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Simplify fractions

Simplifying a fraction means rewriting it as an equivalent fraction with smaller whole-number numerator and denominator by dividing both by a common factor, ideally their greatest common factor, until no common factor greater than 1 remains. Number lines and area models can show that the fraction’s value does not change; this scope concerns positive numerical fractions, including improper fractions, not negative fractions, algebraic rational expressions, or complex fractions.

Detailed Explanation: Simplify fractions

A fraction is simplified when its numerator and denominator have no common factor greater than 11. To simplify, divide the numerator and denominator by the same common factor.

Example: Simplify 1824\frac{18}{24}.

  1. Find a number that divides both 1818 and 2424.
    Both are divisible by 66.

  2. Divide the numerator and denominator by 66:

1824=18÷624÷6=34\frac{18}{24}=\frac{18\div 6}{24\div 6}=\frac{3}{4}
  1. Check whether 34\frac{3}{4} can be simplified more.
    The only factors of 33 are 11 and 33, and 44 is not divisible by 33. So they have no common factor greater than 11.

Therefore,

1824=34\boxed{\frac{18}{24}=\frac{3}{4}}

The value stays the same because the numerator and denominator were divided by the same number.

Learn by doing: Simplify fractions

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    Fraction Division As Fraction - Simple

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