How do you write fractions with a common denominator?

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 #2/3# and #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: #8/12# and #3/12#

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

Try another: #2/6# and #3/5#: The least common multiple of 6 and 5 is 30. (the product of the denominators)

Transform each fraction by multiplying by "1":
#2/6*5/5# = #10/30# and #3/5*6/6# = #18/30#

One last problem: #4/9# and #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!

#4/9*2/2# = #8/18# and #7/6*3/3# = #21/18# Ready to go...

Hope this helped!