Finding the Fraction 6/5: Number Identification Problem

Let's first try to understand what numbers are greater and smaller than the number $\frac{6}{5}$.

Since the denominator is 5, both the larger and smaller numbers will also have a denominator of 5:

\frac{?}{5}<\frac{6}{5}<\frac{?}{5}

Now let's complete the numerators with numbers that will help us reach whole numbers or half numbers in the fractions as follows:

\frac{5}{5}<\frac{6}{5}<\frac{7.5}{5}

Let's now simplify the fractions as follows:

$\frac{5:5}{5:5}=\frac{1}{1}=1$

$\frac{7.5:5}{5:5}=\frac{1.5}{1}=1.5=1\frac{1}{2}$

Therefore, the answer is:

1<\frac{6}{5}<1\frac{1}{2}