# When simplifying a fraction do you find the highest number that goes into both numerator/denominator or the lowest number?

May 31, 2018

The highest common factor.

#### Explanation:

Let's take the example $\frac{6}{18}$.

To simplify, you want to find the highest common factor of the numerator and the denominator, that is the largest number which goes into both numbers.

We can see by looking at the numbers $6$ and $18$ that the highest number to go into both of them is $6$.

Finally, we can divide both the numerator and the denominator by this number, $6$ in this case, to obtain our simplified fraction of $\frac{1}{3}$.

See below:

#### Explanation:

This answer expands on the one provided before.

Consider the fraction $\frac{1}{2}$. We can write this in many different ways, all of which have the same value as $\frac{1}{2}$:

$\frac{2}{4} , \frac{3}{6} , \frac{4}{8} , \ldots$

How can we do that? By using a creative form of the number 1.

Recall that anything divided by itself equals 1:

$1 = \frac{2}{2} = \frac{3}{3} = \frac{4}{4} = \ldots$

And so I can multiply the fraction $\frac{1}{2}$ by 1 (or something that equals it) to make it look differently:

$\frac{1}{2} \left(1\right) = \frac{1}{2} \left(\frac{2}{2}\right) = \frac{1}{2} \left(\frac{3}{3}\right) = \frac{1}{2} \left(\frac{4}{4}\right) = \ldots$

and the result of those multiplications is:

$\frac{1}{2} = \frac{2}{4} = \frac{3}{6} = \frac{4}{8} = \ldots$

We can go the other way as well. By factoring out, from the numerator and denominator, equal values, we get back to the lowest terms fraction. For instance, going from $\frac{4}{8}$ to $\frac{1}{2}$:

$\frac{4}{8} = \frac{4 \times 1}{4 \times 2} = \left(\frac{4}{4}\right) \left(\frac{1}{2}\right) = 1 \left(\frac{1}{2}\right) = \frac{1}{2}$