9/7 + 7/13
Understand the Problem
The question is asking for the sum of two fractions: 9/7 and 7/13. We need to find a common denominator, add the fractions, and simplify the result if necessary.
Answer
The sum of the fractions is $\frac{166}{91}$.
Answer for screen readers
The final sum of the fractions is
$$ \frac{166}{91} $$
Steps to Solve
- Identify the fractions and find a common denominator
We have the fractions $\frac{9}{7}$ and $\frac{7}{13}$. The denominators are 7 and 13. To find a common denominator, we multiply the two denominators together:
$$ \text{Common Denominator} = 7 \times 13 = 91 $$
- Convert fractions to have the common denominator
Convert each fraction to have the common denominator of 91:
For $\frac{9}{7}$:
$$ \frac{9}{7} = \frac{9 \times 13}{7 \times 13} = \frac{117}{91} $$
For $\frac{7}{13}$:
$$ \frac{7}{13} = \frac{7 \times 7}{13 \times 7} = \frac{49}{91} $$
- Add the fractions
Now that both fractions have the same denominator, we can add them:
$$ \frac{117}{91} + \frac{49}{91} = \frac{117 + 49}{91} = \frac{166}{91} $$
- Simplify the result if necessary
The fraction $\frac{166}{91}$ cannot be simplified further because the numerator and the denominator do not have any common factors.
The final sum of the fractions is
$$ \frac{166}{91} $$
More Information
The fractions add up to $\frac{166}{91}$, which is an improper fraction and cannot be simplified because 166 is a prime number relative to 91. This sum can also be expressed as a mixed number if needed, specifically $1 \frac{75}{91}$.
Tips
- Forgetting to find a common denominator or using an incorrect one.
- Failing to convert both fractions correctly to have the same denominator.
- Not simplifying the final result when possible.
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