9/17 + 7/13
Understand the Problem
The question is asking to perform the addition of two fractions, 9/17 and 7/13. This involves finding a common denominator to combine the two fractions and then simplifying the result if necessary.
Answer
The sum of the fractions is $\frac{236}{221}$.
Answer for screen readers
The final answer is $\frac{236}{221}$.
Steps to Solve
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Identify the fractions We have two fractions to add: $\frac{9}{17}$ and $\frac{7}{13}$.
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Find the least common denominator (LCD) The denominators are 17 and 13. The least common multiple of 17 and 13 is $17 \times 13 = 221$, since both are prime numbers.
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Convert fractions to have the same denominator We need to convert each fraction to have the denominator of 221.
For $\frac{9}{17}$: $$ \frac{9}{17} = \frac{9 \times 13}{17 \times 13} = \frac{117}{221} $$
For $\frac{7}{13}$: $$ \frac{7}{13} = \frac{7 \times 17}{13 \times 17} = \frac{119}{221} $$
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Add the fractions Now we can add the fractions: $$ \frac{117}{221} + \frac{119}{221} = \frac{117 + 119}{221} = \frac{236}{221} $$
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Simplify if needed The fraction $\frac{236}{221}$ is already in its simplest form since 236 and 221 have no common factors (other than 1).
The final answer is $\frac{236}{221}$.
More Information
When adding fractions, it's essential to find a common denominator. The process involves converting each fraction, adding the numerators, and then expressing the sum over the common denominator. In this case, the sum of $\frac{9}{17}$ and $\frac{7}{13}$ is $\frac{236}{221}$.
Tips
- Forgetting to find the least common denominator can lead to incorrect results. Always ensure the fractions have the same denominator before adding.
- Not simplifying the final answer when possible. Always check if the resulting fraction can be simplified.
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