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Simplifying Fractions

Simplifying a fraction is writing a number in its most basic form. Sometimes fractions involve very large numbers in both the numerator (top number) and in the denominator (bottom number). As a general rule, it is easier to work with simpler fractions. So, always simplify.

There are three basic rules for simplifying fractions:

  1. Any number written over 1 is that number.
  2. A fraction can be simplified if the top and bottom numbers can both be divided by the same number, without leaving a remainder.
  3. If the top number is larger than the bottom number, and neither number can be divided by the same number, divide the top number by the bottom number.

Example 1

Now, let's work through the example below. The questions below will guide you through the process.

Simplify: seven over one

The correct answer is: 7

Example 2

Simplify six thirds

Can both the top and bottom numbers can be divided by 2, 3, 5, 7, 9, 11  13, or 17? In firefighter math, checking 2, 3, and 5 is usually all that is required.

The correct answer is: Yes

Both the numerator and denominator can be divided by 3.

Next we need to divide both the numerator and denominator by 3. Enter your results in the appropriate boxes.


6÷3 =  

The new fraction is two over one and if we apply the first rule above equals 2.

Example 3

Simplify twenty one sixteenths

Using Rule 3, divide the numerator by the denominator

21÷ 16 =

The correct answer of the long division is 1 with a remainder of 5. This can be expressed in a fraction by making 5 the numerator over the original denominator like this: one and five sixteenths

Can one and five sixteenths be simplified?

The correct answer is: No

one and five sixteenths cannot be simplified further.




1. Simplify fourteen sixteenths

five fourths

Select the correct answer.

2. Simplify five seconds

five fourths

two and a half


one and five seconds

Select the correct answer.