Question

Fill in the blanks:

$\frac{1}{2}+\frac{3}{4}-\_\_\_=\frac{9}{20}$

Answer 1

Step 1: Write all the fractions with the least common denominator (LCD), $20$.

$\frac{1\times 10}{2\times 10}+\frac{3\times 5}{4\times 5}-\_\_\_=\frac{9}{20}$

$\frac{10}{20}+\frac{15}{20}-\_\_\_=\frac{9}{20}$

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

$-\_\_\_=\frac{9}{20}-\frac{10}{20}-\frac{15}{20}$

Step 3: Perform the subtraction keeping the common denominator.

$$\begin{gathered} -\_\_\_=\frac{9-10-15}{20} \\ -\_\_\_=-\frac{16}{20} \end{gathered}$$

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

$\_\_\_=\frac{16}{20}$

Step 5: Divide both the numerator and denominator by the common factor $4$.

$$\begin{gathered} \_\_\_=\frac{16÷4}{20÷4} \\ \_\_\_=\frac{4}{5} \end{gathered}$$

Hence, the required number is $\frac{\mathbf{4}}{\mathbf{5}}$.