Question

Fill in the blanks:

$\_\_\_+3\frac{2}{3}=5$

Answer 1

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

$\_\_\_+\frac{\left(3\times 3\right)+2}{3}=5$

$\_\_\_+\frac{11}{3}=5$

Step 2: Write all the fractions with the least common denominator (LCD), $3$.

$\_\_\_+\frac{11}{3}=\frac{5\times 3}{1\times 3}$

$\_\_\_+\frac{11}{3}=\frac{15}{3}$

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

$\_\_\_=\frac{15}{3}-\frac{11}{3}$

Step 4: Perform the subtraction keeping the common denominator.

$$\begin{gathered} \_\_\_=\frac{15-11}{3} \\ \_\_\_=\frac{4}{3} \end{gathered}$$

Hence, the required number is $\frac{\mathbf{4}}{\mathbf{3}}$.