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### 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 😗(17 votes)
- I doubt that you're stupid. Math can be difficult, especially when you get behind even a little. When it comes to math, everything you learn builds up on what came before and is important to the next thing you learn.

An example is learning division is important to understanding what fractions are. A fraction is just another way of showing division. Now, you might ask: "Then why do we need fractions?" Well, fractions can make other math easier because you don't have to "carry around" clunky decimal values. For instance, 1/3 is much easier to work with than 0.33333333333333333333333... (repeating forever).

I won't try to fool you and say math isn't hard, it definitely can be, and I still remember the difficulty I had in school with fractions. However, persistence will get you there, and Khan Academy is a huge gift for math. If you realize that you don't understand a topic, then you can just go back and watch more videos and practice more.

I know the last thing most people want to do is work math problems, but that's what you have to do in order to really grasp the math. Watch the videos, read the material, and do the problems until you understand. Identify what's hard for you, go back and keep working at that, then come back here and try this again. If something is still hard, then figure out what it is and go learn and practice that, too.

You just might surprise yourself.(6 votes)

- everyone have a blessed wonderful day(3 votes)
- isn't 2/3 x 4 = 2 x 4 ?(1 vote)
- i kinda understand but i there another way to do this cause it's hard to understand(0 votes)
- A simpler way to do this is by multiplying the whole number by the numerator (top or left number) of the fraction.

For example,`4 x 2/3`

:`4 x 2/3 = (4 x 2)/3 = 8/3`

(3 votes)

- is there other way to do this(1 vote)
- 9 day's ago 9x9 = 81(1 vote)
- that would be -4(4 votes)

- do we really have to learn it on a number line😒(0 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.