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% and the BASIC PERCENT EQUATION MSJC ~ Menifee Valley Campus Math Center Workshop Series Janice Levasseur % 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 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 . . . 27% done 100 Ex: Convert 25% to a fraction 25 25% Simplify? YES! 100 1 Simplify? No . . . 4 done Ex: Convert 130% to a fraction 130 130% Simplify? Yes! 100 Improper Fraction 30 1 100 Simplify? Yes! 3 1 Simplify? No . . . 10 done 1 Ex: Convert 3 % to a fraction 1 1 1 Divide % 3 100 3 100 fractions 3 1 100 1 1 3 1 3 100 1 Simplify? No . . . 300 done Ex: Convert 0.5% to a fraction 0.5% 0.5 Divide decimals? 100 Decimal Fraction 1 100 2 1 100 1 1 1 2 1 2 100 200 Simplify? No . . . done Your Turn to Try a Few 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 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 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 1 Ex: Convert % to a decimal 3 • 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) 1 1 1 1 Fraction 100 form of 3 3 100 300 the answer Ex: cont. • Recall: To convert a fraction to a decimal number, divide the numerator by the denominator 1 .0033 0.003 300 300 1.0000 900 1000 900 100 Your Turn to Try a Few 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 Ex: Convert ¼ to a percent 1 1 100 100% % 4 4 1 100 % Simplify? Yes! 4 = 25% Ex: Convert 1 ½ to a percent 1 3 100 1 100% % 2 2 1 300 % Simplify? Yes! 2 = 150% Ex: Convert 5/8 to a percent 5 Simplify? 5 100 100% 500 % % Yes! 8 8 1 8 4 62 % Simplify? Yes! 8 1 62 % Simplify? No . . . 2 done Ex: Convert 5/6 to a percent 5 Simplify? 5 100 100% 500 % % Yes! 6 6 1 6 2 83 % Simplify? Yes! 6 1 83 % Simplify? No . . . 3 done Your Turn to Try a Few 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 Ex: Convert 0.36 to a % 0.36 100% 0.36 = 36% Ex: Convert 0.01 to a % 0.01 100% 0.01 = 1% Ex: Convert 3.19 to a % 3.19 100% 3.19 = 319% Ex: Convert 0.005 to a % 0.005 100% 0.005 = 0.5% Your Turn to Try a Few 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 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 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. 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 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. 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 Ex: Cont. 5% of what is 28? • Now solve the mathematical equation: 5% x b = 28 Rewrite the % in working form Solve the equation by 0.05 x b = 28 dividing both sides by 0.05 or multiply by 100/5 100/5 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. 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 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. Your Turn to Try a Few 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”) • 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 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: p x 206 = 56 Solve the equation by dividing both sides by 206 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. 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”) • 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 • Translate the hybrid sentence into the Basic Percent Equation 125% x original trail = new trail 125% x b = 8 • Now solve the mathematical equation: 1.25 x b = 8 Solve the equation by dividing both sides by 1.25 or multiply by 100/125 100/125 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. 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”) • 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 • 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: 0.05 x b = 38.75 Solve the equation by dividing both sides by 0.05 or multiply by 100/5 100/5 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. 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”) • 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 • 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.