How Do You Know A Fraction Is In Its Simplest Form?

To find out whether a fraction is in its simplest form, you simply need to figure out whether there are any common numbers that the numerator and denominator can be divided into evenly.

Keep reading to find out how this is done:

Is this fraction in its simplest form?

The best way to demonstrate how to work out whether fractions are in their simplest form would be to use an example.

I'll use the fraction 8/12.

What do we know already?

• The number 8 is the numerator
• The number 12 is the denominator
• There are a couple of numbers that fit into both 8 and 12 without leaving any left-overs.
The third point is the most important. If there's still a number that can fit into both the numerator and the denominator without leaving any leftovers, then the fraction is not in its simplest form.

With the example of 8/12: The numbers 1, 2, and 4 fit into 8. The numbers  1, 2, 3, 4, and 6 fit into 12.

We don't count the number 1 (because that fits into every number evenly), which leaves us with two numbers that both 8 and 12 can be divided by: 2 and 4.

You need to pick the highest common number (also known as the lowest common factor), and divide both the numerator and the denominator by it.

In the case of 8/12, 8 divided by 4 is 2. 12 divided by 4 is 3. That means that 8 over 12 in its simplest form is actually 2 over 3, or 2/3.

For more examples of how to simplify fractions, why not check out mathisfun.com.
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When there are no other common factors to divide by.
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When there is no common factors of the numerator and denominator
when numerator<denominator
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Oddman commented
10/7, for example, is in simplest form even though the numerator is greater than the denominator.
Look at the factors of the numerator and the factors of the denominator. If there are any factors in common, the fraction is not in its simplest form. To get it to simplest form, divide numerator and denominator by their common factor.

Example
21/35
Numerator factors: 21 = 3*7
Denominator factors: 35 = 5*7
These have the factor 7 in common.
Divide numerator by 7 to get 3; divide denominator by 7 to get 5. The reduced fraction is 3/5, which cannot be reduced any further.
21/35 = 3/5

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