Addition of Rational Numbers worksheet with eight problems and multiple-choice answers.

Let's solve each problem step by step from the Addition of Rational Numbers worksheet.

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1) $\left(-\frac{1}{12}\right) + \frac{11}{12} + \frac{17}{12}$

All fractions have the same denominator (12), so add numerators:

$$
-\frac{1}{12} + \frac{11}{12} + \frac{17}{12} = \frac{-1 + 11 + 17}{12} = \frac{27}{12}
$$

Simplify:
$$
\frac{27}{12} = \frac{9}{4}
$$

✔ Answer: D) $\frac{9}{4}$

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2) $\left(-\frac{25}{13}\right) + \left(-\frac{12}{13}\right) + \left(-\frac{7}{13}\right)$

Same denominator, add numerators:

$$
-\frac{25 + 12 + 7}{13} = -\frac{44}{13}
$$

✔ Answer: A) $-\frac{44}{13}$

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3) $\left(-\frac{5}{14}\right) + (-15) + \frac{11}{14}$

Group the fractions first:

$$
\left(-\frac{5}{14} + \frac{11}{14}\right) + (-15) = \frac{6}{14} - 15 = \frac{3}{7} - 15
$$

Convert 15 to fraction with denominator 7:

$$
\frac{3}{7} - \frac{105}{7} = -\frac{102}{7}
$$

✔ Answer: B) $-\frac{102}{7}$

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4) $\left(-\frac{3}{7}\right) + \left(-\frac{8}{7}\right) + (-6)$

Add the fractions:

$$
-\frac{3 + 8}{7} = -\frac{11}{7}
$$

Now subtract 6:

$$
-\frac{11}{7} - 6 = -\frac{11}{7} - \frac{42}{7} = -\frac{53}{7}
$$

✔ Answer: A) $-\frac{53}{7}$

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5) $\left(-\frac{1}{6}\right) + \left(-\frac{1}{6}\right) + \frac{5}{6}$

Add numerators:

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

✔ Answer: D) $\frac{1}{2}$

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6) $1 + \frac{3}{10} + \left(-\frac{17}{10}\right)$

Convert 1 to tenths: $1 = \frac{10}{10}$

Now add:

$$
\frac{10}{10} + \frac{3}{10} - \frac{17}{10} = \frac{10 + 3 - 17}{10} = \frac{-4}{10} = -\frac{2}{5}
$$

✔ Answer: D) $-\frac{2}{5}$

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7) $\left(-\frac{8}{9}\right) + \frac{10}{9} + \frac{10}{9}$

Add numerators:

$$
\frac{-8 + 10 + 10}{9} = \frac{12}{9} = \frac{4}{3}
$$

✔ Answer: A) $\frac{4}{3}$

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8) $10 + \left(-\frac{16}{15}\right) + \left(-\frac{23}{15}\right)$

Add the fractions:

$$
-\frac{16 + 23}{15} = -\frac{39}{15} = -\frac{13}{5}
$$

Now add to 10:

$$
10 - \frac{13}{5} = \frac{50}{5} - \frac{13}{5} = \frac{37}{5}
$$

✔ Answer: D) $\frac{37}{5}$

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✔ Final Answers:

| Question | Answer |
|--------|--------|
| 1 | D) $\frac{9}{4}$ |
| 2 | A) $-\frac{44}{13}$ |
| 3 | B) $-\frac{102}{7}$ |
| 4 | A) $-\frac{53}{7}$ |
| 5 | D) $\frac{1}{2}$ |
| 6 | D) $-\frac{2}{5}$ |
| 7 | A) $\frac{4}{3}$ |
| 8 | D) $\frac{37}{5}$ |

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🔍 Explanation Summary:

- When adding rational numbers (fractions), if denominators are the same, just add/subtract the numerators.
- For mixed terms (integers and fractions), convert integers to fractions with matching denominators.
- Always simplify the final answer.
- Negative signs apply to the entire fraction unless specified otherwise.

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