Questions: Divide. Write your answer in simplest form. 3/4 ÷ 5/6

Transcript text: Divide. Write your answer in simplest form. \[ \frac{3}{4} \div \frac{5}{6} \]

Solution

Solution Steps

Step 1: Rewrite the division as multiplication by the reciprocal

To divide fractions, rewrite the division as multiplication by the reciprocal of the second fraction.
\[ \frac{3}{4} \div \frac{5}{6} = \frac{3}{4} \times \frac{6}{5} \]

Step 2: Multiply the numerators and denominators

Multiply the numerators together and the denominators together.
\[ \frac{3 \times 6}{4 \times 5} = \frac{18}{20} \]

Step 3: Simplify the fraction

Simplify the fraction by dividing the numerator and denominator by their greatest common divisor (GCD), which is 2.
\[ \frac{18 \div 2}{20 \div 2} = \frac{9}{10} \]

Final Answer

\(\boxed{\frac{9}{10}}\)

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