Solve Fraction Division: 4/6 ÷ 3/7 Step-by-Step

To solve the fraction division problem $\frac{4}{6} : \frac{3}{7}$, follow these steps:

• Step 1: Simplify the first fraction $\frac{4}{6}$.

Simplify by finding the greatest common divisor (GCD) of 4 and 6, which is 2. Divide both the numerator and denominator by 2:

$\frac{4}{6} = \frac{4/2}{6/2} = \frac{2}{3}$

• Step 2: Find the reciprocal of the second fraction $\frac{3}{7}$.

The reciprocal of $\frac{3}{7}$ is $\frac{7}{3}$.

• Step 3: Multiply the simplified first fraction by the reciprocal of the second.

$\frac{2}{3} \times \frac{7}{3} = \frac{2 \times 7}{3 \times 3} = \frac{14}{9}$

• Step 4: Convert the improper fraction $\frac{14}{9}$ to a mixed number.

Divide 14 by 9, which gives a quotient of 1 and a remainder of 5:

$\frac{14}{9} = 1\frac{5}{9}$

Therefore, the solution to the problem is $1\frac{5}{9}$.