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Algebra I Percents

Algebra I Percents. C. D. H. G. 1) Parallelogram ABCD parallelogram EFGH. Find the value of x. A. B. E. F. 30. E. F. 20. A. B. 18. x. D. G. C. H. 2) Trapezoids ABCD trapezoids EFGH. Find the value of x. 8. 12. x. 6. Warm Up. 1) 12 units. 2) 90 units.

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Algebra I Percents

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  1. Algebra IPercents CONFIDENTIAL

  2. C D H G 1) Parallelogram ABCD parallelogram EFGH. Find the value of x. A B E F 30 E F 20 A B 18 x D G C H 2) Trapezoids ABCD trapezoids EFGH. Find the value of x. 8 12 x 6 Warm Up 1) 12 units 2) 90 units CONFIDENTIAL

  3. Percent • Percent is a ratio that compares a number to 100. For example, • 20% = 20 • 100 • To find the Fractionequivalent of a percent, write the percent as a ratio with a denominator of 100. Then simplify. • 20% =20 = 1 • 100 5 • To find the decimal equivalent of a percent, divide by 100. • 20% =20 = 0.2 • 100 CONFIDENTIAL

  4. The greatest percent shown in the table is 100%, or 1. But percents can be greater than 100% or less than 1%. For example, 130% = 130 = 1.3 and 0.6% = 0.6 = 0.006 100 100 CONFIDENTIAL

  5. Finding the Part You can use the proportion part = percent to find unknown whole 100 values. A) Find 40% of 30. Method 1- Use a proportion: part = percentUse the percent proportion. whole 100 x = 40Let x represent the part. 30 100 100x = 1200Find the cross products. x = 12Since x is multiplied by 100, divide both sides by 100 to undo the multiplication. Check 40% is the same as 2 , and 2 of 30 is 12. 5 5 CONFIDENTIAL

  6. Finding the Part B) Find 110% of 66. Method 2- Use an equation. x = 110% of 66Write an equation. Let x represent the part. x = 1.1 (66) Write the percent as a decimal and multiply. x = 72.6 110% of 66 is 72.6. CONFIDENTIAL

  7. Now you try! Find the Part. 1) 50% of 56 2) 25% of 200 1) 28 2) 50 3) 0.5% of 10 4) 120% of 50 3) 0.05 4) 60 CONFIDENTIAL

  8. Finding the Percent A) What percent of 60 is 15?. Method 1 Use a proportion. part = percentUse the percent proportion. whole 100 15 = xLet x represent the percent. 60 100 60x = 1500Find the cross products. x = 25Since x is multiplied by 60, divide both sides by 60 to undo the multiplication. 15 is 25% of 60. CONFIDENTIAL

  9. B) 440 is what percent of 400? Method 2- Use an equation. 440 = x · 400 Write an equation. Let x represent the percent. 440 = 400x Since x is multiplied by 400, divide both sides by 400 to undo the multiplication. 440 = 400x 400 400 1.1 = x The answer is a decimal. Write the decimal as a percent. This answer is reasonable; 440 is more than 100% of 400. 110% = x 440 is 110% of 400. CONFIDENTIAL

  10. Now you try! Find the Percent. 2) What percent of 45 is 3? 1) What percent of 25 is 5? 1) 20% 2) 6.67 3) 36 is what percent of 9? 4) 14 is what percent of 56? 3) 400% 4) 25% CONFIDENTIAL

  11. Finding the Whole A) 30% of what number is 12? Method 1- Use a proportion. part = percent whole 100 12 = 30Let x represent the whole. x 100 30x = 1200Find the cross products. 30x = 1200Since x is multiplied by 30, 30 30 divide both sides by 30 to undo the multiplication. x = 40 30% of 40 is 12. CONFIDENTIAL

  12. Finding the Whole B) 60 is 0.6% of what number? Method 2 Use an equation. Write an equation. Let x represent the whole. 60 = 0.6% of x 60 = 0.006x Write the percent as a decimal. Since x is multiplied by 0.006, divide both sides by 0.006 to undo the multiplication. 60 = 0.006x 0.006 0.006 10000 = x 60 is 0.6% of 10000 CONFIDENTIAL

  13. Now you try! Find the Percent. 2) 60% of what number is 90? 1) 160% of what number is 80? 1) 50 2) 150 3) 45 is 25% of what number? 4) 70 is 35% of what number? 3) 180 4) 200 CONFIDENTIAL

  14. A) Jewelers use the karat system to determine the amount of pure gold in jewelry. Pure gold is 24 karat, meaning the item is 100% gold. A 14-karat gold ring contains 14 parts gold and 10 parts other metal. What percent of the ring is gold? Round your answer to the nearest percent. • part = percent • whole100 • 14 = x • 100 • 24x = 1400 • 24x = 1400 • 24 24 • x = 58.3 Use the percent proportion. Let x represent the percent. Find the cross products. Since x is multiplied by 24, divide both sides by 24 to undo the multiplication. A 14-karat gold ring is approximately 58% gold. CONFIDENTIAL

  15. B) A man gives 40% of his money to his children and 20% of the remaining to a trust. If he is still left with $9600, what did he originally have? SOLUTION: Let the original amount of money with him be $100. Since 40% of original money is given to children. Therefore, remaining money =$(100 - 40) = $60. Money given to trust = 20% of the remaining = 20 of $60 = $12 100 Next page  CONFIDENTIAL

  16. Therefore, remaining money =$(60 - 12) = $48. It is given that remaining money =$9600. When the remaining amount is $48, original amount = $100. When the remaining amount is $9600, Original amount = $ 100 ×9600 = $20,000 48 The man originally had $20,000. CONFIDENTIAL

  17. Now you try! 1) A certain granola bar has 2 grams of fiber. This is 8% of the recommended daily value. How many grams of fiber are recommended daily? 1) 25 grams 2) After deducting 10% from a sum and then 20% from the remainder, $3600 are left. Find the original amount? 2) $5000 CONFIDENTIAL

  18. Assessment 1) Find 75% of 60. 1) 45 2) Find 115% of 80. 2) 92 3) What percent of 40 is 25? 3) 62.5% 4) What percent of 225 is 135? 4) 60% 5) 56 is what percent of 20? 5) 280% CONFIDENTIAL

  19. 6) 1 is what percent of 16? 6) 6.25% 7) 48 is 32% of what number? 7) 150 8) 16 is 20% of what number? 8) 80 9) 8% of what number is 7? 9) 87.5 10) 105% of what number is 37.8? 10) 36 CONFIDENTIAL

  20. 11) A certain can of iced tea contains 4% of the recommended daily allowance of sodium. The recommended daily allowance is 2500 milligrams. How many milligrams of sodium are in the can of iced tea?. 11) 100 milligrams 12) On average, sloths spend 16.5 hours per day sleeping. What percent of the day do sloths spend sleeping? Round your answer to the nearest percent. 12) 68.75 CONFIDENTIAL

  21. Let’s review Percent • Percent is a ratio that compares a number to 100. For example, • 20% = 20 • 100 • To find the Fractionequivalent of a percent, write the percent as a ratio with a denominator of 100. Then simplify. • 20% =20 = 1 • 100 5 • To find the decimal equivalent of a percent, divide by 100. • 20% =20 = 0.2 • 100 CONFIDENTIAL

  22. review The greatest percent shown in the table is 100%, or 1. But percents can be greater than 100% or less than 1%. For example, 130% = 130 = 1.3 and 0.6% = 0.6 = 0.006 100 100 CONFIDENTIAL

  23. review Finding the Percent A) What percent of 60 is 15?. Method 1 Use a proportion. part = percentUse the percent proportion. whole 100 15 = xLet x represent the percent. 60 100 60x = 1500Find the cross products. x = 25Since x is multiplied by 60, divide both sides by 60 to undo the multiplication. 15 is 25% of 60. CONFIDENTIAL

  24. review Finding the Whole B) 60 is 0.6% of what number? Method 2 Use an equation. Write an equation. Let x represent the whole. 60 = 0.6% of x 60 = 0.006x Write the percent as a decimal. Since x is multiplied by 0.006, divide both sides by 0.006 to undo the multiplication. 60 = 0.006x 0.006 0.006 10000 = x 60 is 0.6% of 10000 CONFIDENTIAL

  25. review A) Jewelers use the karat system to determine the amount of pure gold in jewelry. Pure gold is 24 karat, meaning the item is 100% gold. A 14-karat gold ring contains 14 parts gold and 10 parts other metal. What percent of the ring is gold? Round your answer to the nearest percent. • part = percent • whole100 • 14 = x • 100 • 24x = 1400 • 24x = 1400 • 24 24 • x = 58.3 Use the percent proportion. Let x represent the percent. Find the cross products. Since x is multiplied by 24, divide both sides by 24 to undo the multiplication. A 14-karat gold ring is approximately 58% gold. CONFIDENTIAL

  26. You did a great job today! CONFIDENTIAL

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