Question

Fill in the blanks:

$\_\_\_+3\frac{1}{4}=7\frac{11}{12}$

Answer 1

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

$\_\_\_+\frac{\left(4\times 3\right)+1}{4}=\frac{\left(12\times 7\right)+11}{12}$

$\_\_\_+\frac{13}{4}=\frac{95}{12}$

Step 2: Write all the fractions with the least common denominator (LCD), $12$.

$\_\_\_+\frac{13\times 3}{4\times 3}=\frac{95}{12}$

$\_\_\_+\frac{39}{12}=\frac{95}{12}$

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

$\_\_\_=\frac{95}{12}-\frac{39}{12}$

Step 4: Perform the subtraction keeping the common denominator.

$$\begin{gathered} \_\_\_=\frac{95-39}{12} \\ \_\_\_=\frac{82}{12} \end{gathered}$$

Step 5: Divide the numerator and denominator by the common factor, $2$.

$\frac{82÷2}{12÷2}=\frac{41}{6}$

Hence, the required number is $\frac{\mathbf{41}}{\mathbf{6}}$.