Question
\( \frac{1}{9}+\frac{1}{15}=\square \) (Type a whole number or a fraction.)
Ask by Reyes Floyd. in the United States
Mar 10,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
\(\frac{8}{45}\)
Solution
1. Find the least common denominator (LCD) of \(9\) and \(15\). The LCD of \(9\) and \(15\) is \(45\).
2. Rewrite each fraction with the denominator \(45\):
\[
\frac{1}{9} = \frac{1 \times 5}{9 \times 5} = \frac{5}{45}, \quad \frac{1}{15} = \frac{1 \times 3}{15 \times 3} = \frac{3}{45}
\]
3. Add the fractions:
\[
\frac{5}{45} + \frac{3}{45} = \frac{5+3}{45} = \frac{8}{45}
\]
\(\frac{8}{45}\)
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Simplify this solution Bonus Knowledge
To combine \( \frac{1}{9} \) and \( \frac{1}{15} \), we first need to find a common denominator. The least common multiple of 9 and 15 is 45. Now, we convert both fractions: \( \frac{1}{9} = \frac{5}{45} \) (because \( 1 \times 5 = 5 \) and \( 9 \times 5 = 45 \)) \( \frac{1}{15} = \frac{3}{45} \) (because \( 1 \times 3 = 3 \) and \( 15 \times 3 = 45 \)) Adding these gives: \( \frac{5}{45} + \frac{3}{45} = \frac{8}{45} \) So, \( \frac{1}{9}+\frac{1}{15}=\frac{8}{45} \).
