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Compare the following fractions using <, >, or =. For problems 2a-2d, first make sure the fractions have the same denominator.

Mathematics

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Here are the solutions to the fraction problems from the image.

.9

1. Fill in the << or >> symbol:

  • a) 27\frac{2}{7} << 67\frac{6}{7}
  • b) 910\frac{9}{10} >> 710\frac{7}{10}
  • c) 11100\frac{11}{100} << 17100\frac{17}{100}
  • d) 99100\frac{99}{100} >> 89100\frac{89}{100}

2. First make sure the fractions have the same denominator and then compare them by filling in <<, >> or == symbols:

  • a) 45\frac{4}{5} ___ 910\frac{9}{10}

  1. Convert 45\frac{4}{5} to have a denominator of 10.

    $$
\frac{4}{5} = \frac{4 \times 2}{5 \times 2} = \frac{8}{10}
$$

  2. Compare 810\frac{8}{10} and 910\frac{9}{10}.

    $$
\frac{8}{10} < \frac{9}{10}
$$
So, $\boxed{\frac{4}{5} < \frac{9}{10}}$
    • b) 38\frac{3}{8} ___ 516\frac{5}{16}

  3. Convert 38\frac{3}{8} to have a denominator of 16.

    $$
\frac{3}{8} = \frac{3 \times 2}{8 \times 2} = \frac{6}{16}
$$

  4. Compare 616\frac{6}{16} and 516\frac{5}{16}.

    $$
\frac{6}{16} > \frac{5}{16}
$$
So, $\boxed{\frac{3}{8} > \frac{5}{16}}$
    • c) 56\frac{5}{6} ___ 1112\frac{11}{12}

  5. Convert 56\frac{5}{6} to have a denominator of 12.

    $$
\frac{5}{6} = \frac{5 \times 2}{6 \times 2} = \frac{10}{12}
$$

  6. Compare 1012\frac{10}{12} and 1112\frac{11}{12}.

    $$
\frac{10}{12} < \frac{11}{12}
$$
So, $\boxed{\frac{5}{6} < \frac{11}{12}}$
    • d) 1318\frac{13}{18} ___ 23\frac{2}{3}

  7. Convert 23\frac{2}{3} to have a denominator of 18.

    $$
\frac{2}{3} = \frac{2 \times 6}{3 \times 6} = \frac{12}{18}
$$

  8. Compare 1318\frac{13}{18} and 1218\frac{12}{18}.

    $$
\frac{13}{18} > \frac{12}{18}
$$
So, $\boxed{\frac{13}{18} > \frac{2}{3}}$
    • e) 921\frac{9}{21} ___ 37\frac{3}{7}

  9. Convert 37\frac{3}{7} to have a denominator of 21.

    $$
\frac{3}{7} = \frac{3 \times 3}{7 \times 3} = \frac{9}{21}
$$

  10. Compare 921\frac{9}{21} and 921\frac{9}{21}.

    $$
\frac{9}{21} = \frac{9}{21}
$$
So, $\boxed{\frac{9}{21} = \frac{3}{7}}$
    • f) 611\frac{6}{11} ___ 1233\frac{12}{33}

  11. Convert 611\frac{6}{11} to have a denominator of 33.

    $$
\frac{6}{11} = \frac{6 \times 3}{11 \times 3} = \frac{18}{33}
$$

  12. Compare 1833\frac{18}{33} and 1233\frac{12}{33}.

    $$
\frac{18}{33} > \frac{12}{33}
$$
So, $\boxed{\frac{6}{11} > \frac{12}{33}}$

    3. Arrange these fractions in descending order, by first writing them all with a denominator of 48:
    The fractions are: 56,13,1112,1924,34,78,1124,1224\frac{5}{6}, \frac{1}{3}, \frac{11}{12}, \frac{19}{24}, \frac{3}{4}, \frac{7}{8}, \frac{11}{24}, \frac{12}{24}.

  13. Convert each fraction to have a denominator of 48.

    56=5×86×8=4048\frac{5}{6} = \frac{5 \times 8}{6 \times 8} = \frac{40}{48} 13=1×163×16=1648\frac{1}{3} = \frac{1 \times 16}{3 \times 16} = \frac{16}{48} 1112=11×412×4=4448\frac{11}{12} = \frac{11 \times 4}{12 \times 4} = \frac{44}{48} 1924=19×224×2=3848\frac{19}{24} = \frac{19 \times 2}{24 \times 2} = \frac{38}{48} 34=3×124×12=3648\frac{3}{4} = \frac{3 \times 12}{4 \times 12} = \frac{36}{48} 78=7×68×6=4248\frac{7}{8} = \frac{7 \times 6}{8 \times 6} = \frac{42}{48} 1124=11×224×2=2248\frac{11}{24} = \frac{11 \times 2}{24 \times 2} = \frac{22}{48} 1224=12×224×2=2448\frac{12}{24} = \frac{12 \times 2}{24 \times 2} = \frac{24}{48}

  14. Arrange the fractions with denominator 48 in descending order (largest to smallest).

    4448,4248,4048,3848,3648,2448,2248,1648\frac{44}{48}, \frac{42}{48}, \frac{40}{48}, \frac{38}{48}, \frac{36}{48}, \frac{24}{48}, \frac{22}{48}, \frac{16}{48}

  15. Write the original fractions in descending order.

    1112,78,56,1924,34,1224,1124,13\boxed{\frac{11}{12}, \frac{7}{8}, \frac{5}{6}, \frac{19}{24}, \frac{3}{4}, \frac{12}{24}, \frac{11}{24}, \frac{1}{3}}
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