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1. % and the BASIC PERCENT EQUATION MSJC ~ Menifee Valley Campus Math Center Workshop Series Janice Levasseur

2. % Percents % • Percent means “parts of 100” or “per 100” • A percent can be written using a percent sign (%), as a fraction, or as a decimal

3. Converting a % to a Fraction • To convert a percent to a fraction, translate the % symbol: • Remove the % sign and divide by 100 (“per 100”) Ex: Convert 27% to a fraction No . . . done Simplify ? 27%

4. Ex: Convert 25% to a fraction 25% Simplify? YES! No . . . done Simplify?

5. Ex: Convert 130% to a fraction Yes! Improper Fraction 130% Simplify? Simplify? Yes! Simplify? No . . . done

6. Ex: Convert % to a fraction Divide fractions Simplify? No . . . done

7. Ex: Convert 0.5% to a fraction Divide decimals? Decimal  Fraction 0.5% No . . . done Simplify?

8. Your Turn to Try a Few

9. Converting a % to a Decimal • To convert a percent to a decimal, translate the % symbol: • Remove the % sign and divide by 100 (“per 100”) or • Move the decimal point two places to the left

10. Ex: Convert 27% to a decimal = 0.27 27%  27.0 = 27 100 Ex: Convert 25% to a decimal = 0.25 25%  25.0 = 25 100

11. Ex: Convert 130% to a decimal = 1.30 130%  130.0 = 130 100 Ex: Convert 0.5% to a decimal = 0.005 0.5%  0.5 = 0.5 100

12. Ex: Convert % to a decimal • We are starting with a percent written as a fractional percent • First convert the fractional percent to a fraction (drop the % sign and divide by 100) Fraction form of the answer

13. Ex: cont. • Recall: To convert a fraction to a decimal number, divide the numerator by the denominator .0033 300 1.0000 900 1000 900 100 0.003

14. Your Turn to Try a Few

15. Converting a Fraction to a % • To convert a fraction to a percent, reverse the procedure for converting a percent to a fraction: • Multiply by 100 and add the % sign

16. Ex: Convert ¼ to a percent Simplify? Yes! = 25%

17. Ex: Convert 1 ½ to a percent Simplify? Yes! = 150%

18. Ex: Convert 5/8 to a percent Simplify? Yes! Simplify? Yes! No . . . done Simplify?

19. Ex: Convert 5/6 to a percent Simplify? Yes! Simplify? Yes! No . . . done Simplify?

20. Your Turn to Try a Few

21. Converting a Decimal to a % • To convert a decimal to a percent, reverse the procedure for converting a percent to a decimal: • Multiply by 100 and add the % sign  • Move the decimal point two places to the right

22. Ex: Convert 0.36 to a % 0.36  0.36 = 36% Ex: Convert 0.01 to a % 0.01  0.01 = 1%

23. Ex: Convert 3.19 to a % 3.19  3.19 = 319% Ex: Convert 0.005 to a % 0.005  0.005 = 0.5%

24. Your Turn to Try a Few

25. The BASIC PERCENT EQUATION • The Basic Percent Equation is given by Percent x Base = Amount • The Percent has the percent sign % • The Base always follows the word “of” • The other number is the Amount

26. Ex: 5% of 120 is what? • Identify the three components (remember, the base always follows “of”, the multiplication, and the equals. Percent = 5% Base = 120 (follows “of”) Amount = Unknown “what”  a • Translate the English statement to the Basic Percent Equation: 5% x 120 = a

27. Ex: Cont. 5% of 120 is what? • Now solve the mathematical equation: 5% x 120 = a Rewrite the % in working form 0.05 x 120 = a Perform the math operation 6.00 = a Therefore, 5% of 120 is 6.

28. Ex: What is 6.3% of 150? Identify the three components (remember, the base always follows “of”, the multiplication, and the equals. Percent = 6.3% Base = 150 (follows “of”) Amount = Unknown “what”  a • Translate the English statement to the Basic Percent Equation: a = 6.3% x 150

29. Ex: Cont. What is 6.3% of 150? • Now solve the mathematical equation: a = 6.3% x 150 Rewrite the % in working form a = .063 x 150 Perform the math operation a = 9.45 Therefore, 9.45 is 6.3% of 150.

30. Ex: 5% of what is 28? • Identify the three components (remember, the base always follows “of”, the multiplication, and the equals. Percent = 5% Base = Unknown “what”  b (follows “of”) Amount = 28 • Translate the English statement to the Basic Percent Equation: 5% x b = 28

31. Ex: Cont. 5% of what is 28? • Now solve the mathematical equation: Rewrite the % in working form 5% x b = 28 Solve the equation by dividing both sides by 0.05 or multiply by 100/5 0.05 x b = 28 100/5 x 0.05 x b = 100/5 x 28 20 x 0.05 x b = 20 x 28 b = 560 Therefore, 5% of 560 is 28.

32. Ex: What % of 32 is 20? • Identify the three components (remember, the base always follows “of”, the multiplication, and the equals. Percent = Unknown “what”  p Base = 32 (follows “of”) Amount = 20 • Translate the English statement to the Basic Percent Equation: p x 32 = 20

33. Ex: Cont. What % of 32 is 20? • Now solve the mathematical equation: p x 32 = 20 Solve the equation by dividing both sides by 32 p = 0.625 This is the decimal form of the percent. Rewrite using the % sign p = 0.625 = 62.5% Therefore, 62.5% of 32 is 20.

34. Your Turn to Try a Few

35. Ex: The human body contains 206 bones. The fingers and the toes contain a total of 56 small bones, or phalanges. What percent of the bones of the body are phalanges? Find the sentence that will be your equation (percent, base, amount, of, “is”)

36. Identify the three components (remember, the base always follows “of”, the multiplication, and the equals: What percent of the bones of the body are phalanges? Percent = Unknown “what”  p Base = Bones of the body (follows “of”) Amount = phalanges Multiplication “of” Equals “is” • Write a hybrid sentence – half in math, half in English: p x bones of the body = phalanges

37. Translate the hybrid sentence into the Basic Percent Equation The human body contains 206 bones. The fingers and the toes contain a total of 56 small bones, or phalanges. p x bones of the body = phalanges p x 206 = 56 • Now solve the mathematical equation: Solve the equation by dividing both sides by 206 p x 206 = 56 p = 0.2718 . . . This is the decimal form of the percent. Rewrite using the % sign p = 0.2718 . . .= 27.2% Therefore, about 27.2% of bones are phalanges.

38. Ex: The new 8-mile nature trail is 125% of the length of the original trail. How long was the original trail? Find the sentence that will be your equation (percent, base, amount, of, “is”)

39. Identify the three components (remember, the base always follows “of”, the multiplication, and the equals: The new 8-mile nature trail is 125% of the length of the original trail. Percent = 125% Base = Original trail length = b (follows “of”) Amount = New 8-mile trail Multiplication “of” Equals “is” • Write a hybrid sentence – half in math, half in English: 125% x original trail = new trail

40. Translate the hybrid sentence into the Basic Percent Equation 125% x original trail = new trail 125% x b = 8 • Now solve the mathematical equation: Solve the equation by dividing both sides by 1.25 or multiply by 100/125 1.25 x b = 8 100/125 x 1.25 x b = 100/125 x 8 4/5 x 1.25 x b = 4/5 x 8 32/5 = 6.4 b = 6.4 Therefore, the original trail was 6.4 miles.

41. Ex: A medical supply company charges 5% of the order total as a shipping and handling charge. If the shipping and handling charge is \$38.75, what was the cost of the order? Find the sentence that will be your equation (percent, base, amount, of, “is”)

42. Identify the three components (remember, the base always follows “of”, the multiplication, and the equals: 5% of the order total as a shipping and handling charge. Percent = 5% Base = Order total = b (follows “of”) Amount = S&H charge Multiplication “of” Equals “is” • Write a hybrid sentence – half in math, half in English: 5% x order total = S & H

43. Translate the hybrid sentence into the Basic Percent Equation 5% x order total = S & H 5% x b = 38.75 • Now solve the mathematical equation: Solve the equation by dividing both sides by 0.05 or multiply by 100/5 0.05 x b = 38.75 100/5 x 0.05 x b = 100/5 x 38.75 20 x 0.05 x b = 20 x 38.75 b = 775 Therefore, the cost of the order was \$775.00.

44. More Practice:Ex: 26.1% of the 364 patients admitted in an emergency room are admitted due to an auto accident injury.How many patients are admitted due to an auto accident injury? Find the sentence that will be your equation (percent, base, amount, of, “is”)

45. Identify the three components (remember, the base always follows “of”, the multiplication, and the equals: 26.1% of the 364 patients admitted in an emergency room are admitted due to an auto accident injury. Percent = 26.1% Base = Admitted patients (follows “of”) Amount = Admitted due to auto accident = a Multiplication “of” Equals “is” • Write a hybrid sentence – half in math, half in English: 26.1% x admitted patients = admitted due to auto accident

46. Translate the hybrid sentence into the Basic Percent Equation • 26.1% of the 364 patients admitted in an emergency room are admitted due to an auto accident injury. 26.1% x admitted patients = admitted due to auto accident 26.1% x 364 = a • Now solve the mathematical equation: .261 x 364 = a Solve the equation by multiplying 95.004 = a Therefore, 95 patients were admitted due to an auto accident injury.