Percent word problems connect a part of something, the whole amount, and a percent rate. They matter because discounts, taxes, tips, test scores, interest, and data comparisons all use percent reasoning. A strong method is to identify what is given and what is unknown before choosing an equation.
The Part, Whole, Percent triangle helps organize the information quickly.
Key Facts
- Percent means per 100, so 35% = 35/100 = 0.35.
- Basic percent equation: part = percent × whole, using percent as a decimal.
- To find the whole: whole = part ÷ percent.
- To find the percent: percent = part ÷ whole, then multiply by 100 to write it as a percent.
- Percent proportion: part/whole = percent/100.
- Percent change: percent change = amount of change ÷ original amount × 100%.
Vocabulary
- Percent
- A percent is a ratio that compares a number to 100.
- Part
- The part is the amount being compared to the whole.
- Whole
- The whole is the total or original amount in a percent problem.
- Percent proportion
- A percent proportion is the equation part/whole = percent/100 used to solve percent problems.
- Percent change
- Percent change describes how much a quantity increases or decreases compared with its original value.
Common Mistakes to Avoid
- Using 25 instead of 0.25 in the equation part = percent × whole is wrong because the percent must be written as a decimal unless you use a proportion with 100.
- Choosing the wrong whole is wrong because the whole is the total or original amount being compared, not always the largest number in the sentence.
- Dividing in the wrong order when finding a percent is wrong because percent = part ÷ whole, not whole ÷ part.
- Treating percent increase as just adding the percent number is wrong because a 15% increase means adding 15% of the original amount, not adding 15 units.
Practice Questions
- 1 A jacket costs $80 and is on sale for 25% off. What is the discount amount, and what is the sale price?
- 2 A student answered 42 questions correctly on a quiz and earned 84%. How many questions were on the quiz?
- 3 A store raises the price of a 50, greater than 50.