Percent Word Problems Reference Cheat Sheet

A printable reference covering percent equations, proportions, discounts, tax, tips, commission, simple interest, markup, and percent change for grades 6-9.

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Percent word problems appear in shopping, money, data, and real-life comparisons, so students need a clear way to translate words into equations. This reference helps connect phrases like “of,” “is,” “percent of,” “discount,” and “increase” to the correct mathematical operations. It is designed for quick review when solving problems about prices, taxes, tips, interest, and percent change. Students can use it to choose a formula, identify the known values, and check whether an answer makes sense. The most important idea is that a percent is a rate per $100$ , so $p\% = \frac{p}{100}$ . Many problems use the relationship $\text{part} = \text{percent} \times \text{whole}$ , with the percent written as a decimal or fraction. Money applications often start with a base price and then add or subtract a percent of that price. Percent change compares the amount of change to the original amount using $\frac{\text{change}}{\text{original}} \times 100\%$ .

Key Facts

A percent means “per $100$ ,” so $p\% = \frac{p}{100}$ and $35\% = \frac{35}{100} = 0.35$ .
The core percent equation is $\text{part} = \text{percent} \times \text{whole}$ , where the percent must be written as a decimal or fraction.
To find the percent, use $\text{percent} = \frac{\text{part}}{\text{whole}} \times 100\%$ .
To find the whole, use $\text{whole} = \frac{\text{part}}{\text{percent}}$ , where the percent is written as a decimal.
A discount is $\text{discount amount} = \text{original price} \times \text{discount rate}$ and $\text{sale price} = \text{original price} - \text{discount amount}$ .
Sales tax and tips are added using $\text{total} = \text{base amount} + \text{base amount} \times \text{rate}$ .
Simple interest is $I = Prt$ , where $I$ is interest, $P$ is principal, $r$ is the annual interest rate as a decimal, and $t$ is time in years.
Percent change is $\text{percent change} = \frac{\text{new value} - \text{original value}}{\text{original value}} \times 100\%$ .

Vocabulary

Percent: A percent is a number out of $100$ , written with the symbol $\%$ .
Whole: The whole is the original or total amount that a percent is taken from.
Part: The part is the amount that represents some percent of the whole.
Rate: A rate is the percent written as a decimal or fraction for use in calculations.
Discount: A discount is an amount subtracted from the original price, usually found by multiplying the price by a percent.
Percent Change: Percent change measures how much a value increases or decreases compared with the original value.

Common Mistakes to Avoid

Using $25$ instead of $0.25$ for $25\%$ is wrong because percent values must be converted before multiplying.
Confusing the part and the whole is wrong because the whole is the original or total amount, while the part is the amount being compared to it.
Adding a discount instead of subtracting it is wrong because a discount reduces the original price, so the sale price is $\text{original price} - \text{discount amount}$ .
Using the new value as the denominator in percent change is wrong because percent change compares the change to the original value.
Rounding too early is wrong because it can change the final answer, especially in money problems where the final amount should be rounded to the nearest cent.

Practice Questions

1 A jacket costs $80$ and is on sale for $25\%$ off. What is the sale price?
2 A restaurant bill is $46$ before tax and tip. If the tip is $18\%$ , how much is the tip?
3 A video game increases in price from $40$ to $50$ . What is the percent increase?
4 A store advertises $30\%$ off, then adds $8\%$ sales tax after the discount. Explain why the final price is not the same as simply subtracting $22\%$ from the original price.

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