Question

Fill in the blanks:

$\frac{1}{6}+\_\_\_=\frac{17}{30}$

Answer 1

Step 1: Subtract $\frac{1}{6}$ from both sides of the given equation and simplify.

$\frac{1}{6}+\_\_\_-\frac{1}{6}=\frac{17}{30}-\frac{1}{6}$

$\_\_\_=\frac{17}{30}-\frac{1}{6}$

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

$\_\_\_=\frac{17}{30}-\frac{1\times 5}{6\times 5}$

$\_\_\_=\frac{17}{30}-\frac{5}{30}$

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

$$\begin{gathered} \_\_\_=\frac{17-5}{30} \\ \_\_\_=\frac{12}{30} \end{gathered}$$

Step 4: Divide both the numerator and denominator by the common factor $6$.

$$\begin{gathered} \_\_\_=\frac{12÷6}{30÷6} \\ \_\_\_=\frac{2}{5} \end{gathered}$$

Hence, the required number is $\frac{\mathbf{2}}{\mathbf{5}}$.