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Write these fractions in words. a) 5/8 = b) 7/10 = c) 9/12 = 2. Complete the equivalent fractions. a) 2/3 = /6 b) 3/5 = /10 c) 4/7 = /14 3. Compare the fractions using <, > or =. a) 5/8 7/8 b) 3/4 6/8 c) 2/6 2/3

Mathematics

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Step-by-step solution

16 steps

1. Write these fractions in words.

a) 58\frac{5}{8}

  1. Write the numerator as a cardinal number and the denominator as an ordinal number.

    The numerator is 5, and the denominator is 8 (eighths).

    Five-eighths\boxed{\text{Five-eighths}}

    b) 710\frac{7}{10}

  2. Write the numerator as a cardinal number and the denominator as an ordinal number.

    The numerator is 7, and the denominator is 10 (tenths).

    Seven-tenths\boxed{\text{Seven-tenths}}

    c) 912\frac{9}{12}

  3. Write the numerator as a cardinal number and the denominator as an ordinal number.

    The numerator is 9, and the denominator is 12 (twelfths).

    Nine-twelfths\boxed{\text{Nine-twelfths}}

    2. Complete the equivalent fractions.

    a) \frac{2}{3} = \frac{\text{_}}{6}

  4. Determine the factor by which the denominator was multiplied.

    3×2=63 \times 2 = 6
  5. Multiply the numerator by the same factor.

    2×2=42 \times 2 = 4

    So, 23=46\frac{2}{3} = \frac{4}{6}.

    4\boxed{4}

    b) \frac{3}{5} = \frac{\text{_}}{10}

  6. Determine the factor by which the denominator was multiplied.

    5×2=105 \times 2 = 10
  7. Multiply the numerator by the same factor.

    3×2=63 \times 2 = 6

    So, 35=610\frac{3}{5} = \frac{6}{10}.

    6\boxed{6}

    c) \frac{4}{7} = \frac{\text{_}}{14}

  8. Determine the factor by which the denominator was multiplied.

    7×2=147 \times 2 = 14
  9. Multiply the numerator by the same factor.

    4×2=84 \times 2 = 8

    So, 47=814\frac{4}{7} = \frac{8}{14}.

    8\boxed{8}

    3. Compare the fractions using <,>,<, >, or ==.

    a) 58 ___ 78\frac{5}{8} \text{ \_\_\_ } \frac{7}{8}

  10. Compare the numerators since the denominators are the same.

    5<75 < 7

    Therefore, 58<78\frac{5}{8} < \frac{7}{8}.

    <\boxed{<}

    b) 34 ___ 68\frac{3}{4} \text{ \_\_\_ } \frac{6}{8}

  11. Find a common denominator.

    The least common denominator for 4 and 8 is 8.

  12. Convert 34\frac{3}{4} to an equivalent fraction with a denominator of 8.

    34=3×24×2=68\frac{3}{4} = \frac{3 \times 2}{4 \times 2} = \frac{6}{8}
  13. Compare the equivalent fractions.

    68=68\frac{6}{8} = \frac{6}{8}

    Therefore, 34=68\frac{3}{4} = \frac{6}{8}.

    =\boxed{=}

    c) 26 ___ 23\frac{2}{6} \text{ \_\_\_ } \frac{2}{3}

  14. Find a common denominator.

    The least common denominator for 6 and 3 is 6.

  15. Convert 23\frac{2}{3} to an equivalent fraction with a denominator of 6.

    23=2×23×2=46\frac{2}{3} = \frac{2 \times 2}{3 \times 2} = \frac{4}{6}
  16. Compare the equivalent fractions.

    26<46\frac{2}{6} < \frac{4}{6}

    Therefore, 26<23\frac{2}{6} < \frac{2}{3}.

    <\boxed{<}
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