Solve - Exponents and order of operations;complex fractions - Free Printable

Let's solve each of these fraction problems step by step. These are all operations involving fractions, including addition, subtraction, and simplification. We'll go through them one by one.

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67.

$$
\frac{3}{4} \div \frac{5}{6}
$$

To divide fractions: multiply by the reciprocal.

$$
= \frac{3}{4} \times \frac{6}{5} = \frac{18}{20} = \frac{9}{10}
$$

✔ Answer: $ \frac{9}{10} $

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68.

$$
\frac{5}{8} \div \frac{5}{12}
$$

$$
= \frac{5}{8} \times \frac{12}{5} = \frac{60}{40} = \frac{3}{2} = 1\frac{1}{2}
$$

✔ Answer: $ \frac{3}{2} $ or $ 1\frac{1}{2} $

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69.

$$
\frac{15}{16} \div \frac{5}{6}
$$

$$
= \frac{15}{16} \times \frac{6}{5} = \frac{90}{80} = \frac{9}{8} = 1\frac{1}{8}
$$

✔ Answer: $ \frac{9}{8} $ or $ 1\frac{1}{8} $

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70.

$$
\frac{21}{4} \div \frac{4}{7}
$$

$$
= \frac{21}{4} \times \frac{7}{4} = \frac{147}{16} = 9\frac{3}{16}
$$

✔ Answer: $ \frac{147}{16} $ or $ 9\frac{3}{16} $

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71.

$$
\frac{3 + \frac{1}{4}}{\frac{2}{3}}
$$

First simplify numerator:

$$
3 + \frac{1}{4} = \frac{12}{4} + \frac{1}{4} = \frac{13}{4}
$$

Now divide:

$$
\frac{13}{4} \div \frac{2}{3} = \frac{13}{4} \times \frac{3}{2} = \frac{39}{8} = 4\frac{7}{8}
$$

✔ Answer: $ \frac{39}{8} $ or $ 4\frac{7}{8} $

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72.

$$
\frac{4 + \frac{1}{2}}{\frac{3}{5}}
$$

Numerator: $ 4 + \frac{1}{2} = \frac{8}{2} + \frac{1}{2} = \frac{9}{2} $

Divide:

$$
\frac{9}{2} \div \frac{3}{5} = \frac{9}{2} \times \frac{5}{3} = \frac{45}{6} = \frac{15}{2} = 7\frac{1}{2}
$$

✔ Answer: $ \frac{15}{2} $ or $ 7\frac{1}{2} $

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73.

$$
\frac{5 - \frac{3}{4}}{\frac{5}{6}}
$$

Numerator: $ 5 - \frac{3}{4} = \frac{20}{4} - \frac{3}{4} = \frac{17}{4} $

Divide:

$$
\frac{17}{4} \div \frac{5}{6} = \frac{17}{4} \times \frac{6}{5} = \frac{102}{20} = \frac{51}{10} = 5\frac{1}{10}
$$

✔ Answer: $ \frac{51}{10} $ or $ 5\frac{1}{10} $

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74.

$$
\frac{4 - \frac{3}{5}}{\frac{7}{10}}
$$

Numerator: $ 4 - \frac{3}{5} = \frac{20}{5} - \frac{3}{5} = \frac{17}{5} $

Divide:

$$
\frac{17}{5} \div \frac{7}{10} = \frac{17}{5} \times \frac{10}{7} = \frac{170}{35} = \frac{34}{7} = 4\frac{6}{7}
$$

✔ Answer: $ \frac{34}{7} $ or $ 4\frac{6}{7} $

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75.

$$
\frac{\frac{2}{3} + \frac{3}{4}}{4 - \frac{1}{3}}
$$

Numerator: $ \frac{2}{3} + \frac{3}{4} $

LCM of 3 and 4 is 12:

$$
\frac{8}{12} + \frac{9}{12} = \frac{17}{12}
$$

Denominator: $ 4 - \frac{1}{3} = \frac{12}{3} - \frac{1}{3} = \frac{11}{3} $

Now divide:

$$
\frac{17}{12} \div \frac{11}{3} = \frac{17}{12} \times \frac{3}{11} = \frac{51}{132} = \frac{17}{44}
$$

✔ Answer: $ \frac{17}{44} $

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76.

$$
\frac{\frac{5}{6} + \frac{2}{3}}{3 - \frac{1}{2}}
$$

Numerator: $ \frac{5}{6} + \frac{2}{3} = \frac{5}{6} + \frac{4}{6} = \frac{9}{6} = \frac{3}{2} $

Denominator: $ 3 - \frac{1}{2} = \frac{6}{2} - \frac{1}{2} = \frac{5}{2} $

Divide:

$$
\frac{3}{2} \div \frac{5}{2} = \frac{3}{2} \times \frac{2}{5} = \frac{6}{10} = \frac{3}{5}
$$

✔ Answer: $ \frac{3}{5} $

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77.

$$
\frac{\frac{3}{4} - \frac{1}{3}}{\frac{5}{6} + 2}
$$

Numerator: $ \frac{3}{4} - \frac{1}{3} $

LCM = 12:

$$
\frac{9}{12} - \frac{4}{12} = \frac{5}{12}
$$

Denominator: $ \frac{5}{6} + 2 = \frac{5}{6} + \frac{12}{6} = \frac{17}{6} $

Divide:

$$
\frac{5}{12} \div \frac{17}{6} = \frac{5}{12} \times \frac{6}{17} = \frac{30}{204} = \frac{5}{34}
$$

✔ Answer: $ \frac{5}{34} $

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78.

$$
\frac{\frac{2}{3} + \frac{1}{6}}{\frac{3}{4} - \frac{5}{8}}
$$

Numerator: $ \frac{2}{3} + \frac{1}{6} = \frac{4}{6} + \frac{1}{6} = \frac{5}{6} $

Denominator: $ \frac{3}{4} - \frac{5}{8} = \frac{6}{8} - \frac{5}{8} = \frac{1}{8} $

Divide:

$$
\frac{5}{6} \div \frac{1}{8} = \frac{5}{6} \times 8 = \frac{40}{6} = \frac{20}{3} = 6\frac{2}{3}
$$

✔ Answer: $ \frac{20}{3} $ or $ 6\frac{2}{3} $

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79.

$$
\frac{1\frac{1}{2} - 2\frac{2}{3}}{3\frac{1}{4} + 1\frac{1}{6}}
$$

Convert to improper fractions:

- $ 1\frac{1}{2} = \frac{3}{2} $
- $ 2\frac{2}{3} = \frac{8}{3} $
- $ 3\frac{1}{4} = \frac{13}{4} $
- $ 1\frac{1}{6} = \frac{7}{6} $

Numerator: $ \frac{3}{2} - \frac{8}{3} $

LCM = 6:

$$
\frac{9}{6} - \frac{16}{6} = -\frac{7}{6}
$$

Denominator: $ \frac{13}{4} + \frac{7}{6} $

LCM = 12:

$$
\frac{39}{12} + \frac{14}{12} = \frac{53}{12}
$$

Now divide:

$$
-\frac{7}{6} \div \frac{53}{12} = -\frac{7}{6} \times \frac{12}{53} = -\frac{84}{318} = -\frac{14}{53}
$$

✔ Answer: $ -\frac{14}{53} $

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80.

$$
\frac{1\frac{1}{3} - 4\frac{1}{2}}{2\frac{1}{4} + 3\frac{1}{8}}
$$

Convert:

- $ 1\frac{1}{3} = \frac{4}{3} $
- $ 4\frac{1}{2} = \frac{9}{2} $
- $ 2\frac{1}{4} = \frac{9}{4} $
- $ 3\frac{1}{8} = \frac{25}{8} $

Numerator: $ \frac{4}{3} - \frac{9}{2} $

LCM = 6:

$$
\frac{8}{6} - \frac{27}{6} = -\frac{19}{6}
$$

Denominator: $ \frac{9}{4} + \frac{25}{8} $

LCM = 8:

$$
\frac{18}{8} + \frac{25}{8} = \frac{43}{8}
$$

Divide:

$$
-\frac{19}{6} \div \frac{43}{8} = -\frac{19}{6} \times \frac{8}{43} = -\frac{152}{258} = -\frac{76}{129}
$$

✔ Answer: $ -\frac{76}{129} $

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81.

$$
\frac{2\frac{1}{6} + 4\frac{2}{3}}{2\frac{1}{3} - 5\frac{1}{4}}
$$

Convert:

- $ 2\frac{1}{6} = \frac{13}{6} $
- $ 4\frac{2}{3} = \frac{14}{3} $
- $ 2\frac{1}{3} = \frac{7}{3} $
- $ 5\frac{1}{4} = \frac{21}{4} $

Numerator: $ \frac{13}{6} + \frac{14}{3} = \frac{13}{6} + \frac{28}{6} = \frac{41}{6} $

Denominator: $ \frac{7}{3} - \frac{21}{4} $

LCM = 12:

$$
\frac{28}{12} - \frac{63}{12} = -\frac{35}{12}
$$

Divide:

$$
\frac{41}{6} \div \left(-\frac{35}{12}\right) = \frac{41}{6} \times \left(-\frac{12}{35}\right) = -\frac{492}{210} = -\frac{82}{35} = -2\frac{12}{35}
$$

✔ Answer: $ -\frac{82}{35} $ or $ -2\frac{12}{35} $

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82.

$$
\frac{1\frac{1}{2} + 2\frac{2}{3}}{1\frac{1}{2} - 2\frac{1}{3}}
$$

Convert:

- $ 1\frac{1}{2} = \frac{3}{2} $
- $ 2\frac{2}{3} = \frac{8}{3} $
- $ 2\frac{1}{3} = \frac{7}{3} $

Numerator: $ \frac{3}{2} + \frac{8}{3} $

LCM = 6:

$$
\frac{9}{6} + \frac{16}{6} = \frac{25}{6}
$$

Denominator: $ \frac{3}{2} - \frac{7}{3} $

LCM = 6:

$$
\frac{9}{6} - \frac{14}{6} = -\frac{5}{6}
$$

Divide:

$$
\frac{25}{6} \div \left(-\frac{5}{6}\right) = \frac{25}{6} \times \left(-\frac{6}{5}\right) = -\frac{150}{30} = -5
$$

✔ Answer: $ -5 $

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✔ Final Answers Summary:

| Problem | Answer |
|--------|--------|
| 67 | $ \frac{9}{10} $ |
| 68 | $ \frac{3}{2} $ or $ 1\frac{1}{2} $ |
| 69 | $ \frac{9}{8} $ or $ 1\frac{1}{8} $ |
| 70 | $ \frac{147}{16} $ or $ 9\frac{3}{16} $ |
| 71 | $ \frac{39}{8} $ or $ 4\frac{7}{8} $ |
| 72 | $ \frac{15}{2} $ or $ 7\frac{1}{2} $ |
| 73 | $ \frac{51}{10} $ or $ 5\frac{1}{10} $ |
| 74 | $ \frac{34}{7} $ or $ 4\frac{6}{7} $ |
| 75 | $ \frac{17}{44} $ |
| 76 | $ \frac{3}{5} $ |
| 77 | $ \frac{5}{34} $ |
| 78 | $ \frac{20}{3} $ or $ 6\frac{2}{3} $ |
| 79 | $ -\frac{14}{53} $ |
| 80 | $ -\frac{76}{129} $ |
| 81 | $ -\frac{82}{35} $ or $ -2\frac{12}{35} $ |
| 82 | $ -5 $ |

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