving for the Part, the Percent, or the Whole.
"20 is what percent of 50?"
"28 is 40% of what number?"
Master the concept of applying a percentage change to a new base value, a common scenario in discount and tax problems on the SAT.
+ 20% and - 20%
= 0% change
$100 → +20% → $120.00
$120.00 → -20% → $96.00
The +20% increase adds $20. The -20% decrease is on the NEW, larger value ($120), so it subtracts $24.00. Result < Start.
Understand the critical difference between Simple Interest (linear) and Compound Interest (exponential). This visual tool is key for modeling questions.
Compare Linear (Simple) vs Exponential (Compound) growth. Notice how the 'Increment' stays constant for Simple Interest but grows for Compound Interest.
Review the most common percent-to-fraction equivalents, then test your memory with a flashcard quiz to boost your calculation speed.
| Percent Change | Multiplier |
|---|---|
| 50% | $$ 1/2 $$ |
| 33.33% | $$ 1/3 $$ |
| 12.5% | $$ 1/8 $$ |
Memorize the direct fractional multipliers for common percent changes to solve problems faster, a crucial skill for the no-calculator section.
| Percent Change | Multiplier |
|---|---|
| 16.66% | $$ 7/6 $$ |
| 20% | $$ 6/5 $$ |
| 25% | $$ 5/4 $$ |
| 33.33% | $$ 4/3 $$ |
| 50% | $$ 3/2 $$ |
| 100% | $$ 2 $$ |
Memorize the multipliers for decreases.
| Percent Change | Multiplier |
|---|---|
| 16.66% | $$ 5/6 $$ |
| 20% | $$ 4/5 $$ |
| 25% | $$ 3/4 $$ |
| 33.33% | $$ 2/3 $$ |
| 50% | $$ 1/2 $$ |
Master the powerful 'a% of b = b% of a' rule to simplify complex calculations like "44% of 50" into easy mental math.
$$ A\% \text{ of } B = B\% \text{ of } A $$
You can flip the numbers to make calculation easier.
Calculate: $$ 32\% \text{ of } 50 $$
Hard to do mentally? Flip it!
$$ 50\% \text{ of } 32 = \frac{1}{2} \times 32 = \mathbf{16} $$
Calculate: $$ 160\% \text{ of } 25 $$
Flip it:
$$ 25\% \text{ of } 160 = \frac{1}{4} \times 160 = \mathbf{40} $$
$$ A\% \times B = \frac{A}{100} \times B = \frac{A \times B}{100} $$
$$ B\% \times A = \frac{B}{100} \times A = \frac{B \times A}{100} $$
Since $$ A \times B = B \times A $$, they are identical.
Put your understanding of SAT Percents: A Guide to Real-World Modeling & Calculation Shortcuts to the test with our premium, adaptive practice questions. Build pacing efficiency and eliminate knowledge gaps now.
