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This presentation explains how to convert between percentages and fractions, and provides examples and formulas for finding percentages, rates, and bases. Practical problems are also included.
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PERCENTS • Indicates number of hundredths in a whole • A decimal fraction can be expressed as a percent by moving the decimal point two places to the right and inserting the percent symbol
ESTIMATING • Example: Express 0.0152 as a percent: • Move decimal point two places to right 0.0152 = 1.52 • Insert percent symbol 0.0152 = 1.52%
FRACTIONS TO PERCENTS • To express a common fraction as a percent: • First, express the fraction as a decimal by dividing the numerator by the denominator • Convert the answer to a percent by moving the decimal point two places to the right
FRACTIONS TO PERCENTS • Example: Express as a percent: • First convert the fraction to a decimal by dividing • Then change the decimal to a percent 0.875 = 87.5%
PERCENTS TO FRACTIONS • To express percent as decimal fraction: • Drop the percent symbol • Move decimal point two places to the left
PERCENTS TO FRACTIONS • Example: Express as a decimal and round the answer to 4 decimal places • Convert the fraction to 0.76 • Drop the percent symbol and move the decimal point 2 places to the left: 38.76% = 0.3876
PERCENTS TO FRACTIONS • To express a percent as a common fraction: • First convert percent to a decimal fraction • Then express the decimal fraction as a common fraction
PERCENTS TO FRACTIONS • Example: Express 37.5% as a common fraction • Express 37.5% as a decimal • Express 0.375 as a common fraction
PERCENT TERMS DEFINED • All simple percent problems have three parts: • Rate is the percent (%) • Base represents whole or quantity equal to 100% • Word “of” generally relates to the base • Percentage is part or quantity of percent of the base • Word “is” generally relates to the percentage
PERCENT TERMS DEFINED • Example: Identify base, rate, and percentage What percent of 48 is 12? • Problem is asking for rate (percent) • The number 48 represents whole and is identified by word “of,” so it is the base • The number 12 represents part and is identified by word “is,” so it is the percentage
FINDING THE PERCENTAGE • Proportion formula for all three types of percentage problems: • Where: • B is the base • P is the percentage or part of the base • R is the rate or percent
FINDING THE PERCENTAGE • Example: What is 15% of 60? • The base, B, is 60: the number of which the rate is taken—the whole or a quantity equal to 100% • The problem is asking for the percentage (part): the quantity of the percent of the base
FINDING THE PERCENTAGE • The proportion is: • Use cross-products and division:
FINDING THE RATE • Example: What percent of 12.87 is 9.62 rounded to 1 decimal place? • The base, B, or whole quantity equal to 100% is 12.87 • The percentage, P, or quantity of the percent of the base is 9.620 • The rate, R, is to be found
FINDING THE RATE • The proportion is: • Cross multiply: • Divide:
FINDING THE BASE • Example: 816 is 68% of what number? • The rate, R, is 68% • The percentage, P, is 816 • The base, B, is to be found • The proportion is: • Solve for B:
PRACTICAL PROBLEMS • A 22-liter capacity radiator requires 6.5 liters of antifreeze to give protection to -17ºC. • What percent of the coolant is antifreeze? Round the answer to the nearest whole percent.
PRACTICAL PROBLEMS • In this problem: • The percentage (P) or the part is 6.5 liters • The base (B) is 22 liters • The rate (R) or percent is unknown • Set up the formula and solve
PRACTICAL PROBLEMS • Solve: • The antifreeze is 30% of the coolant