Math worksheet for practicing addition of rational numbers with multiple-choice questions.

Here is the complete solution to the Addition of Rational Numbers worksheet, with step-by-step explanations for each problem.

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Problem 1:

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

✔ Since all denominators are the same (12), add numerators:

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

✔ Simplify by dividing numerator and denominator by 3:

\[
\frac{27 ÷ 3}{12 ÷ 3} = \frac{9}{4}
\]

✔ Answer: D) $\frac{9}{4}$

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Problem 2:

\[
\left(-\frac{25}{13}\right) + \left(-\frac{12}{13}\right) + \left(-\frac{7}{13}\right)
\]

✔ All denominators are 13. Add numerators (all negative):

\[
\frac{-25 -12 -7}{13} = \frac{-44}{13}
\]

✔ Already simplified.

✔ Answer: A) $-\frac{44}{13}$

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Problem 3:

\[
\left(-\frac{5}{14}\right) + (-15) + \frac{11}{14}
\]

✔ Group fractions first:

\[
\left(-\frac{5}{14} + \frac{11}{14}\right) + (-15) = \frac{6}{14} - 15
\]

✔ Simplify $\frac{6}{14} = \frac{3}{7}$

Now compute:
\[
\frac{3}{7} - 15 = \frac{3}{7} - \frac{105}{7} = \frac{3 - 105}{7} = \frac{-102}{7}
\]

✔ Answer: B) $-\frac{102}{7}$

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Problem 4:

\[
\left(-\frac{3}{7}\right) + \left(-\frac{8}{7}\right) + (-6)
\]

✔ Add fractions first:

\[
\frac{-3 -8}{7} = \frac{-11}{7}
\]

Then add -6:

\[
\frac{-11}{7} - 6 = \frac{-11}{7} - \frac{42}{7} = \frac{-53}{7}
\]

✔ Answer: A) $-\frac{53}{7}$

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Problem 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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Problem 6:

\[
1 + \frac{3}{10} + \left(-\frac{17}{10}\right)
\]

✔ Combine fractions:

\[
\frac{3}{10} - \frac{17}{10} = \frac{-14}{10} = -\frac{7}{5}
\]

Now add 1:

\[
1 - \frac{7}{5} = \frac{5}{5} - \frac{7}{5} = -\frac{2}{5}
\]

✔ Answer: D) $-\frac{2}{5}$

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Problem 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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Problem 8:

\[
10 + \left(-\frac{16}{15}\right) + \left(-\frac{23}{15}\right)
\]

✔ Combine fractions:

\[
-\frac{16}{15} - \frac{23}{15} = -\frac{39}{15} = -\frac{13}{5}
\]

Now add 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:

1) D
2) A
3) B
4) A
5) D
6) D
7) A
8) D

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