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Fill in the given fractions and add the missing fractions onto your wall. Fill in >, <, or = to make the following true. Use the fraction wall to help you. True or false? Write these fractions in order from biggest to smallest. Write these fractions in order from smallest to biggest.

Mathematics

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2. Fill in >,<>, < or == to make the following true.

  • a) 15_13\frac{1}{5} \_ \frac{1}{3}

  1. Compare the denominators of the unit fractions.

    Since 5>35 > 3, the fraction with the smaller denominator is larger. 15<13 \frac{1}{5} < \frac{1}{3}

    • b) 34_45\frac{3}{4} \_ \frac{4}{5}

  2. Find a common denominator, which is 20.

    $$
\frac{3}{4} = \frac{15}{20} \quad \text{and} \quad \frac{4}{5} = \frac{16}{20}
$$

  3. Compare the fractions.

    $$
\frac{15}{20} < \frac{16}{20} \implies \frac{3}{4} < \frac{4}{5}
$$
    • c) 48_12\frac{4}{8} \_ \frac{1}{2}

  4. Simplify the fraction 48\frac{4}{8}.

    $$
\frac{4}{8} = \frac{1}{2}
$$

  5. Compare the fractions.

    $$
\frac{1}{2} = \frac{1}{2} \implies \frac{4}{8} = \frac{1}{2}
$$
    • d) 56_45\frac{5}{6} \_ \frac{4}{5}

  6. Find a common denominator, which is 30.

    $$
\frac{5}{6} = \frac{25}{30} \quad \text{and} \quad \frac{4}{5} = \frac{24}{30}
$$

  7. Compare the fractions.

    $$
\frac{25}{30} > \frac{24}{30} \implies \frac{5}{6} > \frac{4}{5}
$$
    • e) 37_23\frac{3}{7} \_ \frac{2}{3}

  8. Find a common denominator, which is 21.

    $$
\frac{3}{7} = \frac{9}{21} \quad \text{and} \quad \frac{2}{3} = \frac{14}{21}
$$

  9. Compare the fractions.

    $$
\frac{9}{21} < \frac{14}{21} \implies \frac{3}{7} < \frac{2}{3}
$$
    • f) 13_14\frac{1}{3} \_ \frac{1}{4}

  10. Compare the denominators of the unit fractions.

    Since 3<43 < 4, the fraction with the smaller denominator is larger. 13>14 \frac{1}{3} > \frac{1}{4}

    • g) 57_25\frac{5}{7} \_ \frac{2}{5}

  11. Find a common denominator, which is 35.

    $$
\frac{5}{7} = \frac{25}{35} \quad \text{and} \quad \frac{2}{5} = \frac{14}{35}
$$

  12. Compare the fractions.

    $$
\frac{25}{35} > \frac{14}{35} \implies \frac{5}{7} > \frac{2}{5}
$$
    • h) 34_46\frac{3}{4} \_ \frac{4}{6}

  13. Simplify 46\frac{4}{6} to 23\frac{2}{3}.

  14. Find a common denominator for 34\frac{3}{4} and 23\frac{2}{3}, which is 12.

    $$
\frac{3}{4} = \frac{9}{12} \quad \text{and} \quad \frac{2}{3} = \frac{8}{12}
$$

  15. Compare the fractions.

    $$
\frac{9}{12} > \frac{8}{12} \implies \frac{3}{4} > \frac{4}{6}
$$

    3. True or false?

    • a) 23=25\frac{2}{3} = \frac{2}{5}

  16. Compare the fractions.

    Since the denominators are different and the numerators are the same, the fractions are not equal.
    False

    • b) 67>45\frac{6}{7} > \frac{4}{5}

  17. Find a common denominator, which is 35.

    $$
\frac{6}{7} = \frac{30}{35} \quad \text{and} \quad \frac{4}{5} = \frac{28}{35}
$$

  18. Compare the fractions.

    3035>2835\frac{30}{35} > \frac{28}{35}.
    True

    • c) 12=48\frac{1}{2} = \frac{4}{8}

  19. Simplify 48\frac{4}{8}.

    $$
\frac{4}{8} = \frac{1}{2}
$$

  20. Compare the fractions.

    12=12\frac{1}{2} = \frac{1}{2}.
    True

    • d) 16<17\frac{1}{6} < \frac{1}{7}

  21. Compare the denominators of the unit fractions.

    Since 6<76 < 7, 16\frac{1}{6} is greater than 17\frac{1}{7}.
    False

    • e) 45<1\frac{4}{5} < 1

  22. Compare the numerator and denominator.

    Since 4<54 < 5, the fraction is less than 1.
    True

    • f) 34<23\frac{3}{4} < \frac{2}{3}

  23. Find a common denominator, which is 12.

    $$
\frac{3}{4} = \frac{9}{12} \quad \text{and} \quad \frac{2}{3} = \frac{8}{12}
$$

  24. Compare the fractions.

    912\frac{9}{12} is not less than 812\frac{8}{12}.
    False

    • g) 36>47\frac{3}{6} > \frac{4}{7}

  25. Simplify 36\frac{3}{6} to 12\frac{1}{2}.

  26. Find a common denominator for 12\frac{1}{2} and 47\frac{4}{7}, which is 14.

    $$
\frac{1}{2} = \frac{7}{14} \quad \text{and} \quad \frac{4}{7} = \frac{8}{14}
$$

  27. Compare the fractions.

    714\frac{7}{14} is not greater than 814\frac{8}{14}.
    False

    • h) 13=28\frac{1}{3} = \frac{2}{8}

  28. Simplify 28\frac{2}{8}.

    $$
\frac{2}{8} = \frac{1}{4}
$$

  29. Compare the fractions.

    13\frac{1}{3} is not equal to 14\frac{1}{4}.
    False

    4. Write these fractions in order from biggest to smallest.
    Fractions: 13,15,12,18,16,14,17\frac{1}{3}, \frac{1}{5}, \frac{1}{2}, \frac{1}{8}, \frac{1}{6}, \frac{1}{4}, \frac{1}{7}

  30. These are unit fractions.

    For unit fractions, the smaller the denominator, the larger the fraction.

  31. Order the denominators from smallest to largest

    $2, 3, 4, 5, 6, 7, 8$.

  32. Write the fractions in the corresponding order from biggest to smallest.

    12,13,14,15,16,17,18\boxed{\frac{1}{2}, \frac{1}{3}, \frac{1}{4}, \frac{1}{5}, \frac{1}{6}, \frac{1}{7}, \frac{1}{8}}

    5. Write these fractions in order from smallest to biggest.
    Fractions: 38,27,45,46,12,34,13\frac{3}{8}, \frac{2}{7}, \frac{4}{5}, \frac{4}{6}, \frac{1}{2}, \frac{3}{4}, \frac{1}{3}

  33. Convert each fraction to a decimal for easier comparison.

    38=0.375\frac{3}{8} = 0.375 27≈0.2857\frac{2}{7} \approx 0.2857 45=0.8\frac{4}{5} = 0.8 46≈0.6667\frac{4}{6} \approx 0.6667 12=0.5\frac{1}{2} = 0.5 34=0.75\frac{3}{4} = 0.75 13≈0.3333\frac{1}{3} \approx 0.3333

  34. Order the decimal values from smallest to biggest.

    0.2857,0.3333,0.375,0.5,0.6667,0.75,0.80.2857, 0.3333, 0.375, 0.5, 0.6667, 0.75, 0.8

  35. Write the original fractions in the corresponding order from smallest to biggest.

    27,13,38,12,46,34,45\boxed{\frac{2}{7}, \frac{1}{3}, \frac{3}{8}, \frac{1}{2}, \frac{4}{6}, \frac{3}{4}, \frac{4}{5}}
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