Fractions

Reducing a Fraction to its Simplest Form

Reducing a fraction to its simplest form means changing it to a fraction that has the same value as the original but uses smaller numbers.

For example if you have a pizza with 4 pieces and you eat 2 pieces of that pizza, you have eaten 1/2 of the pizza. So 2/4 reduced to its simplest form is 1/2.

 

To reduce a fraction to its simplest form you need to be able to divide the same number into both the top number (numerator) of the fraction and the bottom number (denominator) of the fraction.

Reduce a Fraction:

• In the case of the pizza, 2 and 4 can both divided by 2.
   
   
• The simplest form of 2/4 is 1/2.

Now reduce 9/12 to its simplest form.

• Divide the numerator and the denominator by 3.
  
• The simplest form of 9/12 is 3/4.

You can do this more than once and you can divide by any number as long as you can divide evenly by the same number on the top as you do on the bottom. Dividing evenly means there will be no remainder.

For example, to reduce 48/60 to its simplest form, do it in steps.

• Divide the numerator and the denominator by 6 to get 8/10. Then divide both numbers by 2 to get 4/5.
  
• The simplest form of 48/60 is 4/5.

Lets do one more example. Reduce 24/64 to its simplest form.

• You can reduce 24/64 down by dividing by 2 multiple times.
  
• The simplest form of 24/64 is 3/8.
• We found that by dividing by the same number (2) several times.

When there are no more common factors (numbers that can be divided evenly into both the numerator and denominator) you have found the simplest form of that fraction. Because some fractions are already in simplest form you will not always need to reduce. Example: ½ is in its lowest form so you would not need to reduce. For more information on factors review Lesson 5 page 4.