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ACT Math

ACT Math Help: Percents

Review real example questions for Percents in ACT Math.

Question 1

Convert 75%75\%75% to a decimal.

  1. 7.5
  2. 0.75
  3. 0.075
  4. 75.0
Explanation: This question asks us to convert 75%75\%75% to a decimal. To convert a percent to a decimal, divide by 100 or move the decimal point two places left. Calculate: 75%÷100=0.7575\% \div 100 = 0.7575%÷100=0.75. Choice C (0.075) represents the common error of moving the decimal point three places instead of two.

Question 2

What is 40% of 300?

  1. 120
  2. 150
  3. 180
  4. 160
Explanation: This question asks us to find 40% of 300. To find a percent of a number, convert the percent to a decimal and multiply: 40%=0.4040\% = 0.4040%=0.40. Calculate: 0.40×300=1200.40 \times 300 = 1200.40×300=120. Choice B (150) might result from incorrectly calculating 50% of 300 instead of 40%.

Question 3

If a $50 shirt is on sale for 30% off, what is the sale price?

  1. $15
  2. $35
  3. $20
  4. $30
Explanation: This question asks for the sale price after a 30% discount on a 50shirt.Firstfindthediscountamount:3050 shirt. First find the discount amount: 30% of 50shirt.Firstfindthediscountamount:3050 = 0.30 × 50=50 = 50=15. Then subtract from the original price: 50−50 - 50−15 = 35.ChoiceA(35. Choice A (35.ChoiceA(15) incorrectly gives just the discount amount rather than the final sale price.

Question 4

What is 20% of 150?

  1. 20
  2. 15
  3. 75
  4. 30
Explanation: This question asks for 20% of 150. To find a percent of a number, convert the percent to a decimal by dividing by 100, then multiply by the number. 20%=20÷100=0.2020\% = 20 \div 100 = 0.2020%=20÷100=0.20, so 0.20×150=300.20 \times 150 = 300.20×150=30. Choice B incorrectly calculated 20×150÷10020 \times 150 \div 10020×150÷100 in the wrong order, while choice C mistakenly used 150÷2150 \div 2150÷2.

Question 5

What is 30% of 90?

  1. 27
  2. 30
  3. 20
  4. 18
Explanation: This question asks us to find 30% of 90. To find a percent of a number, convert the percent to a decimal and multiply: 30%=0.3030\% = 0.3030%=0.30. Calculate: 0.30×90=270.30 \times 90 = 270.30×90=27. Choice B (30) represents the error of confusing the percent value with the result.

Question 6

A shirt costs \40beforetax.Withanbefore tax. With anbeforetax.Withan8%$ sales tax, what is the total cost?

  1. \72.00$
  2. \48.00$
  3. \40.08$
  4. \43.20$
Explanation: We need to find the total cost of a 40shirtwith840 shirt with 8% sales tax. The tax amount is 8% of 40shirtwith840 = 0.08 × 40=40 = 40=3.20. The total cost is the original price plus tax: 40+40 + 40+3.20 = 43.20.ChoiceC(43.20. Choice C (43.20.ChoiceC(40.08) incorrectly calculates as if the tax were 0.08,not0.08, not 0.08,not3.20.

Question 7

Convert 75%75\%75% to a fraction in simplest form.

  1. 75100\frac{75}{100}10075​
  2. 34\frac{3}{4}43​
  3. 43\frac{4}{3}34​
  4. 75\frac{7}{5}57​
Explanation: We need to convert 75% to a fraction in simplest form. First write 75% as 75/100, then simplify by finding the greatest common factor: 75/100 = (75÷25)/(100÷25) = 3/4. Choice A (75/100) is not in simplest form, and choices C and D represent values greater than 1.

Question 8

A shirt is priced at 40andissoldfor40 and is sold for 40andissoldfor28. What is the discount percentage?

  1. 20%
  2. 30%
  3. 25%
  4. 15%
Explanation: This question asks for the discount percentage when a 40shirtissoldfor40 shirt is sold for 40shirtissoldfor28. Percent decrease is (original−saleprice)÷original×100(original - sale price) \div original \times 100(original−saleprice)÷original×100. Here: (40−28)÷40×100=12÷40×100=0.30×100=30%(40 - 28) \div 40 \times 100 = 12 \div 40 \times 100 = 0.30 \times 100 = 30\%(40−28)÷40×100=12÷40×100=0.30×100=30%. Choice C incorrectly calculated 25%, possibly using the wrong denominator or making an arithmetic error.

Question 9

What is 50% of 180?

  1. 90
  2. 80
  3. 70
  4. 60
Explanation: This question asks us to find 50% of 180. To find a percent of a number, convert the percent to a decimal and multiply: 50%=0.5050\% = 0.5050%=0.50. Calculate: 0.50×180=900.50 \times 180 = 900.50×180=90. Choice B (80) might result from calculating 50% of 160 instead of 180, or making an arithmetic error.

Question 10

If 25% of a number is 10, what is the number?

  1. 40
  2. 30
  3. 50
  4. 20
Explanation: This question asks for the whole number when 25% of it equals 10. Set up the equation: 0.25 × n = 10. Solve for n: n = 10 ÷ 0.25 = 10 × 4 = 40. Choice B (30) represents a common error, possibly from incorrect division or using 1/3 instead of 1/4.