How to Build And Reduce Fractions

What Is a Fraction?

A fraction is a comparison of the part to the whole. When writing a fraction, we use the form 'part over whole.' The part in a fraction is called the numerator. The whole of the fraction is called the denominator.

How to Build a Fraction

Now that we know fractions represent a comparison of the part to the whole, let's see how to build a fraction. To build a fraction, we need to see how many whole items would be included in our set. The number of whole items in our set would be placed on the bottom as the denominator. Next, we would need to see how many parts of our set are included. The part of the set would be placed on the top of the fraction and called the numerator.

For example, Andrew coaches an area soccer team. There are 12 players on his team. At Tuesday's practice, only 8 of the players were able to attend. Andrew wants to know what fraction of his team made it to practice on Tuesday.

Andrew knows that his whole team has 12 players. The number 12 would represent the whole, also known as the denominator, and would be placed on the bottom of our fraction. There were only 8 players who showed up for practice, which is the part of the team. The number 8 would represent the part, also known as the numerator, and would be placed on the top of the fraction. Andrew can now see that only 8/12 of the team arrived at practice on Tuesday.

How to Reduce a Fraction

A fraction is considered reduced, or in simplest form, when the only value that will divide into the numerator and denominator evenly is 1. To reduce a fraction, divide both the numerator and denominator by the greatest common factor, or the GCF. Fractions can also be reduced by dividing by a common factor multiple times until the only common factor remaining is 1.

Let's check back in on Andrew after his team's practice. After practice, Andrew was discussing how only 8/12 of his team showed up for his practice with the other coaches. Andrew wanted to be sure to tell them the fraction in the simplest form. So Andrew started thinking, 'what is the simplest form of the fraction 8/12?' Andrew starts by thinking about his numbers 8 and 12. He knows that both numbers are even, so they would both divide by 2. However, he wants to see if a larger value will divide into both numbers. Andrew realizes that both 8 and 12 will divide by 4, which would be the GCF.

To simplify his fraction, he will divide both the numerator and denominator by 4. 8 divided by 4 is 2 and 12 divided by 4 is 3. Andrew can now see that 8/12 in simplest form is 2/3. Andrew can now tell the other coaches that only 2/3 of his team showed up for practice tonight.