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Percent

Percent. 3. 3.1 Introduction to Percents 3.2 Part, Rate, and Base 3.3 Percent of Increase and Decrease. 3.1 Introduction to Percents. OBJECTIVES. Identify terms used with percents. Write a percent as a decimal. Write a decimal as a percent. Write a percent as a fraction.

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Percent

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  1. Percent 3 3.1Introduction to Percents 3.2Part, Rate, and Base 3.3Percent of Increase and Decrease

  2. 3.1 Introduction to Percents OBJECTIVES Identify terms used with percents. Write a percent as a decimal. Write a decimal as a percent. Write a percent as a fraction. Write a fraction as a percent. Use Excel to format a percent, decimal, or fraction.

  3. Key Terms • percent

  4. Example Objective 2 Write a percent as a decimal. Objective2Write a percent as a decimal. Write the decimal equivalent for 35%. STEPSDrop the percent symbol and divide the number by 100.

  5. Example Objective2Write a percent as a decimal. Write 42% as its decimal equivalent. STEPSDrop the percent symbol and move the decimal point 2 places to the left, adding zeros as needed.42% = 0.42x = 0.42

  6. Example Objective2Write a percent as a decimal. Write 8 % as a decimal. STEPSConvert the fractional part of the mixed number to a decimal. 8 % = 8.25% Convert the resulting percent to its decimal equivalent.8.25% = 0.08x25 = 0.0825

  7. Example Objective3Write a decimal as a percent. Write 0.157 as a percent. STEPSMultiply the decimal number by 100 and add the percent symbol.0.157 × 100 = 15.7%

  8. Example Objective3Write a decimal as a percent. Convert 0.05 to a percent. STEPSMove the decimal point 2 places to the right, adding zeros as needed. Then add a percent symbol.0.05 = 0x05. = 5%

  9. Example Objective 4 Write a percent as a fraction. Convert 5% to a fraction. STEPSDrop the percent symbol and write a fraction, placing the percent as the numerator and 100 as the denominator. Reduce the fraction to lowest terms.5 = =

  10. Example Objective 4 Write a percent as a fraction. Write 12.5% as a fraction. STEPSChange the percent to a decimal.12.5% = 0.125 Change the decimal to a fraction and reduce.0.125 = =

  11. Example Objective 4 Write a percent as a fraction. Write 8 % as a fraction. STEPSDrop the percent symbol and divide the percent by 100. Remember to invert the divisor and multiply.

  12. Example Objective5 Write a fraction as a percent. Write as a percent. STEPSConvert the fraction to its decimal equivalent. Convert the decimal to a percent.0.20 = 0x20.% = 20%

  13. Example Objective6 Use Excel to format a percent, decimal, or fraction. To change to a different number format, open the Format cells dialog box.

  14. Example Objective6 Use Excel to format a percent, decimal, or fraction. Format each percent as a decimal. STEPSFor Cell A4: Click on the Format Cells Number tab and choose Category General.

  15. Example Objective6 Use Excel to format a percent, decimal, or fraction. Format each decimal as a percent. STEPSFor Cell A7: Click on the Format Cells Number tab and choose Category Percentage.

  16. Example Objective6 Use Excel to format a percent, decimal, or fraction. Format each percent as a fraction. STEPSFor Cell A10: Click on the Format Cells Number tab and choose Category Fraction and “Up to three digits” for the Type.

  17. Example Objective6 Use Excel to format a percent, decimal, or fraction. Format each fraction as a percent. STEPSFor Cell A13: Click on the Format Cells Number tab and choose Category Percentage.

  18. 3.2 Part, Rate, and Base OBJECTIVES Identify the terms part, rate, and base. Find the part. Find the rate. Find the base. Identify the elements of percent problems. Use Excel to find the part, rate, and base.

  19. Key Terms • base • part • rate • percentage • ratio • fill handle • relative cell reference • absolute cell reference

  20. Example Objective2Find the part. What is a 30% discount on a $150 jacket? STEPS

  21. Example Objective2Find the part. What is 6.5% of 130? STEPSIdentify each element. Base is 130. Rate is 6.5%. Part is unknown. Change the percent to a decimal.6.5% = 0.065 Apply the formula: Part = Base × RatePart = 130 × 0.065Part = 8.45 So, 8.45 (part) is 6.5% (rate) of 130 (base).

  22. Example Objective2Find the part. Suppose you had a gain of 6 % on $400. What was the gain? STEPSChange the percent to a decimal. Apply the formula: Part = Base × RatePart = $400 × 0.0625Part = $25.00 The gain was $25.

  23. Example Objective3 Find the rate. Find what percent $15 is of $139. STEPSIdentify the elements.What percent of $139 is $15? ↑ ↑ base part Apply the formula: Rate = Part ÷ BaseRate = 15 ÷ 139 = 0.108 Change the decimal to a percent.Rate = 0.108 × 100 = 10.8%

  24. Example Objective4 Find the base. $1,325 is 9.5% of what amount? STEPSIdentify the elements.Part is $1,325. Rate is 9.5%. What is the base? Rate as a decimal: 9.5% = 0.095 Apply the formula: Base = Part ÷ RateBase = $1,325 ÷ 0.095Base = $13,947.37

  25. Example Objective6 Use Excel to find the part, rate, and base. What percent of the $1,494,095 total sales is each employee’s sales? STEPSFor Cell F7: =E7/$E$11Use the fill handle to copy the formula into Column F.

  26. 3.3 Percent of Increase and Decrease OBJECTIVES Identify terms used with percent of increase and percent of decrease. Find the increase and the percent of increase. Find the increase and the total when the percent is given.

  27. 3.3 Percent of Increase and Decrease OBJECTIVES Find the decrease and the percent of decrease. Find the decrease and the total when the percent is given. Determine percentage distribution. Use Excel to calculate increase and decrease and percentage distribution.

  28. Key Terms • rate of increase • rate of decrease • percentage distribution

  29. Example Objective2 Find the increase and the percent of increase. Find the amount of increase.Sales this year: $800,120Sales last year: $620,125 STEPS

  30. Example Objective2 Find the increase and the percent of increase. Use the preceding example—sales this year, $800,120; sales last year, $620,125; amount of increase, $179,995—to find the percent of increase. STEPSPart ÷ Base = Rate$179,995 ÷ $620,125 = 0.29100 × 0.29 = 29%

  31. Example Objective3Find the increase and the total when the percent is given. Ally Dazai earned 15% more this year than last. If her earnings last year were $24,600, find her earnings for this year. STEPSIdentify each element. Base = $24,600; Rate = 15% Part = Base × Rate = $24,600 × 15% = $24,600 × 0.15 = $3,690

  32. Example Objective3Find the increase and the total when the percent is given. Ally Dazai earned 15% more this year than last. If her earnings last year were $24,600, find her earnings for this year. STEPS – Alternate MethodAdd 100% to the rate.15% + 100% = 115% Multiply the sum by the base.$24,600 × 115% = $24,600 × 1.15 = $28,290

  33. Example Objective4Find the decrease and the percent of decrease. Sales this year were $127,430. Sales last year were $145,507. Find the percent of decrease in sales. STEPSFind the decrease by subtracting the current amount from the previous amount.$145,507 – 127,430 = $18,077 Rate = Part ÷ BaseRate = $18,077 ÷ $145,507Rate = 0.12420.1242 × 100 = 12.4%

  34. Example Objective5Find the decrease and the total when the percent is given. Greene College’s enrollment of 8,425 declined by 8%. What was the total college enrollment after the decline? STEPSPart = Base × Rate8,425 × 8% = 8,425 × 0.08 = 674 Subtract the decrease from the base.8,425 – 674 = 7,751

  35. Example Objective5Find the decrease and the total when the percent is given. Greene College’s enrollment of 8,425 declined by 8%. What was the total college enrollment after the decline? STEPS – Alternate MethodChange the percent to its decimal equivalent and subtract from 1.00. (This is its complement.)1.00 – 0.08 = 0.92Multiply the base by the complement.8,425 × 0.92 = 7,751

  36. Example Objective5Find the decrease and the total when the percent is given. First Electronic laid off 15% of its 580 employees. How many people are currently employed by First Electronic? STEPS

  37. Example Objective6Determine percentage distribution. Complete the table below. STEPS

  38. Example Objective7Use Excel to calculate increase and decrease and percentage distribution. Find the amount of increase or decrease and the percent increase or decrease. STEPS For Cell D6: =C6-B6Copy the formula into Column D.

  39. Example Objective7Use Excel to calculate increase and decrease and percentage distribution. Find the amount of increase or decrease and the percent increase or decrease. STEPS For Cell E6: =D6/B6Copy the formula into Column E.

  40. Example Objective7Use Excel to calculate increase and decrease and percentage distribution. Find the percentage distribution. STEPS For Cell C5: =B5/$B$9Copy the formula into Column C.

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