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## Arithmetic

### Course: Arithmetic>Unit 13

Lesson 4: Adding and subtracting fractions with unlike denominators

# Adding fractions with unlike denominators introduction

To add fractions with different denominators, such as 1/2 and 1/3, you need to find a common denominator. The least common multiple of 2 and 3 is 6, so you can rewrite the fractions as 3/6 and 2/6, respectively. This allows you to add the numerators together, resulting in a sum of 5/6.

## Want to join the conversation?

• Still so confused' i have watched it twice and thought i was getting the hang of it but i was doing it wrong. Haha i'll figure it out eventually hopefully.
• Howdy Cheyenne,

It isn't that we can't literally add two fractions with unlike denominators; if we converted the fractions to decimals then we could add them simple enough.

But since we are humans we don't really have super good calculators in our head we need a system of easily adding fractions.

So while it may not seem the easiest it is a great way to add fractions once you get skilled at it. :-)

If we have 3/4 of a cherry pie, and we would like to add that to 2/5 of another cherry pie, how could we write down that much? Well, we could go around saying that we have "3/4 + 2/5 of cherry pie", simply carrying around those pie slices together.

But... as you can tell that isn't all that elegant. It would be nice if we could represent it as one fraction.

Let's imagine that we slice up these pies into "smaller" pieces. If we do this the right way, we could create fractions of the pies with like denominators.

For an example, to give "2/5" and "3/4" a "like" denominator we could easily multiply "2/5" by 4 (numerator & denominator) and "3/4" by 5 in the same way. Remember, if we multiply the numerator & denominator by the same number the value of the fraction doesn't change. All we are doing is cutting up our PIE differently.
(3 * 5)/(4 * 5) = 15/20
(2 * 4)/(5 * 4) = 8/20
NOTE: The way I found the "like" denominator so easily is that if we have a denominator x and a different denominator y we know that both x & y can go into (x * y), or the product of y. So anytime you can't find the smallest number that both can go into, just multiply the numbers by each other!

Now since we have pies that have the same cut slices (like denominators), we can more easily add the slices together. If we have 8/20 of a PIE and 15/20 of PIE we can easily (visually) add this together to get 23/20 of a PIE. Hey, it looks like we actually have more of a PIE left over!

Hope this helps!
- Convenient Colleague
• I still understand. The way you kinda explain it is kinda confusing.
• Multiple denominator and nominator and you get your answer. Example: 5/2 + 5/4 multiple 4 2 times sense other is 2 and you get 8 and then multiple 5 together 25/8
• i have rewatched this video 7 times and i still dont understand
• 3/4 + 4/12 you have to multiply 4 by 3 to get twelve, since you multiplied by 3 on the denominator, you also have to do it to the numerator.
• this is the only video i have seen that is hard.
• same
(1 vote)
• This is sooooo confusing i watched this vid for about 30 times and I still don’t get it can someone help me (this is probably the most hardest vid I’ve ever seen so far idk how people get this)
• just try your best i keep on trying and trying until i get it im still learning ok 😁.
• I'm still so confused I watched the video 50 times
• Hello

So what Sal was trying to say is that when you get two fractions, for example, 1/4 and 1/3, you would need to add. in my opinion, it is easier to convert the fractions to denominators that are the same.
like:
|-----|-----|-----|-----| and |------|------|-----| right, so you need to find the common factor of 4 and 3 is 12 so to make 4 to 12 you would need to times that by 3 and 1/4 times three on the bottom you need to times the top as well so that would equal 3/12.
After you find the common factor between them that is 12 after you converted them into the most common factor, then you add in this case that is 4/12 + 3/12, and when you add 4 and 3, that is seven, so the answer to 1/3 and 1/4 is 7/12 (please ignore my horrible spelling and punctuation.)

Hope this helps
• How do we add 3/1592 with 54/942
• You have to find the least common denominator and make the numerators also equivalent.

--------------------------------------------------

3/4 + 4/12 you have to multiply 4 by 3 to get twelve, since you multiplied by 3 on the denominator, you also have to do it to the numerator

--------------------------------------------------

9/12 + 4/12 = 13/12 or 1 1/12

• can anybody explain for me this
(3/4)- (7/6)-(8/7)+(4/5)+(1/7)+(1/6)+(1/5)+(1/4)= I'm really stuck in the question tried to answer it several times but couldn't answer it like none of my answers are with the choices that are A.2 B.-2 C.0 D.1
• (3/4) - (7/6) - (8/7) + (4/5) + ( 1/7) + (1/6) + (1/5) + (1/4)=
= 3/4 - 7/6 - 8/7 + 4/5 + 1/7 + 1/6 + 1/5 + 1/4
Least common multiple of 4 and 6: 12
9/12 - 14/12
-5/12

= -5/12 - 8/7 + 4/5 + 1/7 + 1/6 + 1/5 + 1/4
Least common multiple of 12, 7 are: 84
35/84 - 96/84
-35 - 96/84
-131/84

= -131/84 + 4/5 + 1/7 + 1/6 + 1/5 + 1/4
Least Common Multiple of 84 and 5: 420
655/420 + 336 /420
-655 + 336/420
-319/420

= -319/420 + 1/7 + 1/6 + 1/5 + 1/4
Least Common Multiple of 420 and 7 : 420
319/420 + 60/420
-319 + 60/420
-259/420
-37/60

= -37/60 + 1/6 + 1/5 + 1/4
Least Common Multiple of 60,6: 60
-37/60 + 10/60
-37 + 10/60
-27/60
-9/20

= -9/20 + 1/5 + 1/4
Least Common Multiple of 20,5: 20
-9/20 + 4/20
-9 + 4/20
-5/20
-1/4

= -1/4 + 1/4
= 0