Question

Fill in the blanks:

$6\frac{1}{6}-5\frac{1}{5}=.....$

Answer 1

Let the value in the blank be x.

$$\begin{gathered} 6\frac{1}{6}-5\frac{1}{5}=x \\ \Rightarrow x=\frac{37}{6}-\frac{26}{5} \\ \Rightarrow x=\frac{37\times 5}{6\times 5}-\frac{26\times 6}{5\times 6} \\ \Rightarrow x=\frac{185}{30}-\frac{156}{30} \\ \Rightarrow x=\frac{185-156}{30} \\ \Rightarrow x=\frac{29}{30} \end{gathered}$$

Thus, $6\frac{1}{6}-5\frac{1}{5}=\underline{\frac{29}{30}}$.