What is the quotient of 5/6÷(1+1/2)

? Write your answer in fraction form and simplify the answer, if possible.(1 point)

1 answer

To find the quotient of \( \frac{5}{6} \div (1 + \frac{1}{2}) \), we first need to simplify the expression inside the parentheses:

\[ 1 + \frac{1}{2} = \frac{2}{2} + \frac{1}{2} = \frac{3}{2} \]

Now we can rewrite the division:

\[ \frac{5}{6} \div \frac{3}{2} \]

Dividing by a fraction is the same as multiplying by its reciprocal, so we have:

\[ \frac{5}{6} \times \frac{2}{3} \]

Next, we multiply the fractions:

\[ \frac{5 \times 2}{6 \times 3} = \frac{10}{18} \]

Now we simplify \( \frac{10}{18} \) by dividing both the numerator and the denominator by their greatest common divisor, which is 2:

\[ \frac{10 \div 2}{18 \div 2} = \frac{5}{9} \]

Thus, the simplified quotient is:

\[ \boxed{\frac{5}{9}} \]

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