Question

Fill in the blanks:

$\frac{1}{4}+\frac{4}{5}-\_\_\_=1$

Answer 1

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

$\frac{1\times 5}{4\times 5}+\frac{4\times 4}{5\times 4}-\_\_\_=\frac{1\times 20}{1\times 20}$

$\frac{5}{20}+\frac{16}{20}-\_\_\_=\frac{20}{20}$

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

$-\_\_\_=\frac{20}{20}-\frac{5}{20}-\frac{16}{20}$

Step 3: Perform the subtraction keeping the common denominator.

$$\begin{gathered} -\_\_\_=\frac{20-5-16}{20} \\ -\_\_\_=-\frac{1}{20} \end{gathered}$$

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

$\_\_\_=\frac{1}{20}$

Hence, the required number is $\frac{\mathbf{1}}{\mathbf{20}}$.