Elementary Algebra

$\frac{1}{2}$
The rules of simplification state that we must first perform division and then move on to addition and subtraction. To perform division first, we introduce parenthesis to isolate the terms being divided from the rest of the expression. Since two fractions cannot be divided, we flip the fraction to the right of the division sign in order to replace the division sign with the multiplication sign: Step 1: $\frac{3}{4}+\frac{1}{3}\div\frac{4}{3}-\frac{1}{2}$ Step 2: $\frac{3}{4}+(\frac{1}{3}\times\frac{3}{4})-\frac{1}{2}$ Then, we reduce the expression in the parenthesis by cancelling out common factors. Step 3: $\frac{3}{4}+(\frac{1}{1}\times\frac{1}{4})-\frac{1}{2}$ Next, we take LCM of the three fractions in order to simplify the fractions: Step 4: $\frac{3}{4}+(\frac{1}{4})-\frac{1}{2}$ Step 5: $\frac{3+1-1(2)}{4}$ Step 6: $\frac{3+1-2}{4}$ Step 7: $\frac{4-2}{4}$ Step 8: $\frac{1}{2}$