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## MAP Recommended Practice

### Course: MAP Recommended Practice > Unit 34

Lesson 17: Adding and subtracting fractions with unlike denominators word problems# Adding fractions word problem: paint

CCSS.Math:

Sal solves a word problem by adding mixed numbers with unlike denominators. Created by Sal Khan.

## Want to join the conversation?

- 2:50you are confusing me about splitting the bar graph(11 votes)
- Splitting the bar graph really isn't at all confusing.It means that you divide something into fractions so you can understand better.The best object to use is a bar graph.Sal divided the first two into different fractions.Then, when you converted the two into fractions with same denominators,you add them together.When you add it,you get the answer,which Sal demonstrated in the third bar graph. So it is not confusing at all.Thanks for reading this reply!(6 votes)

- I am confused Sal said "Cindy and Michael need 1 gallon of orange paint for the giant cardboard pumpkin they are making for Halloween. Cindy has 2/5 of a gallon of red paint. Michael has got 1/2 a gallon of yellow paint. If they mix their paints together, will they have the 1 gallon they need? So let's think about that. We're going to add the 2/5 of a gallon of red paint, and we're going to add that to 1/2 a gallon of yellow paint. And we want to see if this gets to being 1 whole gallon. So whenever we add fractions, right over here we're not adding the same thing. Here we're adding 2/5. Here we're adding 1/2. So in order to be able to add these two things, we need to get to a common denominator. And the common denominator, or the best common denominator to use, is the number that is the smallest multiple of both 5 and 2. And since 5 and 2 are both prime numbers, the smallest number's just going to be their product. 10 is the smallest number that we can think of that is divisible by both 5 and 2. So let's rewrite each of these fractions with 10 as the denominator. So 2/5 is going to be something over 10, and 1/2 is going to be something over 10. And to help us visualize this, let me draw a grid. Let me draw a grid with tenths in it. So, that's that, and that's that right over here. So each of these are in tenths. These are 10 equal segments this bar is divided into. So let's try to visualize what 2/5 looks like on this bar. Well, right now it's divided into tenths. If we were to divide this bar into fifths, then we're going to have-- actually, let me do it in that same color. So it's going to be, this is 1 division, 2, 3, 4. So notice if you go between the red marks, these are each a fifth of the bar. And we have two of them, so we're going to go 1 and 2. This right over here, this part of the bar, represents 2/5 of it. Now let's do the same thing for 1/2. So let's divide this bar exactly in half. So, let me do that. I'm going to divide it exactly in half. And 1/2 literally represents 1 of the 2 equal sections. So this is one 1/2. Now, to go from fifths to tenths, you're essentially taking each of the equal sections and you're multiplying by 2. You had 5 equals sections. You split each of those into 2, so you have twice as many. You now have 10 equal sections. So those 2 sections that were shaded in, well, you are going to multiply by 2 the same way. Those 2 are going to turn into 4/10. And you see it right over here when we shaded it initially. If you Look at the tenths, you have 1/10, 2/10, 3/10, and 4/10. Let's do the same logic over here. If you have 2 halves and you want to make them into 10 tenths, you have to take each of the halves and split them into 5 sections. You're going to have 5 times as many sections. So to go from 2 to 10, we multiply by 5. So, similarly, that one shaded-in section in yellow, that 1/2 is going to turn into 5/10. So we're going to multiply by 5. Another way to think about it. Whatever we did to the denominator, we had to do the numerator. Otherwise, somehow we're changing the value of the fraction. So, 1 times 5 is going to get you to 5. And you see that over here when we shaded it in, that 1/2, if you look at the tenths, is equal to 1, 2, 3, 4, 5 tenths. And now we are ready to add. Now we are ready to add these two things. 4/10 plus 5/10, well, this is going to be equal to a certain number of tenths. It's going to be equal to a certain number of tenths. It's going to be equal to 4 plus 5 tenths. And we can once again visualize that. Let me draw our grid again. So 4 plus 5/10, I'll do it actually on top of the paint can right over here. So let me color in 4/10. So 1, 2, 3, 4. And then let me color in the 5/10. And notice that was exactly the 4/10 here, which is exactly the 2/5. Let me color in the 5/10-- 1, 2, 3, 4, and 5. And so how many total tenths do we have? We have a total of 1, 2, 3, 4, 5, 6, 7, 8, 9. 9 of the tenths are now shaded in. We had 9/10 of a gallon of paint. So now to answer their question, will they have the gallon they need? No, they have less than a whole. A gallon would be 10 tenths. They only have 9 tenths. So no, they do not have enough of a gallon. Now, another way you could have thought about this, you could have said, hey, look, 2/5 is less than 1/2, and you could even visualize that right over here. So if I have something less than 1/2 plus 1/2, I'm not going to get a whole. So either way you could think about it, but this way at least we can think it through with actually adding the fractions."(10 votes)
- Okay so I'm not tryna be rude or anything like that, but I just have to say... what you said was pretty rude and also really unnecessary. Buuuuut for some unknown reason you posted it anyway so now I'm going to answer your mean questions:

First of all the videos are long because Sal has to teach things. I'd like to see you try and squish lots of stuff about subtracting fractions into a two-minute video. The videos are to help people learn, and sometimes that can take a while, but it's worth it to share knowledge.

Second: Sal doesn't teach shortcuts because they're kind of a lazy way to get through math questions. He teaches structured ways that can help you in many problems instead of just having you remember an algorithm. It's better to actually apply yourself than just remember a shortcut.

I hope you take what I said to heart because I really did spend a lot of time answering your questions when they really weren't very good questions at all and were quite petty and rude to Sal. In future, it would be appreciated if you please didn't use this chat page -- which is meant to ask people for help with math -- to complain. Thank you and enjoy your day.(7 votes)- you are nice (:(3 votes)

- thank u for helping me i think ima get a 100(7 votes)
- question when looking for a common denominator

must it be the lowest you can find or can it be just any?(1 vote)- A common denominator cannot be "any" number, because it has to fit both fractions. However, it can be "any" fitting number. The reason you want it to be a smaller number is that it makes adding and simplifying easier. (see simplifying fractions) I hope this helped!(11 votes)

- This is the absolute worst example of how to do fractions. The shortest solution is

Step 1: to a get common denominator multiply the two bottom numbers together.

Step 2: Cross multiply the two ORIGINAL numbers to get 4/10 + 5/10(5 votes) - ok so i dont know how to divide

and im really bad at math(2 votes)- just practice!(6 votes)

- guys thumbs up on this comment let's see the most thumbs ups I could get(4 votes)
- u going to fast slow down(3 votes)

## Video transcript

Cindy and Michael need
1 gallon of orange paint for the giant cardboard pumpkin
they are making for Halloween. Cindy has 2/5 of a
gallon of red paint. Michael has got 1/2 a
gallon of yellow paint. If they mix their
paints together, will they have the
1 gallon they need? So let's think about that. We're going to add the 2/5
of a gallon of red paint, and we're going to add that to
1/2 a gallon of yellow paint. And we want to see if this
gets to being 1 whole gallon. So whenever we add
fractions, right over here we're not adding the same thing. Here we're adding 2/5. Here we're adding 1/2. So in order to be able
to add these two things, we need to get to a
common denominator. And the common denominator,
or the best common denominator to use, is the number that is
the smallest multiple of both 5 and 2. And since 5 and 2 are
both prime numbers, the smallest number's just
going to be their product. 10 is the smallest
number that we can think of that is
divisible by both 5 and 2. So let's rewrite each of
these fractions with 10 as the denominator. So 2/5 is going to
be something over 10, and 1/2 is going to
be something over 10. And to help us visualize
this, let me draw a grid. Let me draw a grid
with tenths in it. So, that's that, and that's
that right over here. So each of these are in tenths. These are 10 equal segments
this bar is divided into. So let's try to visualize what
2/5 looks like on this bar. Well, right now it's
divided into tenths. If we were to divide
this bar into fifths, then we're going
to have-- actually, let me do it in that same color. So it's going to be, this
is 1 division, 2, 3, 4. So notice if you go
between the red marks, these are each a
fifth of the bar. And we have two of them, so
we're going to go 1 and 2. This right over here,
this part of the bar, represents 2/5 of it. Now let's do the
same thing for 1/2. So let's divide this
bar exactly in half. So, let me do that. I'm going to divide
it exactly in half. And 1/2 literally represents
1 of the 2 equal sections. So this is one 1/2. Now, to go from
fifths to tenths, you're essentially taking
each of the equal sections and you're multiplying by 2. You had 5 equals sections. You split each of those into
2, so you have twice as many. You now have 10 equal sections. So those 2 sections
that were shaded in, well, you are going to
multiply by 2 the same way. Those 2 are going
to turn into 4/10. And you see it right over here
when we shaded it initially. If you Look at the
tenths, you have 1/10, 2/10, 3/10, and 4/10. Let's do the same
logic over here. If you have 2
halves and you want to make them into 10 tenths, you
have to take each of the halves and split them into 5 sections. You're going to have 5
times as many sections. So to go from 2 to
10, we multiply by 5. So, similarly, that
one shaded-in section in yellow, that 1/2 is
going to turn into 5/10. So we're going to multiply by 5. Another way to think about it. Whatever we did to
the denominator, we had to do the numerator. Otherwise, somehow
we're changing the value of the fraction. So, 1 times 5 is
going to get you to 5. And you see that over
here when we shaded it in, that 1/2, if you
look at the tenths, is equal to 1, 2,
3, 4, 5 tenths. And now we are ready to add. Now we are ready to
add these two things. 4/10 plus 5/10,
well, this is going to be equal to a certain
number of tenths. It's going to be equal to
a certain number of tenths. It's going to be equal
to 4 plus 5 tenths. And we can once
again visualize that. Let me draw our grid again. So 4 plus 5/10,
I'll do it actually on top of the paint
can right over here. So let me color in 4/10. So 1, 2, 3, 4. And then let me
color in the 5/10. And notice that was
exactly the 4/10 here, which is exactly the 2/5. Let me color in the
5/10-- 1, 2, 3, 4, and 5. And so how many total
tenths do we have? We have a total of 1,
2, 3, 4, 5, 6, 7, 8, 9. 9 of the tenths
are now shaded in. We had 9/10 of a
gallon of paint. So now to answer their
question, will they have the gallon they need? No, they have less than a whole. A gallon would be 10 tenths. They only have 9 tenths. So no, they do not have
enough of a gallon. Now, another way you could
have thought about this, you could have said, hey,
look, 2/5 is less than 1/2, and you could even visualize
that right over here. So if I have something
less than 1/2 plus 1/2, I'm not going to get a whole. So either way you could think
about it, but this way at least we can think it through with
actually adding the fractions.