-6/7 + 1/4. Write your answer in simplest form.
Understand the Problem
The question requires us to perform operations involving fractions and provide the final result in its simplest form. We will need to find a common denominator to combine the fractions and simplify the result.
Answer
$$\frac{-17}{28}$$
Answer for screen readers
The final answer is $$\frac{-17}{28}$$.
Steps to Solve
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Identify the denominators The denominators in the fractions are 7 and 4.
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Find the least common denominator (LCD) The least common denominator of 7 and 4 can be calculated as follows: $$ \text{LCD} = 7 \times 4 = 28 $$
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Convert the fractions to have the LCD Next, we convert each fraction:
- For $-\frac{6}{7}$, multiply the numerator and denominator by 4: $$ -\frac{6}{7} = -\frac{6 \times 4}{7 \times 4} = -\frac{24}{28} $$
- For $\frac{1}{4}$, multiply the numerator and denominator by 7: $$ \frac{1}{4} = \frac{1 \times 7}{4 \times 7} = \frac{7}{28} $$
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Combine the fractions Now add the two fractions: $$ -\frac{24}{28} + \frac{7}{28} = \frac{-24 + 7}{28} = \frac{-17}{28} $$
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Ensure the result is in simplest form The fraction $\frac{-17}{28}$ is already in its simplest form since 17 is a prime number and has no common factors with 28.
The final answer is $$\frac{-17}{28}$$.
More Information
When adding fractions, ensuring both fractions are converted to have the same denominator is crucial. This process often involves finding the least common multiple of the denominators.
Tips
- Forgetting to find a common denominator can lead to incorrect addition.
- Not converting both fractions before attempting to combine them.
