Question
Upstudy AI Solution
Tutor-Verified Answer
Answer
\(-\frac{5}{12}\)
Solution
1. Rewrite the division as a multiplication by the reciprocal:
\[
\frac{5}{18} \div \left(-\frac{2}{3}\right) = \frac{5}{18} \times \left(-\frac{3}{2}\right)
\]
2. Multiply the fractions by multiplying the numerators and the denominators:
\[
\frac{5}{18} \times \left(-\frac{3}{2}\right) = \frac{5 \times (-3)}{18 \times 2} = \frac{-15}{36}
\]
3. Simplify \(\frac{-15}{36}\) by dividing the numerator and the denominator by their greatest common divisor, which is 3:
\[
\frac{-15 \div 3}{36 \div 3} = \frac{-5}{12}
\]
The final answer is:
\[
-\frac{5}{12}
\]
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Simplify this solution The Deep Dive
To solve \( \frac{5}{18} \div\left(-\frac{2}{3}\right) \), we can multiply by the reciprocal of the divisor. This means we rewrite the division as multiplication: \[ \frac{5}{18} \times \left(-\frac{3}{2}\right) \] Next, we can multiply the numerators and the denominators: \[ \frac{5 \times -3}{18 \times 2} = \frac{-15}{36} \] Now, we simplify \( \frac{-15}{36} \) by finding the greatest common divisor, which is 3: \[ \frac{-15 \div 3}{36 \div 3} = \frac{-5}{12} \] So, the final answer is: \[ \frac{5}{18} \div\left(-\frac{2}{3}\right) = \frac{-5}{12} \]
