Simplify #13/3 + 5(5/4 - 3/2) ÷ 11/8# using PEMDAS?

We use PEMDAS as order of operations i.e. first parentheses. then exponents (none here), then multiplication and division and finally addition and subtraction.

To simplify the expression (\frac{13}{3} + 5\left(\frac{5}{4} - \frac{3}{2}\right) \div \frac{11}{8}) using the order of operations (PEMDAS), follow these steps:

1. Simplify the expression inside the parentheses first: [5\left(\frac{5}{4} - \frac{3}{2}\right) = 5\left(\frac{5}{4} - \frac{6}{4}\right) = 5\left(\frac{-1}{4}\right) = -\frac{5}{4}]

2. Rewrite the expression with the simplified part: [\frac{13}{3} + (-\frac{5}{4}) \div \frac{11}{8}]

3. Perform the division operation: [-\frac{5}{4} \div \frac{11}{8} = -\frac{5}{4} \times \frac{8}{11} = -\frac{40}{44} = -\frac{10}{11}]

4. Rewrite the expression with the result of the division: [\frac{13}{3} - \frac{10}{11}]

5. Find a common denominator and combine the fractions: [\frac{13 \times 11}{3 \times 11} - \frac{10 \times 3}{11 \times 3}] [= \frac{143}{33} - \frac{30}{33}]

6. Combine the fractions: [= \frac{143 - 30}{33}] [= \frac{113}{33}]

So, the simplified form of the expression is (\frac{113}{33}).