Solve Fraction Division: 4/9 ÷ 1/3 Step-by-Step

To solve the problem of dividing $\frac{4}{9}$ by $\frac{1}{3}$, we follow these steps:

• Step 1: Convert the division operation into multiplication by the reciprocal of the second fraction.
• Step 2: Perform the multiplication of the fractions.
• Step 3: Simplify the resulting fraction, if possible, and convert it into a mixed number.

Let's proceed with the steps:

Step 1: The expression $\frac{4}{9} : \frac{1}{3}$ is equivalent to multiplying $\frac{4}{9}$ by the reciprocal of $\frac{1}{3}$. The reciprocal of $\frac{1}{3}$ is $\frac{3}{1}$.

Step 2: Multiply the fractions:

$\frac{4}{9} \times \frac{3}{1} = \frac{4 \times 3}{9 \times 1} = \frac{12}{9}.$

Step 3: Simplify the result by dividing both the numerator and the denominator by their greatest common divisor (GCD), which is 3:

$\frac{12}{9} = \frac{12 \div 3}{9 \div 3} = \frac{4}{3}.$

Step 4: Convert the improper fraction $\frac{4}{3}$ into a mixed number. $\frac{4}{3}$ equals $1$ with a remainder of $1$, so it can be written as the mixed number $1\frac{1}{3}$.

Therefore, the solution to the problem $\frac{4}{9} : \frac{1}{3}$ is $\mathbf{1\frac{1}{3}}$.