Question

Fill in the blanks:

$\frac{1}{3}+\_\_\_=\frac{22}{21}$

Answer 1

Step 1: Subtract $\frac{1}{3}$ from both sides of the given equation and simplify.

$\frac{1}{3}+\_\_\_-\frac{1}{3}=\frac{22}{21}-\frac{1}{3}$

$\_\_\_=\frac{22}{21}-\frac{1}{3}$

Step 2: Write both the fractions with the least common denominator (LCD), $21$.

$\_\_\_=\frac{22}{21}-\frac{1\times 7}{3\times 7}$

$\_\_\_=\frac{22}{21}-\frac{7}{21}$

Step 3: Subtract the numerators and write the difference over the common denominator.

$$\begin{gathered} \_\_\_=\frac{22-7}{21} \\ \_\_\_=\frac{15}{21} \end{gathered}$$

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

$$\begin{gathered} \_\_\_=\frac{15÷3}{21÷3} \\ \_\_\_=\frac{5}{7} \end{gathered}$$

Hence, the required number is $\frac{\mathbf{5}}{\mathbf{7}}$.