HAWKES LEARNING SYSTEMS Students Matter. Success Counts. Copyright © 2013 by Hawkes Learning Systems/Quant Systems, Inc. All rights reserved. Section 4.4 Fractions and Percents

HAWKES LEARNING SYSTEMS Students Matter. Success Counts. Copyright © 2013 by Hawkes Learning Systems/Quant Systems, Inc. All rights reserved. Objectives o Change fractions and mixed numbers to percents. o Change percents to fractions and mixed numbers.

HAWKES LEARNING SYSTEMS Students Matter. Success Counts. Copyright © 2013 by Hawkes Learning Systems/Quant Systems, Inc. All rights reserved. Example 1: Changing Fractions to Percents Change to a percent. Solution Note that 8 is not a factor of 100 so we divide by using long division (or use a calculator).

HAWKES LEARNING SYSTEMS Students Matter. Success Counts. Copyright © 2013 by Hawkes Learning Systems/Quant Systems, Inc. All rights reserved. Example 1: Changing Fractions to Percents This can be done with a calculator. Move the decimal point two places right and write the % sign.

HAWKES LEARNING SYSTEMS Students Matter. Success Counts. Copyright © 2013 by Hawkes Learning Systems/Quant Systems, Inc. All rights reserved. Example 2: Changing Mixed Numbers to Percents Change to a percent. Solution There are three ways to do this problem. All give the same answer. Method 1: Change to decimal form directly.

HAWKES LEARNING SYSTEMS Students Matter. Success Counts. Copyright © 2013 by Hawkes Learning Systems/Quant Systems, Inc. All rights reserved. Example 2: Changing Mixed Numbers to Percents Method 2:Change to an improper fraction and divide to find the decimal form: Thus,

HAWKES LEARNING SYSTEMS Students Matter. Success Counts. Copyright © 2013 by Hawkes Learning Systems/Quant Systems, Inc. All rights reserved. Example 2: Changing Mixed Numbers to Percents (cont.) Method 3:Change to an improper fraction and then change the fraction to one with denominator 100. (Note that 4 is a factor of 100.)

HAWKES LEARNING SYSTEMS Students Matter. Success Counts. Copyright © 2013 by Hawkes Learning Systems/Quant Systems, Inc. All rights reserved. Example 3: Changing Fractions to Percents Change to a percent. Solution a.Using a calculator, Rounding the decimal quotient to the nearest thousandth: The answer is rounded and thus not exact.

HAWKES LEARNING SYSTEMS Students Matter. Success Counts. Copyright © 2013 by Hawkes Learning Systems/Quant Systems, Inc. All rights reserved. Example 3: Changing Fractions to Percents (cont.) b.Without a calculator, we can divide and use fractions.

HAWKES LEARNING SYSTEMS Students Matter. Success Counts. Copyright © 2013 by Hawkes Learning Systems/Quant Systems, Inc. All rights reserved. Example 4: Changing Fractions to Percents During the years 1921 to 2005, the New York Yankees baseball team played in 39 World Series Championships and won 26 of them. What percent of these championships did the Yankees win?

HAWKES LEARNING SYSTEMS Students Matter. Success Counts. Copyright © 2013 by Hawkes Learning Systems/Quant Systems, Inc. All rights reserved. Example 4: Changing Fractions to Percents (cont.) Solution a.The percent won can be found by using a calculator and changing the fraction to decimal form and then changing the decimal to a percent. Using a calculator, (rounded)

HAWKES LEARNING SYSTEMS Students Matter. Success Counts. Copyright © 2013 by Hawkes Learning Systems/Quant Systems, Inc. All rights reserved. Example 4: Changing Fractions to Percents (cont.) b.Without a calculator, we can divide and use fractions. The Yankees won or about 66.67% of these championships.

HAWKES LEARNING SYSTEMS Students Matter. Success Counts. Copyright © 2013 by Hawkes Learning Systems/Quant Systems, Inc. All rights reserved. To Change a Percent to a Fraction or a Mixed Number Step 1: Write the percent as a fraction with 100 as the denominator and drop the % sign. Step 2: Reduce the fraction, if possible. Changing Percents to Fractions and Mixed Numbers

HAWKES LEARNING SYSTEMS Students Matter. Success Counts. Copyright © 2013 by Hawkes Learning Systems/Quant Systems, Inc. All rights reserved. Example 5: Changing Percents to Fractions Change 60% to a fraction and reduce, if possible. Solution

HAWKES LEARNING SYSTEMS Students Matter. Success Counts. Copyright © 2013 by Hawkes Learning Systems/Quant Systems, Inc. All rights reserved. Example 6: Changing Percents to Fractions Change 130% to a mixed number. Solution

HAWKES LEARNING SYSTEMS Students Matter. Success Counts. Copyright © 2013 by Hawkes Learning Systems/Quant Systems, Inc. All rights reserved. Common Misunderstanding Concerning Percents The fractions and are often confused with the percents and The differences can be clarified by using decimal numbers. PERCENT DECIMAL FRACTION Changing Percents to Fractions and Mixed Numbers

HAWKES LEARNING SYSTEMS Students Matter. Success Counts. Copyright © 2013 by Hawkes Learning Systems/Quant Systems, Inc. All rights reserved. Common Misunderstanding Concerning Percents (cont.) PERCENT DECIMAL FRACTION % % 0.50 Changing Percents to Fractions and Mixed Numbers

HAWKES LEARNING SYSTEMS Students Matter. Success Counts. Copyright © 2013 by Hawkes Learning Systems/Quant Systems, Inc. All rights reserved. Common Misunderstanding Concerning Percents (cont.) Thus Similarly, Changing Percents to Fractions and Mixed Numbers

HAWKES LEARNING SYSTEMS Students Matter. Success Counts. Copyright © 2013 by Hawkes Learning Systems/Quant Systems, Inc. All rights reserved. Changing Percents to Fractions and Mixed Numbers Common Percent-Decimal-Fraction Equivalents

HAWKES LEARNING SYSTEMS Students Matter. Success Counts. Copyright © 2013 by Hawkes Learning Systems/Quant Systems, Inc. All rights reserved. Changing Percents to Fractions and Mixed Numbers Common Percent-Decimal-Fraction Equivalents (cont.)

HAWKES LEARNING SYSTEMS Students Matter. Success Counts. Copyright © 2013 by Hawkes Learning Systems/Quant Systems, Inc. All rights reserved. Practice Problems Change each fraction or mixed number to a percent Change each percent to a fraction or mixed number. Reduce the fractions % % % % 10.

HAWKES LEARNING SYSTEMS Students Matter. Success Counts. Copyright © 2013 by Hawkes Learning Systems/Quant Systems, Inc. All rights reserved. Practice Problem Answers 1. 24% %3. 5.6% %5. 510%