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 27% Simplify ? No... done

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

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

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

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

10. 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

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

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

13. 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

14. 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

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! Simplify? No... done

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

20. 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

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

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

23. Your Turn to Try a Few

24. 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

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

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

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

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

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

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

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

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

33. 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”)

34. 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 = Base = Amount = Write a hybrid sentence – half in math, half in English: p x bones of the body = phalanges Unknown “what”  p Bones of the body (follows “of”) phalanges Multiplication “of” Equals “is”

35. Now solve the mathematical equation: p x 206 = 56 p = 0.2718... Solve the equation by dividing both sides by 206 This is the decimal form of the percent. Rewrite using the % sign p = 0.2718... = 27.2% 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 206 = 56 p x bones of the body = phalanges Therefore, about 27.2% of bones are phalanges.

37. 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”)

38. 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 = Base = Amount = Write a hybrid sentence – half in math, half in English: 125% x original trail = new trail 125% Original trail length = b (follows “of”) New 8-mile trail Multiplication “of” Equals “is”

39. Now solve the mathematical equation: 1.25 x b = 8 b = 6.4 Solve the equation by dividing both sides by 1.25 or multiply by 100/125 Translate the hybrid sentence into the Basic Percent Equation 125% x b = 8 125% x original trail = new trail Therefore, the original trail was 6.4 miles. 100/125 x 1.25 x b = 100/125 x 8 4/5 x 1.25 x b = 4/5 x 832/5 = 6.4

42. 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”)

43. 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 = Base = Amount = Write a hybrid sentence – half in math, half in English: 5% x order total = S & H 5% Order total = b (follows “of”) S&H charge Multiplication “of” Equals “is”

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

46. 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”)

47. 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 = Base = Amount = Write a hybrid sentence – half in math, half in English: 26.1% x admitted patients = admitted due to auto accident 26.1% Admitted patients (follows “of”) Admitted due to auto accident = a Multiplication “of” Equals “is”

48. Now solve the mathematical equation:.261 x 364 = a 95.004 = a Solve the equation by multiplying 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 364 = a 26.1% x admitted patients = admitted due to auto accident Therefore, 95 patients were admitted due to an auto accident injury.