adding fractions with different denominators

[Marcia]

I am preparing to take my GED at 51yrs old and I am a beginning learner of fractions. I am having difficulty finding the formula that will help me learn how to add and reduce these kind of fraction please help.

[StuartLC]

Originally Posted by Marcia

I am preparing to take my GED at 51yrs old and I am a beginning learner of fractions. I am having difficulty finding the formula that will help me learn how to add and reduce these kind of fraction please help.

As you've figured, the numerators of fractions can only be added directly once they have the same denominator. The 'trick' to getting fractions into a state where they do have the same denominator is to find the Least Common Multiple(LCM), being the lowest whole number into which both denominators can be divided.

The LCM is determined by factoring both denominators into the factors

If this sounds, lets try a simple example

e.g. Lets add One and Two-thirds plus 2 and Three Quarters (you'll note that the denominators 3, and 4, are different)

1 2/3 + 2 3/4

First, you'll need to convert both fractions into vulgar (improper) fractions.
Do this by multiplying through the whole numbers by their denominators:

(3 x 1 + 2) + (4 x 2 + 3)
3 4

= 5 + 11
3 4

Next up is to determine the Least Common Multiple.
3 is a prime number (3 x 1), and 4 has factors (1 x 4 and 2 x 2).
There are no common factors of 3 and 4, so the Least Common Multiple is thus simply 3 x 4 = 12

So if we re-state the addition of our 2 fractions with the LCM of 12:

5 + 11
3 4

= 4 x 5 + 11 x 3
12

(Since we need to multiply the left fraction by 4/4 and the right fraction by 3/3 to get to a common denominator of 12)

= 20 + 33
12

= 53
12

The final step is to convert our answer back into a proper fraction. This is done by dividing the numerator by the

4 5
12

Which is the final answer!

You can check your workings with this, and similar fractions at this website here:

http://statsfiddle.info/Calculator/F...w2=2&n2=3&d2=4