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Chapter 4

Chapter 4. Fractions, Decimals, and Percents. 4.1 – Connect Fractions, Decimals, and Percents, p. 124. What you will learn: Express a percent as a decimal or fraction Solve a problem that involves finding a percent Match a set of fractions to their decimals. Key Ideas.

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Chapter 4

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  1. Chapter 4 Fractions, Decimals, and Percents

  2. 4.1 – Connect Fractions, Decimals, and Percents, p. 124 • What you will learn: • Express a percent as a decimal or fraction • Solve a problem that involves finding a percent • Match a set of fractions to their decimals

  3. Key Ideas • A visual model can help you solve problems involving percents. • Every percent has an equivalent decimal and fraction value. 50% 25% 10% 25% is 0.25 or ¼ 50% is 0.50 or ½ 10% is 0.10 or 1/10

  4. You can use place value or a number line to compare fractions, decimals, and percents. • ½ is between 45% and 0.53. 45% < ½ < 0.53 45% is 0.45 ½ is 0.5 45% ½ 0.53 0 0.5 1

  5. 4.2 – Fractions, Decimals, and Percents • After this lesson, you will be able to… • Convert among fractions, decimals, and percents • Estimate percent values • Distinguish between terminating and repeating decimals • Relate fractions to terminating and repeating decimals

  6. Methods • Convert a fraction to a decimal • Divide the NUmerator by the DEnominator. • Convert a decimal to a percent • Multiply the decimal by 100. NUDE

  7. Convert From Fractions to Decimals and Percents • Ex: The following data were gathered one season for three NBA teams. • A statistic called “team percentage” is the ratio of team wins to total games. • Team percentage = Number of wins Total games played

  8. A) What is the team percentage for each team? Leave your answer as a fraction. • Miami = ___ • New Jersey = ___ • Los Angeles = ___ Team % = Number of wins Total games played Total games played = wins + losses

  9. B) Change each fraction to a decimal number rounded to the nearest thousandth. • Miami =59 = ___ 82 • New Jersey= 42 = ___ 82 • Los Angeles= 34 = ___ 82

  10. B) Change each fraction to a decimal number rounded to the nearest thousandth. • Miami =59 = 0.71951512191… = ___ 82 • New Jersey= 42 = 0.512195121… = ___ 82 • Los Angeles= 34 = 0.414634146… = ___ 82

  11. B) Change each fraction to a decimal number rounded to the nearest thousandth. • Miami =59 = 0.720 82 • New Jersey= 42 = 0.512 82 • Los Angeles= 34 = 0.415 82

  12. C) Use your rounded decimal value to show the approximate percent value for each team. • Miami =59 = 0.720 x 100 = ___ 82 • New Jersey= 42 = 0.512 x 100 = ___ 82 • Los Angeles= 34 = 0.415 x 100 = ___ 82

  13. C) Use your rounded decimal value to show the approximate percent value for each team. • Miami =59 = 0.720 x 100 = 72% 82 • New Jersey= 42 = 0.512 x 100 = 51.2% 82 • Los Angeles= 34 = 0.415 x 100 = 41.5% 82

  14. Show You Know • Convert each fraction to a decimal number. Round each decimal number to the indicated place value. Then, convert to a percent. • 27 (tenths) 56 • 125 (thosandths) 396 • 1496 (hundredths) 2005

  15. Change Fractions to Repeating Decimals • Some common fractions may change to repeating decimal numbers. • Repeating decimal: • a digit, or group of digits, that repeats forever. • Shown with a bar, ex: 0.777… = 0.7

  16. Ex: Use a calculator to change each fraction to a repeating decimal. • 1 3 • 5 9 • 5 6

  17. Solution: Use a bar over the 3 to show the repeating part. • 1 = 1 / 3 = 0.33333… = 0.3 3 • 5 = 5 / 9 = 0.55555… = 0.5 9 • 5 = 5 / 6 = 0.83333… = 0.83 6 Place a bar over only The 3 since the 8 does not repeat.

  18. Show You Know • Show the following fractions as repeating decimals. • 2 3 • 7 9

  19. 60% 0% 50% 100% Estimate Percents 70% 70 98 84 140 94 • Ex: Paige has answered 94 questions correctly out of 140 questions. Estimate her mark as a percent. • Solution: • Think: What is 50% of 140? • Half of 140 is 70. • Think: What is 10% of 140? • 140 / 10 = 14 • Add the 50% and 10% parts together to estimate. • 50% + 10% = 60% of 140. 70 + 14 = 84 -> Too low. • 50% + 10% + 10% = 70% of 140. 70 + 14 + 14 = 98 -> Too high. • The answer is between 60% and 70%, but closer to 70%.

  20. Show You Know • Estimate each of the following as a percent. • 23 out of 80 • 421 out of 560

  21. Changing Terminating Decimal Numbers to Fractions • Terminating Decimal • A decimal number in which the digits stop. • Ex: 0.4, 0.86, 0.125

  22. Ex: What fraction of a dollar is $0.75? • Solution: • The decimal number 0.75 is a terminating decimal. The last digit is in the hundredths place, so the denominator is 100. • 0.75 = 75 of a dollar, or 3 of a dollar. 100 4 $0.75 is 75c 3 quarters

  23. Ex: Change 0.652 to a fraction. • Solution: • The 2 is in the thousandths place, so the denominator is 1000. • 0.652 = 652 1000 • Can you reduce it further?

  24. Show You Know • Change each terminating decimal number to a fraction. • 0.48 • 0.078

  25. Key Ideas • To change a fraction to a decimal, divide the numerator by the denominator. 3 = 3 / 8 = 0.375 8 • Repeating decimal numbers can be written using bar notation. 1 = 0.333… = 0.3 3 • To express a terminating decimal number as a fraction, use place value to determine the denominator. 0.9 = 9 0.59 = 59 1.463 = 1463 10 100 1000 • You can use mental math to estimate percents.

  26. Small Groups -> 1-2 people Practice -> No prob? Try -> Still good? Try -> Prostar? Try -> Go through “Communicate the Ideas,” #1, 2, and 4 P. 137, #5, 8, 10, 12, 14 #7 #16-19 #21 & 22 Assignment

  27. 4.3 – Applications of Percents • After this lesson, you will be able to: • Estimate answers to percent calculations • Solve percent problems

  28. Use Percents to Make Comparisons • Ex: • Lauren bought and planted two packages of flower seeds to use in her science fair project. Package A contained 44 seeds of which 32 grew into plants. Package B contains 36 seeds of which 27 grew into plants. Which package of seeds was better?

  29. Method 1: Estimate the Percents Package A: 32 out of 44 seeds grew. 50% of 44 is half of 44. Half of 44 is 22. 25% is half of 50%. Half of 22 is 11. 50% + 25% = 75% 22 + 11 = 33 A little less than 75% of the seeds from Package A grew. Solution • Package B: • 27 out of 36 seeds grew. • 50% of 36 is half of 36. Half of 36 is 18. • 25% is half of 50%. Half of 18 is 9. • 50% + 25% = 75% 18 + 9 = 27 • Exactly 75% of the seeds from Package B grew. • Package B was better than Package A.

  30. Package A: 32/44= 0.727272… 32 = 0.72 44 0.727 to three decimal places. 0.727 = 72.7% Package A had 72.7% growth. Package B: 27/36= 0.75 27 = 0.75 36 0.75 = 75% Package B had 75% growth. Method 2: Calculate the Percents • Since 75% > 72.7%, Package B was better than Package A. When you round a decimal value, the number becomes approximate. = approximate

  31. Key Ideas • Decimal numbers and percents are often easier to compare than fractions. • When you round a decimal value, the number becomes approximate ( ). Fractions are exact numbers. • 1 and 0.3 are exact numbers. 3 • 0.3 is an approximate number because we have rounded it.

  32. Your Mission: • Small Groups -> • 1-2 people • Practice -> • No prob? Try -> • Still good? Try -> • Prostar? Try -> • Go through “Communicate the Ideas,” #2 and 3 • P. 143, #4 & 5. • If you are having trouble with these two, ASK FOR HELP! THEY ARE KEY! • #6 • #8, 9, 10, 11, 12, 13, 15, 16, 17. • #18-22. • Bold numbers are the most important ones to get correct.

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