# Algebra and General Mathematics: Fraction

(Last Updated On: February 5, 2020) #### FRACTION

Fraction is a number expressed as a quotient in the form:

a / b,     →     b ≠ 0

where:

a is called numerator

b is called denominator

If:

a < b          →      proper fraction

a > b          →      improper fraction

Note: A Fractional expression is a quotient of two algebraic expressions.

#### COMPLEX FRACTIONS

A complex fraction is one which has one or more fractions in the numerator or denominator.

x + (1 / x) / 1 – (2 / x)

#### To simplify a complex fraction:

1. Reduce the numerator and denominator to simple fraction

2. Divide the two resulting fraction.

Example:

[ (x –1) / 5 ] / [ (x + 3) / x ]

= { [ (x – 1) / 5 ] [ x / (x + 3) ] }

= [ x(x – 1)] / [ 5(x + 3) ]

A fraction is in reduced form if its numerator and denominator have no factors aside from ± 1.

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