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### Course: Arithmetic > Unit 9

Lesson 4: Adding and subtracting fractions with like denominators# 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?(201 votes)
- 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.(64 votes)

- Why do the denominators have to be the same?(10 votes)
- 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.(30 votes)

- Why don't you add the denominator?(0 votes)
- 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!(6 votes)

- at0:17, 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?(63 votes)
- 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!(35 votes)

- 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.

Please help :)(8 votes)- 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?(24 votes)

- What if your sum goes over the denominator? Say, 7/14 + 9/14. How do you deal with that?(11 votes)
- 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.(7 votes)

- Does GCF mean greatest common factor ?(5 votes)
- Yes that is what it stands for(6 votes)

- How and why does this work ?(5 votes)
- The top number represents the amount you have, and the bottom number represents the total needed to form a whole item. so if you have 4 slices of pizza on one plate and another 4 slices of pizza on another plate, and 8 slices form a whole pizza, you now know the denominator is 8, because that is the amount you need to make a whole pizza. Now, if you take the numerator (The actual amount) and add it, you aren't changing how many slices you need to make a pizza, but how many you actually have. When you put all slices together on a plate, you have a whole, or 8/8 pizza.(6 votes)

- Why do you divide the fraction by 5 though?(3 votes)
- To help you: Example;

4/8 ,to simplify this we have to divide it by 4 and you got this: 1/2 we need to divide to 4 because if you divide with another numbers like 3 you got residue. (Please I need more than 25 Upvotes)(7 votes)

- at0:17, 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?(3 votes)

## Video transcript

So we're asked to add 3/15 plus
7/15, and then simplify the answer. So just the process when you
add fractions is if they already-- well, first of all, if
they're not mixed numbers, and neither of these are, and
if they have the same denominator. In this example, the
denominators are already the same. The denominator is 15. So if you add these two
fractions, your sum is going to have the same denominator,
15, and your numerator is just going to be the sum of the
numerator, so it's going to be 3 plus 7, or it's going
to be equal to 10/15. Now, if we wanted to simplify
this, we'd look for the greatest common factor in both
the 10 and the 15, and as far as I can tell, 5 is the largest
number that goes into both of them. So divide the 10 by 5 and you
divide the 15 by 5, and you get-- 10 divided by 5 is 2
and 15 divided by 5 is 3. You get 2/3. Now, to understand why this
works, let's draw it out. Let's split something
up into 15 sections. So let me split it up
into 15 sections. Let me see how well
I can do this. Well, actually, even a better
way, an easier way might be to draw circles. So let me do the 15 sections. So let me draw. So that is one section
right over there. That is one section and then if
I copy and paste it, that is a second section, and then
a third section, fourth section, and then we have
a fifth section. Let me copy and paste
this whole thing. So that's five sections
right there. Let me copy and then
paste that. So that is 10 sections,
and then let me do it one more time. So that is 15 sections. So you can imagine this whole
thing is like a candy bar or something, and we have now split
it up into 15 sections. Now, what is 3/15? Well, it's going to be
3 of the 15 sections. So 3/15 is going to be one,
two, three: 3/15. Now, to that, were adding
7 of the 1/15 sections, or 7 of the sections. So we're adding 7
of those to it. So that's one, two, three,
four, five, six, seven. And you see now, if you take the
orange and the blue, you get one, two, three, four, five,
six, seven, eight, nine, ten of the sections, or
10 of the 15 sections. And then to see why this is the
same thing as 2/3, you can just split this candy bar into
thirds, so each third would have five sections in it. So let's do that. One, two, three, four, five,
so that is 1/3 right there. One, two, three, four,
five, that is another third right there. And notice, when you do it like
this, we have filled out exactly two-- one, two--
of the thirds. This is the third third, but
that's not filled in. So 10/15 is the same
thing as 2/3.