Simplest Form of a Fraction

The Lowest Term

Simplifying to the core.

A fraction is in its simplest form when its top and bottom numbers are as small as they can possibly be.
Image 1

Key Points

  1. This means no number (other than 11) can divide perfectly into both the top and the bottom.
  2. For example, 48\frac{4}{8} is not simple because both numbers can be cut in half. But 12\frac{1}{2} is simple because it cannot be shrunk anymore.
  3. Math teachers usually want your final answers in simplest form because it is the easiest version to read!

Olympiad Fact

If the numerator and denominator are consecutive integers (like 1415\frac{14}{15}), they are guaranteed to be coprime, meaning their only common factor is 11, and they are already in simplest form.

The HCF Method

One-step simplification.

The quickest way to simplify a fraction is to find the biggest number that divides perfectly into both the top and the bottom.
Image 1

Key Points

  1. Find the Highest Common Factor (HCF) for both the top and bottom numbers.
  2. Divide the top number by that HCF.
  3. Divide the bottom number by that same HCF.
  4. If finding the biggest factor is hard, just keep dividing both numbers by 22, 33, or 55 until you can't divide them anymore.

Olympiad Fact

If you don't know the HCF immediately, start by dividing by 22 if they are even, or 55 if they end in 00 or 55. Repeated small divisions lead to the same result as one large division.

Swipe to skip‹