Fraction Addition and Subtraction: Problem Type 2

Hello =)

In my previous post, we discussed how to add and subtract fractions with like denominators.  Now we will learn how to add and subtract fractions with unlike denominators, which is not difficult if you practice! Lets proceed with an example: Add 3/4 + 5/12.  First, we simply notice that we have unlike denominators, that is, our bottom numbers are different.  Second, we have to find the least common denominator of the two fractions.  That is, what number can you multiply the one denominator to to get the other denominator, or what number can you multiply to both denominators to get the least common denominator (LCD).  The easiest way to approach this is to list the first few multiples of 4 and 12 and scanning from left to right, we want the smallest multiple that both have.  So, multiples of 4 include: 4, 8, 12, 16, 20.  Multiples of 12 include: 12, 24, 36, 48, 60.  In this example, we are lucky because we have found the least common multiple, which is 12, because scanning from left to right, it is the first common multiple that both have.  So, changing both of our denominators to 12, we now have to find our numerators.  Looking at 3/4, what do we multiply 4 by to get 12? 3.  Now, since we multiplied 4 by 3 to get 12, we have to multiply our numerator, 3, by 3, which is 9.  We are done with our first fraction, and our second fraction does not need to be changed because our denominator is already 12.  So, now our problem is: 9/12 + 5/12 = 14/12. 

Let's try another example.  Subtract the following: 2/5 - 1/8.  We first notice that we have unlike denominators, so we must list the first few multiples of both 5 and 8.  Multiples of 5 include: 5, 10, 15, 20, 25, 30, 35, 40, 45, 50, ...  Multiples of 8 include: 8, 16, 24, 32, 40, 48, 56, 64, 72, ... If you notice, there is a common multiple of 40 for both.  Hint: Once you have been practicing with these problems and you cannot think of a common multiple of each of your denominators readily, then just multiple your denominators together, and use that as your least common denominator.  The only disadvantage is that you may have to simplify your answer at the end because you did not choose a smaller multiple.  Okay, now that I gave you that hint, we can proceed with our problem =).  So, our first fraction: 2/5 will change into ?/40?  We multiply 5 by 8 to get 40, so we must also multiply our numerator by 8 to get our new numerator: 16.  Now looking at our second fraction, we must multiply our denominator by 5 to get 40, so we must multiply our numerator by 5 to get our new numerator: 5.  Finally, our problem is: 16/40 - 5/40 = 11/40.

Let's do one more example.  Solve 4/15 + 7/3.  If you list your multiples of 15 and 3, you should see that your least common multiple of the two is 15.  Our first fraction stays the same because it already has a 15 for its denominator, but our second fraction must change from 7/3 to ?/15? If you guessed 35/15 you were correct!! =).  Since we had to multiply our denominator by 5 to get 15, we had to multiply our numerator, 7, by 5, which is 35. 

Remember: Whatever you have to multiply to your bottom number by to get the new denominator, you must also multiply to the top.    

For more instruction, watch these video to help you: adding fractions with unlike denominators and
subtracting fractions with unlike denominators
You can also go to this website for help with fractions: subtracting fractions

If you have any questions, do not hesitate to ask!