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### Course: Class 6 (Old)>Unit 5

Lesson 5: Adding or subtracting like fractions

# Adding fractions with like denominators

Sal adds 3/15+7/15. Created by Sal Khan and Monterey Institute for Technology and Education.

## Want to join the conversation?

• Does GCD mean greatest common divider. If so than how is it any different from LCM?
• Yes, GCD means Greatest Common Divisor. Another way to think of it is the Greatest Common Factor. When comparing 2 or more numbers, the GCD/GCF is the LARGEST (i.e. greatest) factor that they both share. For example, 12 and 16. The factors of 12 are 1, 2, 3, 4, 6, 12 and the factors of 16 are 1, 2, 4, 8, 16. If you look at both lists, you'll notice that both share the numbers 1, 2 and 4 but the largest of these shared COMMON factors is 4 so the GCD or GCF is 4. You'll notice that this is smaller than both 12 and 16.

LCM is the Lowest/Least Common Multiple. MULTIPLES on the other hand are larger or equal to the numbers you are comparing. Take 3 and 8. The multiples of 3 is just the 3 times table (3, 6, 9, 12, etc.) and the multiples of 8 are the 8 times table (8, 16, 24, 32, and so on). If you continued each table you would eventually find that each table shares some numbers. The SMALLEST (i.e. least/lowest) of these that are shared is the LCM. In this case, continuing 3's multiples: 15, 18, 21, 24, 27... etc. You can see that 8 and 3 can both multiply to 24. So the LCM is 24. Using the previous example of 12 and 16, the LCM is 48 since 12 x 4 = 48 and 16 x 3 = 48.
• Why do the denominators have to be the same?
• The denominators have to be the same so you can add the numerators together without worrying about the denominators being different sizes, because that affects the value of the fraction.

It's like trying to count the number of pieces you can get out of different cakes. If the cakes are different sizes, it wouldn't be fair because some people would get larger pieces than others. By making cakes that are the same size and then counting the number of pieces, you can be sure that everyone is getting a fair amount of cake.

In order to add fractions correctly, the "cakes" need to be the same size, which is why the denominators (bottom numbers in the fractions you are adding) need to be the same value.
• Why don't you add the denominator?
• If you added the denominators, the whole answer would not make sense. If you added 1/2+1/2 and got 2/4, that is wrong, because two halves equal a whole, but 2/4 is just another fraction equivalent to 1/2. In fraction adding, you are just adding the parts (numerators), not the the amount of all the pieces (denominators). Think about it this way:
You have 3 of the 5 pieces left of pumpkin pie and 4 of the 5 pieces of apple pie, and you want to add them. You add 3+4 and get 7 pieces. Now you have 7/5 of a pie. This is because only five pieces fit in a pie and you have 7 pieces of pie left.
Hope this helps!
• at , Sal said that if the denominator is the same, you just add the numerator and then the denominator stays the same? I just dont get it. Is it the same on the problems without the same denominators?
• If the denominators are different, then the formula will not be the same. Let's say you have this problem:
1/3 + 1/3.
The denominators are the same, so they will not change. You simply add the numerators and keep the denominator.
1/3 + 1/3 = 2/3

However, if you have this problem:
1/2+1/4
You have to make the denominators the same. A way to do this is to divide the larger denominator by the smaller denominator to find the GCD (Greatest Common Divisor):
4÷2=2
Then multiply the numerator and denominator of 1/2 by 2 (our GCD):
1 x 2 = 2
2 x 2 = 4
The denominators are now the same, so let's add:
2/4 + 1/4 = 3/4
So:
1/2 + 1/4 = 3/4!
I hope this helped!
• What if i have 6/10 - 8/10 how do I solve that? Because the number is smaller than the other and I dont have a mixed fraction to borrow from.

• You just end up with a negative fraction. Just like `6-8` would end up negative, `6/10 - 8/10` would end up negative as well. Your answer would be a negative 2 tenths, or `-2/10` or simplified `-1/5`. Does that make sense?
• What if your sum goes over the denominator? Say, 7/14 + 9/14. How do you deal with that?
• you still add the numerator together. Like 16/14.But this will become an improper fraction, the actual answer is 1 2/14. A mixed fraction.
• Does GCF mean greatest common factor ?
• Yes that is what it stands for
• How and why does this work ?