Percents — Pre-Algebra Unit 4 practice.
This unit covers percent conversions, percent of a number, percent change and discounts and tax — essential concepts for Pre-Algebra. Use our interactive study games to test your understanding, or review questions in traditional format below.
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This unit covers percent conversions, percent of a number, percent change and discounts and tax — essential concepts for Pre-Algebra. Use our interactive study games to test your understanding, or review questions in traditional format below.
Key Concepts Breakdown
1 Percent Conversions
Students must be able to convert fluently between percents, decimals, and fractions. Percent means 'per hundred,' so conversions always involve multiplying or dividing by 100. Exams frequently require converting in both directions without a calculator.
Key Points
- Percent to decimal: divide by 100 (move decimal point 2 places left). Example: 45% = 0.45
- Decimal to percent: multiply by 100 (move decimal point 2 places right). Example: 0.07 = 7%
- Percent to fraction: write the percent over 100, then simplify. Example: 60% = 60/100 = 3/5
- Fraction to percent: divide numerator by denominator, then multiply by 100. Example: 3/4 = 0.75 = 75%
Convert 0.6% to a decimal and to a fraction in simplest form.
To convert 0.6% to a decimal, divide by 100: 0.6 ÷ 100 = 0.006. To convert to a fraction, write 0.6/100 = 6/1000, then simplify by dividing both by 2 to get 3/500. Note: 0.6% is much smaller than 0.6, so be careful with small percents.
2 Percent of a Number
Students must be able to find a percent of a number by converting the percent to a decimal and multiplying. Exams also test finding the whole when a part and percent are given, or finding the percent when the part and whole are known. The proportion method (part/whole = percent/100) works for all three cases.
Key Points
- To find the part: multiply the whole by the decimal form of the percent. Part = Whole × Rate
- To find the whole: divide the part by the decimal form of the percent. Whole = Part ÷ Rate
- To find the percent: divide the part by the whole, then multiply by 100. Rate = (Part ÷ Whole) × 100
- Proportion setup: part/whole = percent/100 — cross multiply to solve for the missing value
18 is what percent of 72?
Set up the proportion: 18/72 = x/100. Cross multiply to get 72x = 1800, then divide both sides by 72 to get x = 25. So 18 is 25% of 72. You can check: 25% of 72 = 0.25 × 72 = 18. ✓
3 Percent Change
Students must calculate percent increase or percent decrease using the formula: Percent Change = (Amount of Change ÷ Original) × 100. The original value is always the starting value — using the wrong base is the most common exam error. Students must also be able to determine whether a change is an increase or a decrease.
Key Points
- Formula: Percent Change = [(New − Original) ÷ Original] × 100
- Positive result = percent increase; negative result = percent decrease
- Always divide by the ORIGINAL (starting) value, never the new value
- Amount of change = |New Value − Original Value|
A jacket cost $80 last month. This month it costs $92. What is the percent increase?
First, find the amount of change: 92 − 80 = 12. Then divide by the original price: 12 ÷ 80 = 0.15. Finally, multiply by 100 to get 15%. The jacket increased in price by 15%.
4 Discounts and Tax
Students must calculate sale prices after a discount and final prices after tax, and often both applied in sequence. Discounts are subtracted from the original price; tax is added to the price. Exams commonly chain these operations — apply the discount first, then add tax to the sale price.
Key Points
- Discount amount = Original Price × Discount Rate (as a decimal)
- Sale price = Original Price − Discount Amount (or: Original Price × (1 − discount rate))
- Tax amount = Sale Price × Tax Rate (as a decimal)
- Final price = Sale Price + Tax Amount (or: Sale Price × (1 + tax rate))
A $120 pair of shoes is on sale for 25% off. If the sales tax is 8%, what is the final price?
First, find the sale price: 25% of $120 = 0.25 × 120 = $30 discount, so the sale price is $120 − $30 = $90. Next, calculate the tax on the sale price: 8% of $90 = 0.08 × 90 = $7.20. Finally, add the tax: $90 + $7.20 = $97.20. The final price is $97.20.
Questions, answered.
What is Percents?
Percents is Unit 4 of Pre-Algebra, covering percent conversions, percent of a number, percent change and discounts and tax.
How to study for Pre-Algebra Unit 4?
Start with the Quick Summary above, review the Key Concepts, then test yourself with our interactive study games. Aim for 80%+ accuracy before moving on.
How many questions are in this unit?
This unit has 25+ review questions across 5 different game modes.