# Fractions - Simplest Form

•  Simplest Form Simplest Form -When the numerator and denominator of a fraction have no common factors other than one.

To reduce a fraction into simplest form, follow the steps below:

Example:    4     (Four/sixths)

6

Explanation A:

Step 1Think: What are all the factors of 4?

The factors of 4 are 1, 2, and 4.

Step 2Think: What are all the factors of 6?

The factors of 6 are 1, 2, 3, and 6.

Step 3 – What is the greatest common multiple? In other words, looking at the factors of both the numerator (top number) and denominator (bottom number), what is the largest factor (number) that is the same? 2

Step 4 – Divide the both the numerator and denominator by the greatest common multiple.

4 divided by 2 = 2         (Two thirds is the

6 divided by 2 = 3         fraction in simplest form)

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Explanation B:

Step 1Think: What are all the factors of 4?       1 x 4 = 4

2 x 2 = 4

4 x 1 = 4

The factors of 4 are 1, 2, and 4.

Step 2Think: What are all the factors of 6?        1 x 6 = 6

2 x 3 = 6

3 x 2 = 6

6 x 1 = 6

The factors of 6 are 1, 2, 3, and 6.

Step 3 – What is the greatest common multiple? In other words, looking down the right column of the factors, in the multiplication problems listed, what is largest factor (number) that is the same? 2

Step 4 – Divide the both the numerator and denominator by the greatest common multiple.

4 divided by 2 = 2         (Two thirds is the fraction

6 divided by 2 = 3         in simplest form)