Add -3/5 + 1/6. Write your answer in simplest form.
Understand the Problem
The question is asking to add two fractions, -3/5 and 1/6, and to present the answer in its simplest form. This involves finding a common denominator, performing the addition, and simplifying the result if needed.
Answer
$-\frac{13}{30}$
Answer for screen readers
The final answer is $-\frac{13}{30}$.
Steps to Solve
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Identify the fractions The fractions to add are $-\frac{3}{5}$ and $\frac{1}{6}$.
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Find a common denominator The denominators are 5 and 6. The least common multiple (LCM) of 5 and 6 is 30. So, the common denominator is 30.
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Convert fractions to have the common denominator To convert the first fraction: $$ -\frac{3}{5} = -\frac{3 \times 6}{5 \times 6} = -\frac{18}{30} $$
To convert the second fraction: $$ \frac{1}{6} = \frac{1 \times 5}{6 \times 5} = \frac{5}{30} $$
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Add the fractions Now, add the fractions: $$ -\frac{18}{30} + \frac{5}{30} = \frac{-18 + 5}{30} = \frac{-13}{30} $$
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Simplify the result The fraction $\frac{-13}{30}$ is already in its simplest form since 13 and 30 have no common factors other than 1.
The final answer is $-\frac{13}{30}$.
More Information
When adding fractions, always find a common denominator first. The result, in this case, is negative since the larger absolute value fraction was negative.
Tips
- Forgetting to convert both fractions to the common denominator before adding.
- Failing to simplify the fractions after addition, even if it is not necessary in this case.
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