Arithmetic Fraction is a fraction which is in the form of a / b. Algebraic fractions contain polynomials either in the numerator or denominator. Get the definition of Arithmetic Fraction and Algebraic Fraction, some solved example questions in the further sections of this page.

Arithmetic Fraction Definition

Arithmetic fractions are represented as p / q. Where p is the numerator and q is the denominator which is not equal to zero. A number or expression in the form of a numerator/denominator is called the arithmetic fraction. It can also be expressed as p ÷ q. Some examples are 1/2, 3/10, 5/4, etc

When the numerator, denominator of arithmetic fractions are multiplied or divided by the same quantity, then the value of the fraction remains the same. Arithmetic fractions are mostly monomial quantities or they can be reduced to monomials.

Some Examples of Arithmetic Fraction

• 12/16 is an arithmetic fraction having numerator 12 and denominator 16.
• 17/85 is also an arithmetic fraction having numerator 17 and denominator 85.
• 18/81 = 2/9
• 16/32 = 1/2

Algebraic Fraction Definition

An algebraic Fraction is also a fraction whose numerator, denominators are algebraic expressions. Both numerator and denominator are polynomials.

Examples of Algebraic Fraction

• If both denominator and numerator are monomials.
  • a/b, x/y, ax²/bc, my²/n, etc
• If the denominator is monomial and the numerator is polynomial or binomial.
  • x+y / z, a²+bc+b² / ab, ab+bc+ca / a, etc
• If the denominator is binomial/polynomial and the numerator is monomial.
  • a/b+c, x/y-z, a/ab+bc+ca, etc
• If numerator and denominator are binomial or polynomial.
  • x+y/x-y, a+b+c/a+c, a²+2bc+c/a+b, etc