What is the quotient of 5/6÷1 1/2

Question

? Write your answer in fraction form and simplify the answer, if possible.

Answer 1

To divide the fraction \( \frac{5}{6} \) by the mixed number \( 1 \frac{1}{2} \), we first need to convert the mixed number to an improper fraction.

1. Convert \( 1 \frac{1}{2} \) into an improper fraction: \[ 1 \frac{1}{2} = \frac{2 \cdot 1 + 1}{2} = \frac{3}{2} \]

2. Now we can rewrite the division: \[ \frac{5}{6} \div \frac{3}{2} \]

3. Dividing by a fraction is the same as multiplying by its reciprocal: \[ \frac{5}{6} \div \frac{3}{2} = \frac{5}{6} \times \frac{2}{3} \]

4. Multiply the fractions: \[ \frac{5 \cdot 2}{6 \cdot 3} = \frac{10}{18} \]

5. Now, simplify \( \frac{10}{18} \):

   • The greatest common divisor (GCD) of 10 and 18 is 2. \[ \frac{10 \div 2}{18 \div 2} = \frac{5}{9} \]

Thus, the quotient \( \frac{5}{6} \div 1 \frac{1}{2} \) is \( \frac{5}{9} \).