Question

Identify the following fractions as mixed, vulgar, complex and decimal fractions.

$\frac{{\displaystyle \frac{5}{3}}}{{\displaystyle \frac{12}{5}}}$

Answer 1

• Mixed fraction- a mixed fraction consists of a whole number and a proper fraction, e.g. $1\frac{2}{5}$
• Vulgar fraction- it is also known as simple fraction, it is a fraction whose numerator and denominator are both whole numbers, e.g. $\frac{5}{12},\frac{13}{5}$
• Decimal fraction- a fraction whose denominator is a multiple of $10$ i.e., in the form of ${10}^n$
• Complex fraction- complex fractions are those fractions in which either numerator or denominator or both are fractions, e.g. $\frac{{\displaystyle \frac{7}{5}}}{2},\frac{3}{{\displaystyle \frac{1}{2}}},\frac{{\displaystyle \frac{17}{13}}}{{\displaystyle \frac{10}{23}}}$
• Proper fractions- a fraction whose numerator is less than the denominator is called a proper fraction, e.g.$\frac{1}{2},\frac{3}{5}$
• Improper fraction- a fraction whose numerator is greater than or equal to the denominator is called an improper fraction, e.g.$\frac{7}{5},\frac{12}{7}$

So, here we have $\frac{{\displaystyle \frac{5}{3}}}{{\displaystyle \frac{12}{5}}}$ in which both numerator and denominator is in are in fractions,

Hence $\frac{{\displaystyle \frac{5}{3}}}{{\displaystyle \frac{12}{5}}}$ is a complex fraction.