Solve Fraction Division: 8/9 ÷ 2/3 Step-by-Step

Complete the following exercise:

$\frac{8}{9}:\frac{2}{3}=\text{?}$

To solve the fraction division $\frac{8}{9} \div \frac{2}{3}$, follow these steps:

• Step 1: Identify the given fractions $\frac{8}{9}$ and $\frac{2}{3}$.
• Step 2: Find the reciprocal of the second fraction. The reciprocal of $\frac{2}{3}$ is $\frac{3}{2}$.
• Step 3: Multiply the first fraction by the reciprocal of the second fraction: $\frac{8}{9} \times \frac{3}{2}$.
• Step 4: Perform the multiplication: multiply the numerators together and the denominators together.

Let's compute the multiplication:

$\frac{8}{9} \times \frac{3}{2} = \frac{8 \times 3}{9 \times 2} = \frac{24}{18}$

Step 5: Simplify the resulting fraction $\frac{24}{18}$.

To simplify, find the greatest common divisor (GCD) of 24 and 18, which is 6. Divide both the numerator and the denominator by 6:

$\frac{24}{18} = \frac{24 \div 6}{18 \div 6} = \frac{4}{3}$

Step 6: If necessary, convert the improper fraction to a mixed number.

Since $\frac{4}{3}$ is an improper fraction, it can be converted to a mixed number:

$\frac{4}{3} = 1 \frac{1}{3}$

Therefore, the solution to the problem $\frac{8}{9} : \frac{2}{3}$ is $1 \frac{1}{3}$.