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## 4th grade

### Course: 4th grade > Unit 9

Lesson 1: Multiplying fractions and whole numbers visually# Fraction multiplication on the number line

Sal uses number lines to help solve multiplication equations.

## Want to join the conversation?

- I only understand this a little bit not alot but a little bit 😗(14 votes)
- can you just like do 1 2/3?(4 votes)

- this was so helpful thanks so much sal(7 votes)
- dont worry, its not yr fault. it will just get put into tips and thanks(2 votes)

- What is 2x2.I just put a queations so I can sat hi(3 votes)
- I need you to solve this what is 10x10? I know the answer!(7 votes)

- that would be -4(4 votes)

- i kinda understand but i there another way to do this cause it's hard to understand(4 votes)
- thanks this helped me can you do more but regrouping cause i only a little bit know it if you can thanks!(3 votes)
- I know all this but my dad is making me do it(3 votes)
- I do"not understand at all(2 votes)
- The second part is another problem that is different from the top one, am I right? It's a bit confusing as Sal suddenly changed to another number line and I'm not sure...(2 votes)

## Video transcript

- [Instructor] So, what
we're gonna think about in this video is multiplying fractions. So, let's say that we wanted to take 2/3 and we want to multiply it by four, what is this going to be equal to? Pause this video and try to
think about it on your own. Alright, now let's work
through this together. And, to help us, I will use a number line, and let's say that each
of these hash marks represent a third. So, this is zero, this is 1/3, 2/3, 3/3, 4/3, 5/3, 6/3, 7/3, 8/3, and 9/3, and so
where is 2/3 times one? Well, 2/3 times one is
just going to be 2/3, we just take a jump of
2/3, so that is times 1. If we multiply by, or if
we take 2/3 times two, that'll be two jumps, so one 2/3, two 2/3, three
2/3, and then four 2/3. So, we just took four jumps of 2/3 each. You could view that as 2/3
plus 2/3 plus 2/3 plus 2/3, and where does that get us to? It got us to 8/3. So, notice, 2/3 times
four is equal to 8/3. Now, we could go the other way, we could look at a number line and think about what are ways to represent what the number line is showing us? And, on Khan Academy, we
have some example problems that do it that way, so I thought it would be good
to do an example like that. And, so, let's label this number line a little bit different. Instead of each of these
lines representing a third, let's say they represent a half, so zero, 1/2, 2/2, 3/2, 4/2, 5/2, why did I write 5/6, my
brain is going ahead, 5/2, 6/2, 7/2, 8/2, and 9/2. And, let's say we were to
see something like this. So, if you were to just
see this representation, so I'm going to try to draw it like this, so if you were to just
see this representation, what is that trying to represent? What type of multiplication
is that trying to represent? Well, you could view that
as 3/2 plus another 3/2 plus another 3/2, 'cause, notice, each of these jumps are three 1/2, or 3/2. So, you could view this
as 3/2 plus 3/2 plus 3/2, or another way of thinking about it is this is three jumps of 3/2. So, you can also view this
as doing the same thing as three times 3/2, and
what are these equal to? Well, 3/2 plus 3/2 plus
3/2, or three times 3/2, it gets you to 9/2.