Solve (3/2)(3/5) - 1/2: Mixed Fraction Operations

To solve the expression $\frac{3}{2} \cdot \frac{3}{5} - \frac{1}{2}$, we will follow these steps:

Step 1: Multiply the Fractions
To multiply $\frac{3}{2}$ by $\frac{3}{5}$, we multiply the numerators and the denominators:

$\frac{3}{2} \cdot \frac{3}{5} = \frac{3 \cdot 3}{2 \cdot 5} = \frac{9}{10}$

Step 2: Subtract Fractions
Now, subtract $\frac{1}{2}$ from $\frac{9}{10}$:

• First, find a common denominator. The least common multiple of 10 and 2 is 10.
• Convert $\frac{1}{2}$ to have a denominator of 10: $\frac{1}{2} = \frac{1 \cdot 5}{2 \cdot 5} = \frac{5}{10}$
• Subtract the fractions: $\frac{9}{10} - \frac{5}{10} = \frac{9 - 5}{10} = \frac{4}{10}$
• Simplify $\frac{4}{10}$ by dividing both the numerator and denominator by 2: $\frac{4 \div 2}{10 \div 2} = \frac{2}{5}$

Therefore, the solution to the problem is $\frac{2}{5}$.