What is 7/15 + 13/15 - 8/15? Give your answer in its simplest form.
Understand the Problem
The question is asking us to perform a mathematical operation involving fractions. Specifically, we need to add and subtract the fractions given and then provide the final answer in its simplest form.
Answer
The answer is \( \frac{4}{5} \).
Answer for screen readers
The final answer is ( \frac{4}{5} ).
Steps to Solve
- Add the first two fractions We need to add the fractions ( \frac{7}{15} ) and ( \frac{13}{15} ). Since they have the same denominator, we can simply add the numerators:
[ \frac{7 + 13}{15} = \frac{20}{15} ]
- Subtract the third fraction Now, we will subtract ( \frac{8}{15} ) from the result of the previous step. Again, since the denominator is the same, we can focus on the numerators:
[ \frac{20}{15} - \frac{8}{15} = \frac{20 - 8}{15} = \frac{12}{15} ]
- Simplify the fraction To simplify ( \frac{12}{15} ), we find the greatest common divisor (GCD) of 12 and 15, which is 3. We divide both the numerator and the denominator by 3:
[ \frac{12 \div 3}{15 \div 3} = \frac{4}{5} ]
The final answer is ( \frac{4}{5} ).
More Information
The process of adding and subtracting fractions involves making sure the denominators are the same. After performing the operations, simplifying the resulting fraction to its lowest terms ensures that the answer is presented clearly.
Tips
- Forgetting to find a common denominator before adding or subtracting fractions can lead to incorrect results. Always check that the denominators match.
- Failing to simplify the fraction at the end is a common mistake. Always look for opportunities to reduce fractions to their simplest forms.
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