Question

Fill in the blanks:

$\frac{3}{10}+\_\_\_=\frac{23}{30}$

Answer 1

Step 1: Subtract $\frac{3}{10}$ from both sides of the given equation and simplify.

$\frac{3}{10}+\_\_\_-\frac{3}{10}=\frac{23}{30}-\frac{3}{10}$

$\_\_\_=\frac{23}{30}-\frac{3}{10}$

Step 2: Write both the fractions with the least common denominator (LCD), $30$.

$\_\_\_=\frac{23}{30}-\frac{3\times 3}{10\times 3}$

$\_\_\_=\frac{23}{30}-\frac{9}{30}$

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

$$\begin{gathered} \_\_\_=\frac{23-9}{30} \\ \_\_\_=\frac{14}{30} \end{gathered}$$

Step 4: Divide both the numerator and denominator by the common factor $2$.

$$\begin{gathered} \_\_\_=\frac{14÷2}{30÷2} \\ \_\_\_=\frac{7}{15} \end{gathered}$$

Hence, the required number is $\frac{\mathbf{7}}{\mathbf{15}}$.