Percent Problems
Grade 7 · Math · Study Guide
Solve real-world percent problems including finding the percent, the part, or the whole — plus tax, tip, and discount.
A percent is a ratio that compares a number to 100. The word 'percent' means 'per hundred,' so 47% means 47 out of 100. Every percent can be written as a fraction over 100 (47/100) or as a decimal (0.47). Converting between these forms is essential for solving percent problems.
There are three core percent problem types: (1) find the part — what is 30% of 80? (multiply: 0.30 × 80 = 24), (2) find the percent — 24 is what percent of 80? (divide: 24 ÷ 80 = 0.30 = 30%), and (3) find the whole — 24 is 30% of what? (divide: 24 ÷ 0.30 = 80). All three come from the same relationship: Part = Percent × Whole.
Percents appear constantly in everyday money situations. Sales tax is a percent added to a price: total = original price × (1 + tax rate). A 20% discount is subtracted: sale price = original × (1 − 0.20) = original × 0.80. A waiter's tip: tip amount = bill × tip percent. These multiplier shortcuts are faster than finding the percent first and then adding or subtracting.
Percent change measures how much something increased or decreased relative to its starting value. The formula is: percent change = (change ÷ original) × 100%. A price that goes from $80 to $100 increased by (20 ÷ 80) × 100% = 25%. If the price drops, it is a percent decrease.
Proportion is another reliable method: set up part/whole = percent/100, then cross-multiply. This approach works for all three problem types and avoids the confusion of converting to decimals. Whichever method you use, always identify what you are looking for (part, percent, or whole) before choosing your approach.
| Find This | Formula | Example |
|---|---|---|
| The part | Part = Percent × Whole | 30% of 70 = 0.30 × 70 = 21 |
| The percent | Percent = Part ÷ Whole | 21 ÷ 70 = 0.30 = 30% |
| The whole | Whole = Part ÷ Percent | 21 ÷ 0.30 = 70 |
| Situation | Formula | Example |
|---|---|---|
| Sales tax | Total = Price × (1 + tax rate) | $50 + 6% tax = $50 × 1.06 = $53 |
| Discount | Sale price = Price × (1 − discount rate) | $80 − 25% off = $80 × 0.75 = $60 |
| Tip | Tip = Bill × tip percent | 15% tip on $40 = 0.15 × 40 = $6 |
| Percent increase | (New − Old) ÷ Old × 100% | ($60 − $50) ÷ $50 × 100% = 20% |
| Percent decrease | (Old − New) ÷ Old × 100% | ($50 − $40) ÷ $50 × 100% = 20% |
Key terms
- Percent
- A ratio out of 100; 47% means 47 per 100
- Part = Percent × Whole
- The core percent equation connecting all three quantities
- Percent change
- How much something increased or decreased relative to the original: (change ÷ original) × 100%
- Discount
- A reduction in price; sale price = original × (1 − discount rate)
- Tax/Tip multiplier
- Adding a percent: multiply by (1 + rate). A 8% tax means multiply by 1.08
Practice questions
What is 35% of 120?
- 42
- 85
- 35
- 3.43
Show answer
Answer: 42
A 20% discount on a $90 item means the sale price is $70.
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Answer: False
18 is what percent of 72? ___%
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Answer: 25
A jacket costs $64 and is on sale for 25% off. What is the sale price?
- $16
- $40
- $48
- $56
Show answer
Answer: $48
If a price increases from $40 to $50, the percent increase is 25%.
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Answer: True
Fun facts
- The 15% tip 'standard' in the US comes from restaurant industry norms in the 1950s — today many people tip 20% because the mental math is easier: just find 10% and double it.
- Stores that advertise '50% off everything, then an additional 30% off' are not giving you 80% off — they are giving you 65% off because the second discount applies to the already-reduced price.
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