Percentages show up everywhere on the SAT® Math section: from sale prices to compound interest. Therefore, mastering percentages, percent change, and growth factors can boost a score quickly. This guide offers clear explanations, step-by-step examples, and a quick-reference chart so that any high-school student can turn tricky SAT® percentage problems into easy points.

Percent Basics – The Language of “Per Hundred”

A percent tells how many parts out of 100. The symbol “\%” literally means “per hundred.” Understanding this single idea unlocks every other percentage skill on the SAT®.

What Is a Percent?

• 25\% means “25 out of 100.”
• 100\% represents the entire quantity.
• 250\% indicates 2.5 times the original amount.

Converting Among Fractions, Decimals, and Percents

Because SAT® questions switch formats often, quick conversion is essential.

Quick rules:

• Percent ➔ Decimal: move decimal point two places left.
• Decimal ➔ Percent: move decimal point two places right.
• Fraction ➔ Percent: divide to create a decimal, then convert.

Example

Convert 37.5\% to a fraction in simplest form.

Step 1. Percent to decimal:

37.5\% = 0.375

Step 2. Decimal to fraction:

0.375 = \dfrac{375}{1000} = \dfrac{3}{8}

Answer: \dfrac{3}{8}

Visual Analogy: Percent Bar

Imagine a rectangle split into 100 equal squares. Shading 60 squares lets anyone “see” 60\%. On the test, a quick sketch like this helps check work.

Finding a Percent of a Number

Formula:

\text{part} = \text{percent (decimal)} \times \text{whole}

Example

What is 18\% of 250?

1. Convert 18\% to decimal ➔ 0.18
2. Multiply: 0.18 \cdot 250 = 45

Therefore, 18\% of 250 equals 45.

Finding What Percent One Number Is of Another

Formula:

\text{percent} = \dfrac{\text{part}}{\text{whole}} \times 100%

Example

44 is what percent of 80?

1. Divide: \frac{44}{80} = 0.55
2. Convert to percent: 0.55 \times 100% = 55%

So, 44 is 55\% of 80.

Percent Change & Growth Factor

Percent change compares an old value to a new value.

\text{percent change} = \dfrac{\text{new} - \text{old}}{\text{old}} \cdot 100%

• If new > old, the result is a percent increase.
• If new < old, the result is a percent decrease.

Growth Factor Connection

Add 1 to an increase rate or subtract from 1 for a decrease rate. For example, a 5\% increase matches a growth factor of 1 + 0.05 = 1.05. A 12% decrease uses 1 - 0.12 = 0.88.

Example: Percent Increase

A price jumps from \$60 to \$75.

1. Difference: 75 - 60 = 15
2. Divide by old: \dfrac{15}{60} = 0.25
3. Percent: 0.25 \times 100% = 25%

Growth factor = 1.25.

Example: Percent Decrease

A mass drops from 120 g to 96 g.

1. Difference: 96 - 120 = -24
2. Divide: \frac{-24}{120} = -0.20
3. Percent: -0.20 \times 100% = -20%

It is a 20\% decrease; growth factor = 0.80.

Percentages ≥ 100\% simply mean the new value is greater than the original. A 150\% increase, for instance, means the amount becomes 2.5 times larger (growth factor = 2.50).

Real-World Applications You’ll See on the SAT®

Discounts and Sale Prices

Two methods exist.

Method A – Subtract then multiply:

\text{Sale price} = \text{original} – \text{discount amount}

Method B – Use growth factor:

\text{Sale price} = \text{original} \cdot (1 – \text{discount decimal})

Example

An \$80 jacket is 30\% off. What is the sale price?

Growth factor = 1 - 0.30 = 0.70.

80 \times 0.70 = 56

Sale price = \$56.

Sales Tax and Tips

Add-on percentages raise the cost.

\text{Total cost} = \text{price} \cdot (1 + \text{tax decimal} + \text{tip decimal})

Example

A meal costs \$25. After 8\% tax and 15\% tip (on the pre-tax price), what is the total?

1. Tax: 25 \times 0.08 = 2
2. Subtotal: 25 + 2 = 27
3. Tip: 25 \times 0.15 = 3.75
4. Total: 27 + 3.75 = 30.75

Simple Interest

Formula: I = P r t where P = principal, r = annual interest rate (decimal), t = years.

Example

\$600 earns simple interest at 8\% annually for 3 years.

Interest: 600 \times 0.08 \times 3 = 144

Total balance: 600 + 144 = 744

Successive Percent Changes & Compound Situations

Multiply factors, never add percents.

Example

A laptop is 10\% off, then an 8\% sales tax is applied to the discounted price.

1. Discount factor: 0.90
2. Tax factor: 1.08
3. Combined factor: 0.90 \times 1.08 = 0.972

So, the final price equals 97.2\% of the original.

Percentages Beyond 100 %

Suppose a population grows from 400 to 1{,}000. The growth factor equals \frac{1000}{400} = 2.5. Therefore, the percent increase is (2.5 - 1) \times 100% = 150%. Numbers like 250\% or a factor of 2.5 simply indicate values more than double the starting amount.

SAT®-Style Multi-Step Challenge Problem

A store marks a computer at \$1{,}200. During a promotion, the computer is discounted 15\%. After the discount, a coupon takes another \$75 off. Finally, a 6\% sales tax is added to the discounted price after the coupon. What is the final amount paid?

Solution

1. First discount: growth factor 0.85
   • 1200 \times 0.85 = 1020
2. Apply \$75 coupon: 1020 - 75 = 945
3. Add tax: 945 \times 1.06 = 1001.70

Final price = \$1{,}001.70

Common Pitfalls & Quick Checks

• Forgetting to convert the percent to a decimal before multiplying.
• Subtracting the percent number instead of the factor. For instance, 20\% off is not “100\% – 20\% = 80”; instead, use factor = 0.80.
• Adding successive percents instead of multiplying factors.
• Neglecting estimation. A 10\% change is roughly “move the decimal one place,” a quick sanity check against wild answers.

Quick Reference Chart – Key Vocabulary & Formulas

Term	Definition	Sample Conversion / Formula
Percent	Parts per 100	45\% = \frac{45}{100} = 0.45
Growth Factor	Multiplier linked to percent change	12\% increase ➔ factor 1.12
Percent Change	How much a value rises or falls relative to the original	\dfrac{\text{new} - \text{old}}{\text{old}} \cdot 100%
Simple Interest	Interest earned without compounding	I = P r t
Discount Factor	Multiplier after a markdown	30\% off ➔ 0.70
Compound Change	Successive changes multiplied	20\% off then 5\% tax ➔ 0.80 \times 1.05

Practice Questions

1. A video game priced at \$50 is discounted 12\%. What is the sale price?
2. After an 18\% decrease, a stock is worth \$65.80. What was its original value?
3. A bank account earns 4.5\% simple interest each year. How much interest will \$1{,}200 earn in 2 years?
4. A shirt costs \$30 before tax. A store runs a 20\% off sale and then charges 7\% sales tax on the discounted price. What is the final cost?

Solutions

1. Sale price = \$44.
2. Original value = \$80.
3. Interest earned = \$108.
4. Final cost = 30 \times 0.856 = \$25.68.

Final Takeaways & Next Steps

Percentages unlock many SAT® Math points, whether calculating percent change, applying growth factors, or dissecting multi-step discounts and taxes. Regular practice using factors, not raw percents, keeps errors away. Next, explore more SAT® Math guides and timed quizzes to sharpen these percentage skills even further. Good luck and keep practicing!

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