What Is Simplest Form?

In math, simplest form refers to writing fractions in their basic forms. Fractions with common factors in their numerators and denominators may be canceled out, allowing them to be reduced to their simplest forms.

An example of reducing a fraction to its simplest form is found on Syracuse University's math website and is as follows: 8/12 = 2x4 / 3x4. In that case, the fraction can be simplified by canceling out the common factor, 4, from both the numerator and the denominator of the fraction.

When that is done, the fraction can be reduced down to 2/3, which can be multiplied by 4 to be equal to 8/12 once again.

The best way to break down fractions into their simplest forms is to write down the prime factors of the numerators and denominators. At that point, the fraction can be rewritten showing the numerator and denominator in their prime factors. Any prime factors can be canceled out, and then the remaining factors should be multiplied.

This can be a difficult subject to understand, so practice with simple fractions can be helpful. For instance, 10/24 can be broken down into the simplest form of 5/12. The steps to complete this change include writing out the prime factors for the numerator and denominator.

In this fraction, the numerator breaks down into 2 and 5, which multiply to 10. The denominator breaks down to 2, 2, 2 and 3, which multiply together to make 24. When rewritten, a person cancels out the matching 2 and multiplies the rest of the numbers to find 5/12.