Mastering Percentages for SAT Math Success
Introduction
Percentage problems are a common feature of the SAT Math section. They test your ability to work with ratios, proportions, and changes in quantities. Whether it’s calculating a discount, tax, or percentage increase, knowing these problems inside and out can help you gain easy points.
This guide will cover:
- Key formulas for percentage calculations.
- Solving step-by-step percentage problems.
- Common SAT percentage question types.
Key Percentage Formulas
Percent means “per hundred.” The basic formula is:
\[
\text{Percentage} = \left( \frac{\text{Part}}{\text{Whole}} \right) \times 100
\]Percentage Increase/Decrease
\[
\text{Change} = \frac{\text{New Value} – \text{Original Value}}{\text{Original Value}} \times 100
\]Finding the Whole Given the Part
\[
\text{Whole} = \frac{\text{Part}}{\text{Percentage}} \times 100
\]
Solving Percentage Problems Step-by-Step
Example 1: Basic Percentage Calculation
Question: What is 20% of 150?
Solution:
\[
\text{Percentage} = \left( \frac{20}{100} \right) \times 150 = 30
\]Example 2: Percentage Increase
Question: A jacket costs \$80 and the price increases by 25%. What is the new price?
Solution:
- Find the increase:
\[
\text{Increase} = \left( \frac{25}{100} \right) \times 80 = 20
\]- Add to original price:
\[
\text{New Price} = 80 + 20 = 100
\]Example 3: Percentage Decrease
Question: A phone is discounted by 30% from \$200. What is the sale price?
Solution:
- Find the discount:
\[
\text{Discount} = \left( \frac{30}{100} \right) \times 200 = 60
\]- Subtract from original price:
\[
\text{Sale Price} = 200 – 60 = 140
\]
SAT Percentage Problem Types
Finding the Percentage of a Number
- Use the basic percentage formula: \( \text{Percentage} = \frac{\text{Part}}{\text{Whole}} \times 100 \).
Percentage Increase and Decrease
- Always compare the change relative to the original value.
Reverse Percentage Problems
- Find the original price or value before a percentage increase or decrease.
Practice Question
Question: The price of a shirt increased from \$50 to \$65. What is the percentage increase?
Solution:
- Find the change:
\[
\text{Change} = 65 – 50 = 15
\]- Divide by the original value:
\[
\text{Percentage Increase} = \frac{15}{50} \times 100 = 30\%
\]Answer: The percentage increase is 30%.
Common Mistakes to Avoid
- Confusing Increase/Decrease: Always compare to the original value.
- Skipping Steps: Write out each step to avoid calculation errors.
- Misreading “of” vs. “off”: “20% of 100” means multiplication; “20% off 100” involves subtraction.
Summary
Mastering percentages for the SAT requires understanding key formulas and problem types. With practice, you’ll solve these questions quickly and accurately to boost your score.
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