Evaluate: -5/9 - (-1/15). Write your answer in simplest form.
Understand the Problem
The question is asking to evaluate a mathematical expression involving fractions, specifically involving subtraction of two fractions. The goal is to simplify the answer as much as possible.
Answer
$\frac{-22}{45}$
Answer for screen readers
The final answer is $\frac{-22}{45}$.
Steps to Solve
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Identify the Operation We need to evaluate the expression $-\frac{5}{9} - \left(-\frac{1}{15}\right)$. The double negative turns the subtraction into addition.
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Rewrite the Expression Rewriting the expression, we have: $$ -\frac{5}{9} + \frac{1}{15} $$
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Find a Common Denominator The least common multiple (LCM) of the denominators 9 and 15 is 45. We will convert both fractions to have this common denominator.
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Convert the First Fraction Convert $-\frac{5}{9}$ to have a denominator of 45: $$ -\frac{5}{9} = -\frac{5 \times 5}{9 \times 5} = -\frac{25}{45} $$
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Convert the Second Fraction Convert $\frac{1}{15}$ to have a denominator of 45: $$ \frac{1}{15} = \frac{1 \times 3}{15 \times 3} = \frac{3}{45} $$
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Combine the Fractions Now we can combine the fractions: $$ -\frac{25}{45} + \frac{3}{45} = \frac{-25 + 3}{45} = \frac{-22}{45} $$
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Simplify the Result The fraction $\frac{-22}{45}$ is already in simplest form, as 22 and 45 have no common factors.
The final answer is $\frac{-22}{45}$.
More Information
This result shows how to handle operations with negative fractions. It illustrates the importance of finding a common denominator when adding or subtracting fractions.
Tips
- Confusing subtraction of a negative fraction with addition; remember that subtracting a negative is the same as addition.
- Failing to convert fractions to a common denominator before combining them.
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