Solve Mixed Number Expression: 3(b/a)×1⅜a + ⅝b + Other Terms

To solve this problem, we'll simplify the algebraic expression and combine like terms:

• Convert mixed numbers to improper fractions and simplify.
• Simplify each part of the expression.
• Combine like terms by variable type.

Let's go through each step:

First, convert and simplify $3\frac{b}{a} \cdot 1\frac{3}{8}a$: - Change $1\frac{3}{8}$ to an improper fraction: $1\frac{3}{8} = \frac{11}{8}$.

Thus, multiply: $3\frac{b}{a} \cdot \frac{11}{8}a = \frac{33b}{8}$.

Then, look at each term:

• The expression now consists of: $\frac{33b}{8} + \frac{5}{8}b + \frac{9}{10}a + \frac{4}{18}m + \frac{2}{3}m$.
• Simplify each component: - $\frac{4}{18}m = \frac{2}{9}m$ (reducing the fraction).
• Now, add like terms: - Combine terms involving $b$: $\frac{33b}{8} + \frac{5b}{8} = \frac{33b + 5b}{8} = \frac{38b}{8} = 4\frac{3}{4}b$.
• There are no like terms with $a$, so $\frac{9}{10}a$ remains unchanged.
• Combine terms involving $m$: $\frac{2}{9}m + \frac{2}{3}m = \frac{2m}{9} + \frac{6m}{9} = \frac{8m}{9}$.

After the simplification, the expression becomes: $4\frac{3}{4}b + \frac{9}{10}a + \frac{8}{9}m$.

Therefore, the solution to the problem is $4\frac{3}{4}b + \frac{9}{10}a + \frac{8}{9}m$.