Simplest form

Both common fractions and algebraic expressions may be simplified, or written in simplest form.

Common fractions

A common fraction is in simplest form when the greatest common factor of the numerator and the denominator is 1.

To express in simplest form, think:
What is the greatest common factor (GCF) of 6 and 8? The answer is 2. Use 2 as the numerator and denominator of a common fraction (). This common fraction is equivalent to 1.
Divide by this value for 1.
Think: What is the greatest common factor of 3 and 4?
is expressed in simplest form as .

Did you know?

Many years ago, expressing a fraction in simplest form was called "reducing the fraction." However, the fraction is not reduced — its value stays the same! That's why we no longer use the expression "reducing the fraction."

An expression is in simplest form when no terms can be combined.

To express 3 + (2 × 5) in simplest form:
First: perform the operation within parantheses.
2 × 5 = 10
Next: perform the addition.
3 + 10 = 13
Thus, 3 + (2 × 5), expressed in simplest form, is 13.

Also called lowest terms, lowest terms of a fraction.

See also greatest common factor, order of operations, simplify..

Related word simplify.