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Math 010: Percent (Ch. 8)

Math 010: Percent (Ch. 8). November 20, 2013. When do we use percents ?. What do we know about percents ?. What does “percent” mean?. Watch: http://www.khanacademy.org/math/arithmetic/decimals/percent_tutorial/v/describing-the-meaning-of-percent

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Math 010: Percent (Ch. 8)

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  1. Math 010: Percent (Ch. 8) November 20, 2013

  2. When do we use percents? What do we know about percents?

  3. What does “percent” mean? Watch: http://www.khanacademy.org/math/arithmetic/decimals/percent_tutorial/v/describing-the-meaning-of-percent “Per” means “out of” or “divided by” “Cent” means “one hundred” So “percent” literally means “out of 100” or “divided by 100”

  4. Converting percents to fractions Think about the meaning of percent. To convert a percent to a fraction, just put the number over 100. Simplify fractions whenever possible 41% = What fraction is equivalent to 60%? 60% =

  5. Converting fractions to percents First, convert to a decimal. Perform the division operation. Then move the decimal point two places to the right and add the % sign. Example: convert to a percent. 2 ÷ 7 ≈ 0.2857 28.57%

  6. Decimals  Percents To convert a decimal to a percent, move the decimal point two places to the right and add the % sign. Example: 0.56 = 56% 1 = 100% 1.5 = 150% 4 = 400%

  7. Percents Decimals To convert a percent to a decimal, remove the % sign and move the decimal point two places to the left. Example: 25% = 0.25 100% = 1 “Sales increased 400% this year!” means that sales increased by 4 times last year’s amount, because 400% = 4.

  8. Fractions, decimals, percents • 9 out of 100 squares are shaded • Fraction: • Decimal: 0.09 • Percent: 9% • 77 out of 100 squares are shaded • Fraction: • Decimal: 0.77 • Percent: 77% 96 out of 100 squares are shaded Fraction: Decimal: 0.96 Percent: 96%

  9. Check your understanding http://www.polleverywhere.com/multiple_choice_polls/mpM1npuC8GrWp2O Correct answer: 8/10,000 Eight hundredths of a percent means 0.08 divided by 100, which is 0.0008 or eight ten-thousandths

  10. Think about it What is 5% of 100? % means out of 100, so 5% of 100 is 5. What is 5% of 200? 5 out of each 100  5 ∙ 2 = 10 What is 5% of 300? 5 ∙ 3 = 15 You can use this method with any multiple of 100.

  11. 8.2 The Basic Percent Equation Percent ∙ Base = Amount Base is the quantity we are drawing from Base quantity usually comes after the word “of” or “out of” Example: “What is 25% of 800?” Percent = 25% Base = 800 Amount = unknown = x

  12. What is 25% of 800? Percent ∙ Base = Amount 25% ∙ 800 = x Need to convert the percent to a decimal 0.25 ∙ 800 = 200 So 25% of 800 is 200. Does that make sense? 25% is one-fourth. 200 is one-fourth of 800.

  13. What is of 90? Percent ∙ Base = Amount ∙ 90 = x = 33.3333333% (3 recurring) 0.33333 ∙ 90 = 30 So of 90 is 30. Another way to think: means one-third. One-third of 90 is 30.

  14. 20 is what percent of 32? Percent ∙ Base = Amount Percent is unknown Base is 32 Amount is 20 x ∙ 32 = 20 Divide each side by 32 x = 20 ÷ 32 x = 0.625 Need to convert to a percent 20 is 62.5% of 32.

  15. Work on Problems #9-14 in assigned groups of 3.

  16. Answers to #9-14 on worksheet 9) 40%of 30 is 12. 10) 60% of 500 is 300. 11) 8 is 25% of 32. 12) 24 is 12% of 200. 13) 58.5% of 50 grams is 29.25 grams. 14) 29 students is 20% of 145 students.

  17. 8.3 Percent Increase & Decrease Given original amount and new amount Need to find amount increase/decrease before finding percent increase/decrease Use the same formula: Percent ∙ Base = Amount To find percent increase or decrease, use the original amount as your base.

  18. Example #2 • The price of an item increases from $15 to $18. Find the percent increase. • Amount increase = $3 • Base = $15 (original price) • Percent = unknown • Percent ∙ Base = Amount • x ∙ $15 = $3 • Divide each side by $15 • x = 0.2 = 20%

  19. Work on Problems #3-8 in your groups.

  20. Answers to #3-8 • 3) Amount decrease = $10, Base = $48 • $10 ÷ $48 = 0.208 = 20.8% • 4) Amount increase = 0.7 mi/gal, Base = 17.5 mi/gal • 0.7 ÷ 17.5 = 0.04 = 4% • 5) Amount increase = $4032, Base = $2498 • $4032 ÷ $2498 = 1.61 = 161% • 6) Percent decrease = 45% = 0.45, Base = 1200 • Amount increase = (0.45)(1200) = 540; New number = 1200 – 540 = 660 • 7) Percent decrease = 25% = 0.25, Base = $16.50 • Amount decrease = (0.25)($16.50) = $4.125 • New price = $16.50 - $4.125 = $12.375 ≈ $12.38 (the store gets half a cent) • 8) Percent increase = 20% = 0.2, Base = $47.25 • Amount increase = (0.2)($47.25) = $9.45 • Bill total = $47.25 + $9.45 = $56.70

  21. Quiz Answer on a separate sheet of paper. 1.) Write 0.08% as a decimal and as a fraction. 2.) Write one-fifth as a decimal and as a percent. 3.) If a quantity doubles, what is the percent increase?

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