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## Arithmetic

### Course: Arithmetic>Unit 10

Lesson 1: Multiplying fractions and whole numbers visually

# Fraction multiplication on the number line

Sal uses number lines to help solve multiplication equations.

## 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.