Percents

In plain words

Examples

Try it. Then open the steps.

Example 1 of 5

The markdown (a price cut)

A jacket costs $80. It is 25% off. What is the sale price?

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1. 25% means 25 out of 100. Divide 25 by 100 to write the percent as a decimal.
2. 25 ÷ 100 = 0.25
3. The discount is that decimal times the $80 price.
4. 0.25 × 80 = 20
5. The $20 discount is subtracted from the original $80 price.
6. 80 − 20 = 60
7. A shorter path uses the part still paid. Start from the whole price, 100%, and take away the 25% discount.
8. 100% − 25% = 75%
9. 75% means 75 out of 100. Write that percent as a decimal before multiplying.

10. 75 ÷ 100 = 0.75
11. 80 × 0.75 = 60

Answer: $60

Example 2 of 5

The raise

A lawn job paid $40. Next week it pays 15% more. What is the new pay?

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1. A 15% raise means add 15% of the original $40.
2. 15% = 15/100 = 0.15. Find the extra pay:
   0.15 × 40 = 6

3. Add the $6 raise to the original pay:
   40 + 6 = 46
4. The new pay is $46. Check: $46 − $40 = $6.

Answer: $46

Example 3 of 5

Find the percent

A plant grows from 50 cm to 65 cm. What is the percent increase?

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1. The plant grew 65 − 50 = 15 cm.
2. Compare that growth with the starting height of 50 cm:
   15 ÷ 50 = 0.30

3. 0.30 is 30 out of 100, or 30%. The height increased by 30%.
4. Check: 0.30 × 50 = 15 cm, and 50 + 15 = 65 cm.

Answer: 30%

Example 4 of 5

The mall jacket

A big red SALE sign at the mall

A jacket is $60. It is 30% off. What is the sale price?

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1. 30% off means you pay 70% of the original. Or take 30% away.
2. 0.30 × 60 = 18
3. Eighteen dollars off.

4. 60 − 18 = 42
5. Same answer the short way: 60 × 0.70 = 42.

Answer: $42

Example 5 of 5

The stadium crowd

Soccer, second half

The stadium holds 25,000 seats. 40% are filled. How many people are in the seats?

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1. 40% means 40 out of 100. Divide 40 by 100 to write the percent as a decimal.
2. 40 ÷ 100 = 0.40
3. “Of” means multiply, so take 0.40 of the 25,000 seats.

4. 0.40 × 25,000 = 10,000
5. 10,000 seats are filled. The other 60% is the unfilled portion: 15,000 seats.

Answer: 10,000 people

Things to watch for

• Easy to miss: Using the final amount instead of the starting amount when finding percent change. Another trap is assuming two increases of 20% give a total increase of 40%.

  Do this: Percent change tells how large the change is compared with the starting amount. Divide the size of the change by the starting amount, then multiply by 100 to write the percentage. For a change from 80 to 60, the decrease is 20; 20 ÷ 80 = 0.25, which is 25%.

• Easy to miss: Forgetting that 'of' means multiply.

  Do this: “Of” means multiply. 15% of 80 is 0.15 × 80.