Solve the Division Problem: 10/9 ÷ 5 Step-by-Step

To solve the problem $\frac{10}{9} : 5$, we will convert the division into a multiplication with a reciprocal.

• Step 1: Recognize that dividing by $5$ is the same as multiplying by $\frac{1}{5}$.
• Step 2: Rewrite the problem as: $\frac{10}{9} \times \frac{1}{5}$.
• Step 3: Multiply the fractions: $\frac{10 \times 1}{9 \times 5} = \frac{10}{45}$.
• Step 4: Simplify the fraction $\frac{10}{45}$ by dividing both the numerator and denominator by their greatest common divisor (GCD), which is 5.
• Step 5: $\frac{10 \div 5}{45 \div 5} = \frac{2}{9}$.

Therefore, the solution to the problem is $\frac{2}{9}$.