Ask a New Question
Menu

Calculate the decimal number for each fraction and identify the ascending numerical order of the decimal numbers:

5/8
, 1/4
, 3/8
, 2/3
, 6/7


8/5
, 4/1
, 8/3
, 3/2
, 7/6
Start Fraction 8 over 5 End Fraction , Start Fraction 4 over 1 End Fraction , Start Fraction 8 over 3 End Fraction , Start Fraction 3 over 2 End Fraction , Start Fraction 7 over 6 End Fraction

0.25, 0.375, 0.625, 0.667, 0.857
0.25, 0.375, 0.625, 0.667, 0.857

0.625, 0.25, 0.375, 0.667, 0.857
0.625, 0.25, 0.375, 0.667, 0.857

5/8
, 1/4
, 3/8
, 2/3
, 6/7)

1 answer

To find the decimal representations of the fractions you provided, let's calculate them one by one.

First set of fractions:

  1. \( \frac{5}{8} \)
    \( 5 \div 8 = 0.625 \)

  2. \( \frac{1}{4} \)
    \( 1 \div 4 = 0.25 \)

  3. \( \frac{3}{8} \)
    \( 3 \div 8 = 0.375 \)

  4. \( \frac{2}{3} \)
    \( 2 \div 3 \approx 0.6667 \) (rounded to 4 decimal places)

  5. \( \frac{6}{7} \)
    \( 6 \div 7 \approx 0.8571 \) (rounded to 4 decimal places)

Decimal representatives of the first set:

  • \( \frac{5}{8} = 0.625 \)
  • \( \frac{1}{4} = 0.25 \)
  • \( \frac{3}{8} = 0.375 \)
  • \( \frac{2}{3} \approx 0.6667 \)
  • \( \frac{6}{7} \approx 0.8571 \)

Now, let's arrange these decimals in ascending order:

  • 0.25
  • 0.375
  • 0.625
  • 0.6667
  • 0.8571

The ascending order is:

  1. \( 0.25 \) (which corresponds to \( \frac{1}{4} \))
  2. \( 0.375 \) (which corresponds to \( \frac{3}{8} \))
  3. \( 0.625 \) (which corresponds to \( \frac{5}{8} \))
  4. \( 0.6667 \) (which corresponds to \( \frac{2}{3} \))
  5. \( 0.8571 \) (which corresponds to \( \frac{6}{7} \))

For the second set of fractions:

  1. \( \frac{8}{5} \)
    \( 8 \div 5 = 1.6 \)

  2. \( \frac{4}{1} \)
    \( 4 \div 1 = 4.0 \)

  3. \( \frac{8}{3} \)
    \( 8 \div 3 \approx 2.6667 \)

  4. \( \frac{3}{2} \)
    \( 3 \div 2 = 1.5 \)

  5. \( \frac{7}{6} \)
    \( 7 \div 6 \approx 1.1667 \)

Decimal representatives of the second set:

  • \( \frac{8}{5} = 1.6 \)
  • \( \frac{4}{1} = 4.0 \)
  • \( \frac{8}{3} \approx 2.6667 \)
  • \( \frac{3}{2} = 1.5 \)
  • \( \frac{7}{6} \approx 1.1667 \)

Now, let's arrange these decimals in ascending order:

  • \( 1.1667 \)
  • \( 1.5 \)
  • \( 1.6 \)
  • \( 2.6667 \)
  • \( 4.0 \)

The ascending order for the second set is:

  1. \( 1.1667 \) (which corresponds to \( \frac{7}{6} \))
  2. \( 1.5 \) (which corresponds to \( \frac{3}{2} \))
  3. \( 1.6 \) (which corresponds to \( \frac{8}{5} \))
  4. \( 2.6667 \) (which corresponds to \( \frac{8}{3} \))
  5. \( 4.0 \) (which corresponds to \( \frac{4}{1} \))

Final Results:

  1. First set in ascending order:

    • \( \frac{1}{4}, \frac{3}{8}, \frac{5}{8}, \frac{2}{3}, \frac{6}{7} \)

  2. Second set in ascending order:

    • \( \frac{7}{6}, \frac{3}{2}, \frac{8}{5}, \frac{8}{3}, \frac{4}{1} \)