9/17 + 7/13
Understand the Problem
The question is asking to perform the addition of two fractions, 9/17 and 7/13. To solve this, we need to find a common denominator, add the numerators, and simplify if necessary.
Answer
$ 1 \frac{15}{221} $
Answer for screen readers
The final answer is $ 1 \frac{15}{221} $.
Steps to Solve
- Finding the Least Common Denominator (LCD)
To add the fractions $ \frac{9}{17} $ and $ \frac{7}{13} $, we first need to find the least common denominator. The denominators are 17 and 13, which are both prime numbers.
To find the LCD: $$ \text{LCD} = 17 \times 13 = 221 $$
- Rewriting the Fractions
Next, we need to rewrite each fraction with the common denominator of 221.
For $ \frac{9}{17} $: $$ \frac{9}{17} = \frac{9 \times 13}{17 \times 13} = \frac{117}{221} $$
For $ \frac{7}{13} $: $$ \frac{7}{13} = \frac{7 \times 17}{13 \times 17} = \frac{119}{221} $$
- Adding the Fractions
Now we can add the two fractions: $$ \frac{117}{221} + \frac{119}{221} = \frac{117 + 119}{221} = \frac{236}{221} $$
- Simplifying the Result
The fraction $ \frac{236}{221} $ is an improper fraction. We can express it as a mixed number: $$ \frac{236}{221} = 1 \frac{15}{221} $$
The final answer is $ 1 \frac{15}{221} $.
More Information
Adding fractions involves finding a common denominator, which is crucial for combining them. The result, $ 1 \frac{15}{221} $, shows that the sum of the fractions is slightly more than one whole.
Tips
- Forgetting to Find the LCD: Always remember that you need a common denominator to add fractions.
- Simplifying Incorrectly: Make sure to simplify the final result properly, especially when dealing with improper fractions.
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