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Pre-Algebra

Percents

Lesson

Percent means “per hundred.” So 25%25\% means 25100\frac{25}{100}, which is 0.250.25 as a decimal.

To convert between forms:

  • Percent → decimal: divide by 100 (move decimal two places left). 40%=0.4040\% = 0.40
  • Decimal → percent: multiply by 100 (move decimal two places right). 0.7=70%0.7 = 70\%

The most useful percent question type is “What is X% of Y?”:

X% of Y=X100⋅YX\% \text{ of } Y = \frac{X}{100} \cdot Y

Worked example 1 — finding a percent of a number

What is 20% of 80?

0.20⋅80=160.20 \cdot 80 = 16

Worked example 2 — finding the original

15 is 25% of what number?

Set it up: 0.25⋅x=150.25 \cdot x = 15.

x=150.25=60x = \frac{15}{0.25} = 60

Worked example 3 — percent change

A shirt is 30% off. The original price is $40. What’s the discount in dollars?

0.30⋅40=120.30 \cdot 40 = 12

The discount is $12. (The sale price would be 40−12=2840 - 12 = 28.)

Practice

Work through these. Stuck? Click Get a hint.

Warm-Up

Quick problems to get going.

Problem 1

10% of 5010\% \text{ of } 50

Problem 2

50% of 8050\% \text{ of } 80

Problem 3

25% of 10025\% \text{ of } 100

Problem 4

100% of 17100\% \text{ of } 17

Practice

Standard problems matching the lesson.

Problem 5

20% of 8020\% \text{ of } 80

Problem 6

15% of 6015\% \text{ of } 60

Problem 7

40% of 3540\% \text{ of } 35

Problem 8

75% of 20075\% \text{ of } 200

Problem 9

8% of 2508\% \text{ of } 250

Problem 10

15 is 25% of what?15 \text{ is } 25\% \text{ of what?}

Problem 11

18 is 30% of what?18 \text{ is } 30\% \text{ of what?}

Problem 12

Convert 0.42 to a percent (no % sign)\text{Convert } 0.42 \text{ to a percent (no \% sign)}

Problem 13

Convert 65% to a decimal\text{Convert } 65\% \text{ to a decimal}

Problem 14

25% off of 60 — discount?25\% \text{ off of } 60 \text{ — discount?}

Problem 15

30% off of 80 — sale price?30\% \text{ off of } 80 \text{ — sale price?}

Problem 16

7% of 2007\% \text{ of } 200

Problem 17

25% off of 40 — sale price?25\% \text{ off of } 40 \text{ — sale price?}

Problem 18

18 out of 24: percent (no % sign)?\text{18 out of 24: percent (no \% sign)?}

Challenge

Harder problems — edge cases, trickier numbers, multiple steps.

Problem 19

12% of 7512\% \text{ of } 75

Problem 20

42 is what % of 60? (no % sign)\text{42 is what \% of 60? (no \% sign)}

Problem 21

Percent increase from 50 to 65 (no % sign)\text{Percent increase from 50 to 65 (no \% sign)}

Problem 22

Percent decrease from 40 to 30 (no % sign)\text{Percent decrease from 40 to 30 (no \% sign)}

Problem 23

27 is 45% of what?27 \text{ is } 45\% \text{ of what?}

Problem 24

120, 15% off, then 8% tax — final?\text{120, 15\% off, then 8\% tax — final?}

Problem 25

80 after 20% off — original?\text{80 after 20\% off — original?}

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