Solve: (4/9 × 1.5/2) + (3/4 × 3/3) Mixed Operations Problem

$\frac{4}{9}\times\frac{1.5}{2}+\frac{3}{4}\times\frac{3}{3}=$

To solve the equation $\frac{4}{9}\times\frac{1.5}{2}+\frac{3}{4}\times\frac{3}{3}=$, we will carefully apply the orders of operations, which include handling fractions with attention to multiplication and addition.

Step 1: First, evaluate the multiplication of fractions on the left side of the addition sign. Handle the multiplication $\frac{4}{9}\times\frac{1.5}{2}$. We'll convert the decimal to a fraction: $1.5 = \frac{3}{2}$.

• Thus, $\frac{4}{9}\times\frac{1.5}{2} = \frac{4}{9}\times\frac{3}{2}$
• Multiply the fractions: $\frac{4}{9} \times \frac{3}{2} = \frac{4 \times 3}{9 \times 2} = \frac{12}{18} = \frac{2}{3}$ after simplification.

Step 2: Next, consider the multiplication in the second part: $\frac{3}{4}\times\frac{3}{3}$.

• Since $\frac{3}{3}$ is essentially 1, it does not change the value of the other fraction. Hence, $\frac{3}{4}\times\frac{3}{3} = \frac{3}{4}$.

Step 3: With both products calculated, the equation becomes $\frac{2}{3} + \frac{3}{4}$.

Step 4: Now, you need a common denominator to add the fractions. The least common multiple of 3 and 4 is 12.

• Convert $\frac{2}{3}$ to a fraction with denominator 12: $\frac{2}{3} = \frac{8}{12}$.
• Convert $\frac{3}{4}$ to a fraction with denominator 12: $\frac{3}{4} = \frac{9}{12}$.

Step 5: Add the fractions: $\frac{8}{12} + \frac{9}{12} = \frac{17}{12}$.

Thus, the simplified solution for the equation is $\frac{17}{12}$ or as a mixed number, $1\frac{5}{12}$.