Question

Fill in the blanks:

$\frac{2}{3}+\frac{3}{4}-\_\_\_=\frac{1}{2}$

Answer 1

Step 1: Write all the fractions with the least common denominator (LCD), $12$.

$\frac{2\times 4}{3\times 4}+\frac{3\times 3}{4\times 3}-\_\_\_=\frac{1\times 6}{2\times 6}$

$\frac{8}{12}+\frac{9}{12}-\_\_\_=\frac{6}{12}$

Step 2: Transpose the fractions to the right side of the equation and solve for blank.

$-\_\_\_=\frac{6}{12}-\frac{8}{12}-\frac{9}{12}$

Step 3: Perform the subtraction keeping the common denominator.

$$\begin{gathered} -\_\_\_=\frac{6-8-9}{12} \\ -\_\_\_=-\frac{11}{12} \end{gathered}$$

Step 4: Multiply both sides of the equation by $-1$.

$\_\_\_=\frac{11}{12}$

Hence, the required number is $\frac{\mathbf{11}}{\mathbf{12}}$.