Questions: Divide, Write your answer in simplest form, 3/8 ÷ 5/6

Transcript text: Divide, Write your answer in simplest form, \[ \frac{3}{8} \div \frac{5}{6} \]

Solution

Solution Steps

Step 1: Understand the Division of Fractions

To divide fractions, we multiply the first fraction by the reciprocal of the second fraction. The reciprocal of a fraction is obtained by swapping its numerator and denominator.

Step 2: Find the Reciprocal

The reciprocal of \(\frac{5}{6}\) is \(\frac{6}{5}\).

Step 3: Multiply the Fractions

Now, multiply \(\frac{3}{8}\) by \(\frac{6}{5}\):

\[ \frac{3}{8} \times \frac{6}{5} = \frac{3 \times 6}{8 \times 5} = \frac{18}{40} \]

Step 4: Simplify the Fraction

To simplify \(\frac{18}{40}\), find the greatest common divisor (GCD) of 18 and 40, which is 2. Divide both the numerator and the denominator by 2:

\[ \frac{18 \div 2}{40 \div 2} = \frac{9}{20} \]

Final Answer

The simplest form of \(\frac{3}{8} \div \frac{5}{6}\) is \(\boxed{\frac{9}{20}}\).

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