How do you simplify #1/2 + (-3/4) -(-3/5)# using PEMDAS?

As there are only two operations to perform—addition and subtraction—any order in which they are performed—as long as the appropriate sign and term are used—is not really required for this question.

All we will have to work with after the brackets are removed are fractions.

To simplify ( \frac{1}{2} + \left(-\frac{3}{4}\right) - \left(-\frac{3}{5}\right) ) using PEMDAS:

Step 1: Start with the subtraction inside the parentheses: ( -\frac{3}{4} + \frac{3}{5} )

Step 2: Find a common denominator, which is 20.

Step 3: Rewrite the fractions with the common denominator: ( -\frac{15}{20} + \frac{12}{20} )

Step 4: Perform the addition: ( -\frac{15}{20} + \frac{12}{20} = -\frac{3}{20} )

Step 5: Now, substitute the result back into the original expression: ( \frac{1}{2} - \left(-\frac{3}{20}\right) )

Step 6: Simplify the subtraction of a negative fraction by changing it to addition of the positive fraction: ( \frac{1}{2} + \frac{3}{20} )

Step 7: Find a common denominator, which is 20.

Step 8: Rewrite the fractions with the common denominator: ( \frac{10}{20} + \frac{3}{20} )

Step 9: Perform the addition: ( \frac{10}{20} + \frac{3}{20} = \frac{13}{20} )

Therefore, ( \frac{1}{2} + \left(-\frac{3}{4}\right) - \left(-\frac{3}{5}\right) = \frac{13}{20} ).