-1/3 - (-8/7)
Understand the Problem
The question is asking to simplify or evaluate the mathematical expression presented in the image. It includes fractions and likely requires step-by-step calculations to arrive at the final answer.
Answer
The simplified expression is $\frac{17}{21}$.
Answer for screen readers
The final answer is $\frac{17}{21}$.
Steps to Solve
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Identify the expression to simplify The expression is given as $-\frac{1}{3} - \left(-\frac{8}{7}\right)$. We can rewrite this as $-\frac{1}{3} + \frac{8}{7}$ because subtracting a negative number is the same as adding the positive.
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Find a common denominator To add the fractions, we need a common denominator. The denominators are 3 and 7. The least common multiple (LCM) of 3 and 7 is 21.
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Convert fractions to have the common denominator Convert $-\frac{1}{3}$ and $\frac{8}{7}$ to have a denominator of 21:
- For $-\frac{1}{3}$: $$ -\frac{1}{3} = -\frac{1 \cdot 7}{3 \cdot 7} = -\frac{7}{21} $$
- For $\frac{8}{7}$: $$ \frac{8}{7} = \frac{8 \cdot 3}{7 \cdot 3} = \frac{24}{21} $$
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Combine the fractions Now we combine the two fractions: $$ -\frac{7}{21} + \frac{24}{21} = \frac{-7 + 24}{21} $$
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Simplify the result Now we can simplify: $$ -7 + 24 = 17 $$ So we have: $$ \frac{17}{21} $$
The final answer is $\frac{17}{21}$.
More Information
The expression simplifies to a single fraction of $\frac{17}{21}$, which is already in its simplest form since 17 and 21 have no common factors (17 is a prime number).
Tips
- Confusing subtraction of a negative with addition and making sign errors.
- Not finding a common denominator correctly or forgetting to convert both fractions.
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