Solve the Fraction Division: 3/4 ÷ 1/6 Step-by-Step

To solve the division of fractions problem $\frac{3}{4}:\frac{1}{6}$, we will use multiplication by the reciprocal. Let us break down the steps:

• Step 1: Identify the fractions. The first fraction is $\frac{3}{4}$ and the second fraction is $\frac{1}{6}$.
• Step 2: Find the reciprocal of the second fraction. The reciprocal of $\frac{1}{6}$ is $\frac{6}{1}$ or just $6$.
• Step 3: Multiply the first fraction by the reciprocal of the second fraction:

$\frac{3}{4} \times \frac{6}{1} = \frac{3 \times 6}{4 \times 1} = \frac{18}{4}$

• Step 4: Simplify the resulting fraction. Divide both the numerator and the denominator by their greatest common divisor (GCD), which is 2:

$\frac{18}{4} = \frac{18 \div 2}{4 \div 2} = \frac{9}{2}$

• Step 5: Convert the improper fraction to a mixed number. Divide 9 by 2, which gives 4 with a remainder of 1:

$\frac{9}{2} = 4\frac{1}{2}$

Thus, the solution to the problem $\frac{3}{4}:\frac{1}{6}$ is $4\frac{1}{2}$.