Explain fractions and their types with examples.

Proper fractions are those fractions where the numerators are smaller than the denominators. 

Example: $\frac{5}{6}$, $\frac{3}{11}$, $\frac{2}{9}$, and so on are proper fractions

Improper fractions are those fractions where the numerators are greater than the denominators. 

Example: $\frac{6}{5}$, $\frac{10}{3}$, $\frac{15}{9}$, and so on are improper fractions

Mixed fractions are those fractions where there is a whole number part and a proper fraction part.

Example:  1 $\frac{1}{2}$, 3 $\frac{1}{3}$ and so on are mixed fractions

Improper fractions can be converted into Mixed fractions and

Example: $\frac{9}{4}$ = 2 $\frac{1}{4}$;  $\frac{11}{5}$ = 2 $\frac{1}{5}$ and so on

Mixed fractions can be converted into improper fractions

Example: 4 $\frac{1}{3}$ = (4x3+1)/3 = $\frac{13}{3}$

Like fractions are those fractions with the same denominators and

Eg: $\frac{1}{2}$, $\frac{3}{2}$ are like fractions

Unlike fractions are those fractions with different denominators

Eg; $\frac{1}{2}$, $\frac{1}{3}$, $\frac{3}{4}$are unlike fractions

Unlike fractions can be converted into Like fractions and vice versa