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Understanding Fractions, Decimals, and Percents

Learn how to convert between fractions, decimals, and percents and solve practical problems involving percentages. Practice worksheets included.

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Understanding Fractions, Decimals, and Percents

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  1. GEPA Lesson 6 Fractions, Decimals, and Percents

  2. Percent means hundredths • 75% means: 75/100 or 0.75 • 4% means: 4/100 or 0.04 • 150% means: 150/100 or 1.50 (think in terms of money: 75 cents, 4 cents, one dollar and 50 cents)

  3. You can also think of changing a percent to a decimal by dropping the % symbol and moving the decimal point 2 places to the left 30% = 0.30 3% = 0.03 125% = 1.25

  4. Example # 1

  5. Jed changed 8% to a decimal in order to determine the amount of tax he would have to pay on his purchase of a guitar. Which correctly represents 8%?A. 0.08 B. 0.8 C. 8.0 D. 800 8% means 0.08 (think in terms of money: 8 cents out of 100 cents, or .08) or 8% = 0.08 (move decimal point 2 places to the left) Thus, 8% is represented by 0.08, choice A.

  6. Example # 2

  7. 35% of the students in the eighth grade at Ramsey Junior High are in sports. What fraction of the students is that?A. 35/10 B. 3/5 C. 7/20 D. 35/1000 35% means 35/100 Now reduce this fraction to lowest terms. 35/100 = 7/20 (divide the numerators and denominator by 5) Thus, the fraction of students is 7/20, choice c.

  8. TRY THESE: # 1.) Write 6% as a decimal. #2.) Write 145% as a decimal. #3.) Write 40% as a fraction reduced to lowest terms. #4.) What are two ways you can change a percent into a decimal? #5.) How can you change a percent into a fraction?

  9. You can change a fraction to a percent by dividing the numerator by the denominator. If the division is not exact, carry our the division to the thousandths place. Then, you might round the results to the nearest hundredth and write the results as a percent. However, the GEPA might indicate an APPROXIMATION in the multiple choice that is NOT this rounded answer. (this is illustrated in the following example.)

  10. Example # 3

  11. Six-sevenths of Ms. Jamison’s girl scout troopplanned to attend a baseball game. APPROXIMATELY what percent of the troop was that?A. 11% B. 67% C. 76% D. 85% Divide 7 into 6.000 7 into 6.000 = 0.857 But, the APPROXIMATE answer from dividing mentally to two decimal places is 0.85. As a percent, 0.85 is 85% Thus, the APPROXIMATE % is 85%, choice D

  12. TRY THESE: # 6.) Two-sevenths of Mr. Johnson’s math class failed the last math test. APPROXIMATELY what percent of the class was that? A. 2% B. 28% C. 35% D. 280%

  13. Example # 4

  14. Find a number between 7/25 and 30% Write 7/25 and 30% each as a decimal. 7/25 = 7 ÷ 25 = 0.28 30% = 0.30 So, a number between 0.28 and 0.30 could be: 0.29

  15. Example # 5

  16. Which number below does NOT represent the shaded portion of the figure?A. 5/8 B. 62.5 C. 62 ½ D. 0.625 5 out of 8 blocks are shaded. 5/8 of the region is shaded. First change 5/8 to a decimal, in hundredths. Divide 8 into 5.00 5/8 = 0.625 OR 0.62 ½ Write 0.62 ½ as a percent : 62 ½ % So, 5/8 , 0.625 , or 62 ½% all represent the shaded portion of the figure. The shaded portion is NOT represented by the only remaining choice, 62.5, choice B.

  17. TRY THESE: # 7.) Which number below does NOT represent the shade portion of the figure ? A. 0.0375 B. 37.5% C. 37 ½% D. 3/8 # 8.) How do you find a percent between a fraction and a percent? # 9.) Find a percent between 1/20 and 3%.

  18. Example # 6

  19. Which of the numbers below is equivalent to 0.3?A. 3% B. 0.9 C. 30% D. 0.31 - 1 Write each multiple choice as a decimal to compare with 0.3 . • First consider choice A. 3% = 0.03 (this is not 0.3) 2) Now consider choice B. 0.9 = 0.948683298 (this is not 0.3) 3) Now consider choice C. 30% = 0.30 (this IS 0.3 or 0.30) So, 0.3 is equivalent to 30%, choice C.

  20. TRY THIS: # 10.) Which numbers below is NOT equivalent to 0.02 ? A. 2% B. 0.0004 C. 200% D. 1/50

  21. Now complete the second worksheet (example7). Read each direction carefully. Show your work.

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