Question

How do you write fractions with a common denominator?

Answer 1

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!