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Learn: Solving Math Percent Problems

Concept-focused guide for Solving Math Percent Problems (no answers revealed).

~5 min read

Overview

Welcome, #uniexam learners! In this session, we’ll break down the essential concepts behind solving math percent problems. You’ll discover how to interpret percent-based questions, translate real-world scenarios into equations, and apply logical steps to find solutions—whether it’s about discounts, increases, or percentages of totals. By the end, you’ll be able to tackle any percent problem with confidence and accuracy.

Concept-by-Concept Deep Dive

1. Understanding Percent as a Mathematical Concept

Percent means "per hundred." It’s a way of expressing a number as a fraction of 100. For example, 20% simply means 20 out of 100, or 20/100.

Converting Between Percent, Decimal, and Fraction

  • To convert a percent to a decimal, divide by 100 (e.g., 25% = 0.25).
  • To convert a percent to a fraction, write it over 100 and simplify if possible (e.g., 40% = 40/100 = 2/5).

Common Misconception

Many learners forget to convert percent to decimal form before using it in calculations. Remember, 15% is not 0.15 of a number until you divide by 100!

2. Calculating a Percentage of a Quantity

This is a core skill for tips, discounts, and class composition questions.

Step-by-Step Recipe

  1. Convert the percent to a decimal: Divide the given percent by 100.
  2. Multiply by the total quantity: Multiply the decimal by the whole to find the part.

Example: “What is 30% of 200?”

  • Convert 30% to 0.3.
  • 0.3 × 200 = 60.

Misconception

Some mistakenly multiply by the percent without converting (e.g., 30 × 200 = 6000, which is incorrect).

3. Finding the Percent Given Two Quantities

Sometimes you’re given a part and a whole, and asked what percent the part is of the whole.

Step-by-Step Recipe

  1. Divide the part by the whole: Part/Whole.
  2. Convert to percent: Multiply the result by 100.

Example: "What percent of 50 is 20?"

  • 20 ÷ 50 = 0.4
  • 0.4 × 100 = 40%

Misconception

Forgetting to multiply by 100 at the end, leading to answers in decimal instead of percent.

4. Percentage Increase and Decrease

These problems ask you to find the new value after an increase or decrease by a certain percent, or to find the percent change between two values.

Calculating Increase or Decrease

  • Increase: New Value = Original + (Original × Percent increase as decimal)
  • Decrease: New Value = Original − (Original × Percent decrease as decimal)

Finding Percent Change

  • Percent Change = (Difference ÷ Original) × 100

Example: If a price drops from 100 to 80:

  • Difference = 100 − 80 = 20
  • Percent decrease = (20 ÷ 100) × 100 = 20%

Misconception

Using the new value as the denominator instead of the original when finding percent change.

5. Solving for the Original or the Whole Given a Part and Percent

Here, you know a part and what percent it represents, and need to find the total.

Step-by-Step Recipe

  1. Convert percent to decimal.
  2. Divide the part by the decimal: Total = Part ÷ (percent as decimal)

Example: "20% of what number is 50?"

  • 0.2 × X = 50
  • X = 50 ÷ 0.2 = 250

Misconception

Accidentally multiplying instead of dividing when solving for the whole.

6. Reverse-Engineering Quantities from Percent Correct/Wrong

Test score problems sometimes ask for how many questions were answered incorrectly, given the percent correct (or vice versa).

Step-by-Step Recipe

  • Find the number correct: Percent correct (as decimal) × Total questions.
  • Find incorrect: Total questions − Number correct.

Misconception

Confusing the percent with the number of questions or misapplying the percent to the wrong quantity.

Worked Examples (generic)

Example 1: Calculating a Percentage of a Quantity

  • Setup: Find 15% of 300.
  • Solution: 15% = 0.15. 0.15 × 300 = 45.

Example 2: Finding the Percent Given Two Quantities

  • Setup: If 30 out of 120 apples are red, what percent are red?
  • Solution: 30 ÷ 120 = 0.25. 0.25 × 100 = 25%.

Example 3: Calculating New Value After a Percentage Increase

  • Setup: A salary of ₱10,000 is increased by 8%. What is the new salary?
  • Solution: 8% = 0.08. Increase = 0.08 × 10,000 = 800. New salary = 10,000 + 800 = 10,800.

Example 4: Finding the Whole When Given a Part and Percent

  • Setup: 12 is 40% of what number?
  • Solution: 40% = 0.4. 12 ÷ 0.4 = 30.

Common Pitfalls and Fixes

  • Forgetting to Convert Percent to Decimal: Always divide the percent by 100 before multiplying.
  • Mixing Up Part and Whole: Clearly identify which number is the “part” and which is the “whole” in each question.
  • Using the Wrong Base for Percent Change: Always use the original value as the base when calculating percent increase or decrease.
  • Arithmetic Errors: Double-check multiplication and division, especially when working with decimals.
  • Reversing Steps When Solving for the Whole: If you’re given the part and the percent, remember to divide, not multiply.

Summary

  • Percent means "per hundred"—always convert to decimal before calculations.
  • To find a percent of a number, multiply; to find what percent one number is of another, divide then multiply by 100.
  • For percent increases and decreases, use the original value as your base.
  • When given a part and percent, divide to find the whole.
  • Read each problem carefully to determine what’s being asked and which numbers represent the part, whole, or percent.
  • Practice these patterns and recipes to master any percent problem you encounter!