301 Moved Permanently - Free Printable

Here is the solution for each problem on the worksheet, with a step-by-step explanation.

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1) $(-1) - \left(-\frac{12}{7}\right) - \frac{3}{2}$

- Subtracting a negative is adding: $-1 + \frac{12}{7} - \frac{3}{2}$
- Find common denominator (LCM of 1, 7, 2 = 14):
- $-1 = -\frac{14}{14}$
- $\frac{12}{7} = \frac{24}{14}$
- $\frac{3}{2} = \frac{21}{14}$
- Now: $-\frac{14}{14} + \frac{24}{14} - \frac{21}{14} = \frac{-14 + 24 - 21}{14} = \frac{-11}{14}$

✔ Answer: C) $-\frac{11}{14}$

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2) $\frac{4}{3} - \frac{4}{3} + \frac{4}{5}$

- $\frac{4}{3} - \frac{4}{3} = 0$
- So: $0 + \frac{4}{5} = \frac{4}{5}$

✔ Answer: D) $\frac{4}{5}$

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3) $\frac{4}{3} - \frac{5}{3} - 2$

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

✔ Answer: C) $-\frac{7}{3}$

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4) $(-2) - \left(-\frac{2}{3}\right) - \left(-\frac{11}{6}\right)$

- Subtracting negatives: $-2 + \frac{2}{3} + \frac{11}{6}$
- Common denominator (LCM of 1, 3, 6 = 6):
- $-2 = -\frac{12}{6}$
- $\frac{2}{3} = \frac{4}{6}$
- $\frac{11}{6} = \frac{11}{6}$
- Sum: $-\frac{12}{6} + \frac{4}{6} + \frac{11}{6} = \frac{-12 + 4 + 11}{6} = \frac{3}{6} = \frac{1}{2}$

✔ Answer: D) $\frac{1}{2}$

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5) $\frac{2}{5} - 1 + \left(-\frac{13}{8}\right)$

- Rewrite: $\frac{2}{5} - 1 - \frac{13}{8}$
- Common denominator (LCM of 5, 1, 8 = 40):
- $\frac{2}{5} = \frac{16}{40}$
- $1 = \frac{40}{40}$
- $\frac{13}{8} = \frac{65}{40}$
- So: $\frac{16}{40} - \frac{40}{40} - \frac{65}{40} = \frac{16 - 40 - 65}{40} = \frac{-89}{40}$

✔ Answer: A) $-\frac{89}{40}$

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6) $\left(-\frac{10}{7}\right) - \frac{1}{2} - 1$

- Common denominator (LCM of 7, 2, 1 = 14):
- $-\frac{10}{7} = -\frac{20}{14}$
- $\frac{1}{2} = \frac{7}{14}$
- $1 = \frac{14}{14}$
- So: $-\frac{20}{14} - \frac{7}{14} - \frac{14}{14} = \frac{-20 - 7 - 14}{14} = \frac{-41}{14}$

✔ Answer: C) $-\frac{41}{14}$

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7) $\frac{3}{7} + \frac{1}{5} - 2$

- Common denominator (LCM of 7, 5, 1 = 35):
- $\frac{3}{7} = \frac{15}{35}$
- $\frac{1}{5} = \frac{7}{35}$
- $2 = \frac{70}{35}$
- So: $\frac{15}{35} + \frac{7}{35} - \frac{70}{35} = \frac{15 + 7 - 70}{35} = \frac{-48}{35}$

✔ Answer: B) $-\frac{48}{35}$

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8) $(-6) - \left(-\frac{4}{3}\right) + \frac{3}{5}$

- Subtracting negative: $-6 + \frac{4}{3} + \frac{3}{5}$
- Common denominator (LCM of 1, 3, 5 = 15):
- $-6 = -\frac{90}{15}$
- $\frac{4}{3} = \frac{20}{15}$
- $\frac{3}{5} = \frac{9}{15}$
- So: $-\frac{90}{15} + \frac{20}{15} + \frac{9}{15} = \frac{-90 + 20 + 9}{15} = \frac{-61}{15}$

✔ Answer: B) $-\frac{61}{15}$

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✔ Final Answers:

1. C
2. D
3. C
4. D
5. A
6. C
7. B
8. B