Arithmetic Worksheets

Practice and master arithmetic with our helpful walkthroughs and downloadable practice worksheets from our team of elite math educators.

How to Reduce Fractions

By Alison Rodriguez

Reducing fractions is a very important skill when it comes to anything that involves fractions. You can use it at the beginning of a problem to make it easier to work with and you always use it at the end if you are given a fraction that is not fully reduced once all calculations are complete. The process of reducing fractions can also be seen in other topics besides just operations with fractions including ratios!

Why is this concept useful?

Sometimes it is much easier for us to work with simplified fractions. When you reduce the fraction, you are not actually changing it’s value, but finding a smaller equivalent fraction. It becomes very helpful to work with the smaller numbers and it is almost always expected that final answers should be in reduced form.

Where does this concept fit into the curriculum?

It begins in 4th grade

How can we reduce fractions?

A fraction is considered fully reduced when there are no common factors between the numerator and the denominator. In the diagram below, 2/4 is not a simplified fraction because both 2 and 4 can be divided by 2. When we divide the numerator and denominator by 2, you get the equivalent fraction of ½ . You can see in the diagram, that while the values do not have the same numbers, the amounts shaded in are equivalent.

To reduce fractions, you must find the greatest common factor between the two numbers. You can do this one of two ways:

Way #1 - list of factors

  1. List all factors of the numerator and the denominator.
  2. Determine the largest factor that is common between both numbers.
  3. Divide the numerator and the denominator by that number and write the reduced fraction.

Way #2 - simultaneous factoring

  1. Find a common factor between the numbers and divide both the numerator and denominator.
  2. Continue to divide the new set of numbers until one of the original numbers becomes 1 or the two numbers are co-primes.
  3. Multiply all the factors that were divided out together to determine the greatest common factor.
  4. Divide the numerator and denominator by that number and write the reduced fraction.

Sample Math Problems

Question

Reduce the fraction

412\frac{4}{12}

Solution

412÷4÷4=13\frac{4}{12} \frac{\div4}{\div4} = \frac{1}{3}

The greatest common factor is 4, so we can divide the numerator and denominator by 4.

Question

Reduce the fraction

90252\frac{90}{252}

Solution

90252÷18÷18=514\frac{90}{252} \frac{\div 18}{\div18} = \frac{5}{14}

Question

Reduce the fraction

1449\frac{14}{49}

Solution

1449÷7÷7=27\frac{14}{49} \frac{\div 7}{\div7} = \frac{2}{7}

Question

Reduce the fraction

20100\frac{20}{100}

Solution

20100÷20÷20=15\frac{20}{100} \frac{\div 20}{\div20} = \frac{1}{5}

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Practice Math Problems

1. Reduce the fraction

1232\frac{12}{32}

2. Reduce the fraction

80112\frac{80}{112}

3. Reduce the fraction

108117\frac{108}{117}

3. Reduce the fraction

1845\frac{18}{45}

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