Question

Fill in the blanks:

$\_\_\_+8\frac{1}{4}=10\frac{1}{2}$

Answer 1

Step 1: Write the mixed number as an improper fraction.

$\_\_\_+\frac{\left(4\times 8\right)+1}{4}=\frac{\left(2\times 10\right)+1}{2}$

$\_\_\_+\frac{33}{4}=\frac{21}{2}$

Step 2: Write all the fractions with the least common denominator (LCD), $4$.

$\_\_\_+\frac{33}{4}=\frac{21\times 2}{2\times 2}$

$\_\_\_+\frac{33}{4}=\frac{42}{4}$

Step 3: Transpose the fractions to the right side of the equation and solve for blank.

$\_\_\_=\frac{42}{4}-\frac{33}{4}$

Step 4: Perform the subtraction keeping the common denominator.

$$\begin{gathered} \_\_\_=\frac{42-33}{4} \\ \_\_\_=\frac{9}{4} \end{gathered}$$

Hence, the required number is $\frac{\mathbf{9}}{\mathbf{4}}$.