# How do you calculate 18/12 - 7/9?

Jan 21, 2015

The answer is $\frac{13}{18}$.

Here's how to calculate it:

You'll notice that $\frac{18}{12}$ and $\frac{7}{9}$ have different denominators.

In order to subtract these fractions, we need to find equivalent fractions ( i.e. fractions that are the same as our originals) that have the same denominator as one another.

To do this, let's find the least common denominator, or the smallest number that can be divided by both denominators.

One way to do this to write out the multiples of both denominators until a number repeats in the the list:

Multiples of 12: 12, 24, 36 , 48, 60
Multiples of 9: 9, 18, 27, 36

Since 36 appears in both lists, we can make both denominators 36 to create equivalent fractions.

Since $12 \cdot 3 = 36$, we can multiply $\frac{18}{12} \cdot \frac{3}{3}$ (since $\frac{3}{3}$ = 1) ...

$\frac{18}{12} \cdot \frac{3}{3} = \frac{54}{36}$

And since $9 \cdot 4 = 36$, we can multiply $\frac{7}{9} \cdot \frac{4}{4}$ ...

$\frac{7}{9} \cdot \frac{4}{4} = \frac{28}{36}$

Now, we have equivalent fractions with a denominator of 36 and can subtract:

$\frac{54}{36} - \frac{28}{36} = \frac{26}{36}$

And then divide the numerator and the denominator by 2 to simplify:

$\frac{26}{36} = \frac{13}{18}$