Percentages
Students struggle with percentage calculations when they can't visualize that 25% means 1 out of every 4 parts. Teaching percentages through concrete examples like "15% tip on a $40 dinner bill" builds number sense before introducing abstract decimal conversions.
Why it matters
Percentages appear in every aspect of adult life, from calculating a 20% tip on a $50 restaurant bill to understanding that a 30% discount saves $60 on a $200 jacket. Students encounter percentages in sports statistics (a basketball player shooting 75% from the free-throw line), academic grades (scoring 85% on a test), and financial literacy (earning 3% annual interest on savings). CCSS 6.RP and 7.RP standards emphasize these real-world connections because percentage fluency directly impacts consumer decision-making. When students master finding 15% of $80 for a tip calculation or determining that $45 is 18% of a $250 purchase, they develop mathematical reasoning skills that transfer to complex problem-solving in algebra and beyond.
How to solve percentages
Percentages — how to
- Convert the percent to a decimal by dividing by 100.
- Multiply the decimal by the base number.
- For discounts: subtract the discount from the original.
Example: 20% of 80 → 0.20 × 80 = 16.
Worked examples
What is 10% of 10?
Answer: 1
- Convert percent to fraction → 10% = 1/10 — 10% is a common fraction — memorise these.
- Apply to the base → 10 × 10/100 = 1 — Take a tenth of 10.
- Verify → 1 × 100 ÷ 10 = 10% ✓ — Check backwards.
A book costs $200.00. You get 30% off. How much is the discount?
Answer: 60
- Convert percent to decimal → 30% = 0.3 — 30% means 30 per hundred, so divide by 100.
- Multiply by the base → 0.3 × 200 = 60 — Multiplying the decimal by the base gives the percentage amount.
- Verify → 60 ÷ 200 × 100 = 30% ✓ — Working backwards confirms the percent.
125 is what percent of 250?
Answer: 50%
- Set up the ratio → 125 / 250 — The part divided by the whole.
- Convert to percent (× 100) → 125 / 250 × 100 = 50% — Multiply the ratio by 100 to get percent.
- Verify → 50% × 250 = 125 ✓ — Check by multiplying back.
Common mistakes
- Students often multiply by the percentage directly instead of converting to a decimal first, calculating 20% of 50 as 20 × 50 = 1,000 instead of 0.20 × 50 = 10.
- When finding what percent one number is of another, students frequently divide the larger by the smaller, calculating 30 is what percent of 120 as 120 ÷ 30 = 4 = 400% instead of 30 ÷ 120 = 0.25 = 25%.
- Students confuse discount problems by subtracting the percentage from 100 incorrectly, finding a 25% discount on $80 as $80 - 25 = $55 instead of $80 - (0.25 × $80) = $60.
- Many students forget to convert their final decimal answer back to a percentage, writing 0.35 instead of 35% when asked what percent 70 is of 200.