# How do you write fractions with a common denominator?

Nov 17, 2014

To write fractions with a common denominator, you will most likely need to scale some numbers up! I will explain how.

Let's try it with the fractions $\frac{2}{3}$ and $\frac{3}{12}$

12 is larger than 3, so we will have to multiply the 3 by some number to equal 12. (We are really finding the Least Common Multiple of the two denominators!) To do this, you have to multiply the 3 by 4, because 3x4=12. But now the numerator doesn't match the denominator. When you scale the denominator up, you have to scale the numerator up too! So the 2 must be multiplied by 4 also.

Now you have the following: $\frac{8}{12}$ and $\frac{3}{12}$

These fractions now have common denominators! Now they're all set for adding or subtracting fractions.

Try another: $\frac{2}{6}$ and $\frac{3}{5}$: The least common multiple of 6 and 5 is 30. (the product of the denominators)

Transform each fraction by multiplying by "1":
$\frac{2}{6} \cdot \frac{5}{5}$ = $\frac{10}{30}$ and $\frac{3}{5} \cdot \frac{6}{6}$ = $\frac{18}{30}$

One last problem: $\frac{4}{9}$ and $\frac{7}{6}$ What is the least common multiple of 9 and 6? Could you use 54? Absolutely, but it is not the LEAST number that you could use. How about 18? YES!

$\frac{4}{9} \cdot \frac{2}{2}$ = $\frac{8}{18}$ and $\frac{7}{6} \cdot \frac{3}{3}$ = $\frac{21}{18}$ Ready to go...

Hope this helped!