Question
Divide. Write your answer in lowest terms. Leave your answer as an improper fraction or whole number, if necessary. \( \frac{2}{15} \div \frac{22}{5} \)
Ask by Estrada Ruiz. in the United States
Jan 22,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
The answer is \( \frac{1}{33} \).
Solution
To divide the fractions \( \frac{2}{15} \div \frac{22}{5} \), follow these steps:
1. **Rewrite the division as multiplication by the reciprocal:**
\[
\frac{2}{15} \div \frac{22}{5} = \frac{2}{15} \times \frac{5}{22}
\]
2. **Multiply the numerators and the denominators:**
\[
\frac{2 \times 5}{15 \times 22} = \frac{10}{330}
\]
3. **Simplify the fraction by dividing both the numerator and the denominator by their greatest common divisor (10):**
\[
\frac{10 \div 10}{330 \div 10} = \frac{1}{33}
\]
So, the answer in its lowest terms is:
\[
\boxed{\dfrac{1}{33}}
\]
Reviewed and approved by the UpStudy tutoring team
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Simplify this solution The Deep Dive
To divide fractions, you multiply by the reciprocal of the second fraction. So, \[ \frac{2}{15} \div \frac{22}{5} = \frac{2}{15} \times \frac{5}{22}. \] Now, multiply the numerators and the denominators: \[ \frac{2 \times 5}{15 \times 22} = \frac{10}{330}. \] Next, we simplify \( \frac{10}{330} \). Both the numerator and the denominator can be divided by 10: \[ \frac{10 \div 10}{330 \div 10} = \frac{1}{33}. \] So, the final answer in lowest terms is \( \frac{1}{33} \).
