Questions: Perform the indicated operation and simplify your answer. 2/7 + (-1/3) + (-1/6)

Perform the indicated operation and simplify your answer.
2/7 + (-1/3) + (-1/6)
Transcript text: Perform the indicated operation and simplify your answer. \[ \frac{2}{7}+\left(-\frac{1}{3}\right)+\left(-\frac{1}{6}\right) \]
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Solution

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Solution Steps

Step 1: Find the Least Common Denominator (LCD)

The denominators are 77, 33, and 66. The LCD of these numbers is 4242.

Step 2: Rewrite Each Fraction with the LCD

27=2×67×6=1242 \frac{2}{7} = \frac{2 \times 6}{7 \times 6} = \frac{12}{42} 13=1×143×14=1442 -\frac{1}{3} = -\frac{1 \times 14}{3 \times 14} = -\frac{14}{42} 16=1×76×7=742 -\frac{1}{6} = -\frac{1 \times 7}{6 \times 7} = -\frac{7}{42}

Step 3: Combine the Fractions

1242+(1442)+(742)=1214742=942 \frac{12}{42} + \left(-\frac{14}{42}\right) + \left(-\frac{7}{42}\right) = \frac{12 - 14 - 7}{42} = \frac{-9}{42}

Step 4: Simplify the Fraction

942=314 \frac{-9}{42} = \frac{-3}{14}

Final Answer

314\boxed{-\frac{3}{14}}

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