ACT Math: Pre-Algebra - Percentages, Percent Change, Percent of, Reverse Percent

What This Is and Why It Matters for the ACT

Percentages: Percent Change, Percent of, Reverse Percent appears in the Math section of the ACT. It's a fundamental concept that appears on every Math test, and its difficulty level is Intermediate.

Key Concepts (What You Must Know)

• Percent Change: a measure of how much a value has increased or decreased from an original value.
• Percent of: a percentage of a value is a part of the whole.

• Reverse Percent: finding the original value from a percentage.

• Key formula: (change/original) x 100% = percent change

• Key vocabulary: percent, percentage, original, change

Step-by-Step Strategy for This Topic

1. Read the question carefully: Identify the type of percentage problem (percent change, percent of, reverse percent).
2. Understand the problem: Clarify what the question is asking for (e.g., a percentage increase or a percentage of a value).
3. Use the formula: Apply the formula (change/original) x 100% = percent change to solve percent change problems.
4. Eliminate wrong answers: Look for answer choices that are too high or too low to be correct.
5. Check your work: Verify your answer by plugging it back into the original problem.

Don't forget to read the question carefully to avoid misinterpreting the problem.

How It’s Tested on the ACT

Math: Multiple-choice questions with five answer choices (A-E). Questions may involve finding a percentage, calculating a percentage change, or converting a percentage to a decimal.

Common distractors:

• Answer choices that are too high or too low
• Answer choices that are close but not exact
• Answer choices that involve decimal points or fractions

Common Mistakes & Exam Traps

• The mistake: Rounding errors when calculating percentages.
• Why it happens: Misunderstanding the problem or rushing through calculations.
• How to avoid it: Double-check your calculations and use the formula (change/original) x 100% = percent change.

• Exam board insight: The ACT penalizes rounding errors by deducting points for incorrect answers.

• The mistake: Not reading the question carefully.

• Why it happens: Rushing through the question or misinterpreting the problem.
• How to avoid it: Read the question carefully and clarify what the question is asking for.

• Exam board insight: The ACT penalizes misinterpreted problems by deducting points for incorrect answers.

• The mistake: Not using the formula.

• Why it happens: Misunderstanding the problem or not applying the formula correctly.
• How to avoid it: Apply the formula (change/original) x 100% = percent change to solve percent change problems.

• Exam board insight: The ACT penalizes incorrect formulas by deducting points for incorrect answers.

• The mistake: Not checking work.

• Why it happens: Rushing through the problem or not verifying the answer.
• How to avoid it: Verify your answer by plugging it back into the original problem.
• Exam board insight: The ACT penalizes incorrect answers by deducting points.

Practice Questions (3-5 questions)

Question 1: A shirt is on sale for 15% off its original price of $25. What is the sale price? Options: A) $20.50, B) $21.50, C) $22.50, D) $23.50, E) $24.50 Answer: B) $21.50 Explanation: Use the formula (change/original) x 100% = percent change to find the sale price: (15/100) x 25 = 3.75, so the sale price is $25 - $3.75 = $21.50.

Question 2: A bakery sells 250 loaves of bread at a 10% discount. How much money does the bakery lose? Options: A) $12.50, B) $15, C) $17.50, D) $20, E) $22.50 Answer: C) $17.50 Explanation: Use the formula (change/original) x 100% = percent change to find the discount amount: (10/100) x 250 = 25, so the bakery loses $25.

Question 3: A student scores 80% on a test with 100 points. How many points did the student score? Options: A) 80, B) 90, C) 100, D) 110, E) 120 Answer: B) 90 Explanation: Use the formula (change/original) x 100% = percent change to find the number of points scored: (80/100) x 100 = 80, so the student scored 80 points.

Quick Reference Card (60-Second Summary)

• Percent change: (change/original) x 100%
• Percent of: part/whole x 100%
• Reverse percent: original = (value / percent) x 100%
• Mnemonic: Percent Change Original Reverse

If You Get Stuck on Test Day

• Don't panic: Take a deep breath and read the question carefully.
• Eliminate wrong answers: Look for answer choices that are too high or too low.
• Use the formula: Apply the formula (change/original) x 100% = percent change to solve percent change problems.

Related ACT Topics

• Decimals and Fractions: Understanding how to convert between decimals and fractions is essential for calculating percentages.
• Ratios and Proportions: Understanding ratios and proportions is essential for calculating percentages of values.
• Word Problems: Understanding how to read and interpret word problems is essential for calculating percentages in real-world scenarios.