Question

Insert two fractions between: $\frac{5}{6}\text{and}1\frac{1}{5}$

Answer 1

Step 1: Re - writing the mixed fraction as improper fraction.

An improper fraction is obtained by adding the whole part with a fractional part of a mixed fraction.

$1\frac{1}{5}$ can be expressed into improper fraction as $\frac{1\times 5+1}{5}=\frac{5+1}{5}=\frac{6}{5}$

Step 2: Inserting the two fractions between the given fractions.
If $\frac{a}{b}\text{and}\frac{c}{d}$ are two fractions, then $\frac{a+c}{b+d}$ is a fraction that lies between them.
By using above property, fraction between $\frac{5}{6}\text{and}\frac{6}{5}$ is,
$\frac{5+6}{6+5}=\frac{11}{11}=1$

fraction between $\frac{6}{5}\text{and}\frac{1}{1}$ is,
$\frac{6+1}{5+1}=\frac{7}{6}$

Hence,$1\text{and}1\frac{1}{6}$ are the two fractions between $\frac{5}{6}\text{and}1\frac{1}{5}$.