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## 5th grade (Eureka Math/EngageNY)

### Unit 4: Lesson 3

Topic C: Multiplication of a whole number by a fraction- Multiplying fractions by whole numbers on a number line
- Multiplying fractions and whole numbers visually
- Multiply fractions and whole numbers
- Multiplying unit fractions and whole numbers
- Multiplying fractions and whole numbers
- Multiply fractions and whole numbers visually
- Multiplying fractions word problem: movies
- Multiplying fractions word problem: milk
- Multiply fractions and whole numbers word problems
- Interpret multiplying fraction and whole number word problems

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# Multiplying fractions and whole numbers

Multiplying fractions is about combining parts of a whole. When you multiply two fractions together, you're taking a part of a part. When you multiply a fraction by a whole number, you're taking multiple copies of that fraction. In both cases, the result is a new fraction that represents a different part of a whole. Created by Sal Khan.

## Want to join the conversation?

- If you have to add a fraction by a whole number can we just add the number and not turn it into a fraction?(21 votes)
- Yes. This will create what math likes to call a 'mixed number', at least, when you're adding.

Take this example:

You order two large pepperoni pizzas for a big party you're throwing with your friends. They eat a few slices, and you're left with only two thirds for one pizza. However, the other pizza is still whole.

We can solve this problem by creating a mixed number, which is made by simply adding a whole number and a fraction together, like so: one and two thirds. You can also express it as 1 2/3 or 1+2/3.

Hope this helped.(5 votes)

- i stil dont get how 2/3 times 6 is equal to 4(7 votes)
- Whenever you have a series of mulitplications and divisons they are meant to be done left to right. In this case, 2/3 = 0.666.... repeating. 0.6666... x 6 = 3.9999....6. The reason for this number is that the 0.666 is meant to be endless. The more 6s you would add, the closer the result would be to 4.

Another way to do this, which is more precise, would be to treat the numbers as fractions, 2/3 x 6/1. In this case, 2x6 = 12, then 12/3 = 4. We cannot do 2/(3x6) because that would be the same as multiplying by 1/6, not 6/1.(9 votes)

- Im just suprised how smart u guys are(10 votes)
- What if the whole number is a one(6 votes)
- if the whole number is a one then you just cant simplify the problem anymore. For example, 1/2 x 1/1 or 1 would equal 1/2. Hope this helps!😃(5 votes)

- Is there another way to do this?(3 votes)
- The easiest way to think about multiplying fractions by whole numbers is to multiply the numerator of the fraction by your integer and then bring over the deonominator.

3/4 * 8 can be thought of as (3*8)/4, or 24/4, or 6.

1/2 * 7 is (1*7)/2, or 7/2

6/23 * 3 is(6*3)/23, or 12/23(9 votes)

- What if you're multiplying a whole number by a fraction? Is it the same approach?(5 votes)
- He is demonstrating another method of finding the fraction of the whole number he used. If 6/6 = 6 then 2/3 = 4/6. Therefore, 2/3 or 4/6 of 6 equals 4 because 4 is 2 out of every 3 in 6. Also, if 3 x 2 = 6, then 2 x 2 = 4 and 2/3 = 4 out of the whole 6(5 votes)
- I still don't understand the process because I thought of it as actually multiplying 2/3 x 6 and that completely through me off(6 votes)
- How do you simplify fraction and how do you do a fraction number line(4 votes)
- Adding 2/3 together 3 times is one way to do it. But you could also multiply 6/1 by 2/3. Right? Because 6 over 1 is six ones so its 6 wholes.(4 votes)

## Video transcript

Let's think a little
bit about what it means to multiply
2/3 times 6. One way to think about it
is to literally take six 2/3 and add them together. This is six 2/3 right over here. And if we wanted to
actually compute this, this would be equal
to-- well, we're going to take these six
2's and add them together. So we could view it
as 2 times 6 over 3. 2 times 6 over 3, which
is the same thing, of course, as 2, 4,
6, 8, 10, 12, 12/3. And what is 12/3 equal to? Well, we could rewrite
12 as-- so this is equal to-- we could rewrite 12
as 3 plus 3 plus 3 plus 3 over the yellow 3. Let me do it like
this so I don't have to keep switching colors. This is going to be
the same thing as 3/3 plus 3/3 plus 3/3 plus 3/3. And each of these are
obviously a whole. Each of these equal 1. That's 1 and that's 1, so this
is going to be equal to 4. So that's one way to
conceptualize 2/3 times 6. Another way to think
of it is as 2/3 of 6. So let's think about that. Let me draw a number line here. And I'm going to draw
the number line up to 6. So what I care about is the
section of the number line that goes to 6. So that looks pretty good. So this is 1, 2, 3, 4, 5, and 6. So if we want to
take 2/3 of 6, we can think of this whole
section of the number line between 0 and
6 as the whole. And then we want to
take 2/3 of that. So how do we do that? Well, we divide it into thirds,
to three equals sections. So that's one equal
section, two equal sections, and three equal sections. And we want two of those thirds. So we want 1/3 and 2/3. Now where does that get us? That gets us to 4. So we get, obviously,
to the same answer. We would be in a tough
situation if somehow we got two different answers. Either way, 2/3
times 6 or 6 times 2/3, either way, that is
going to be equal to 4. But there are two different
ways of viewing this. This first way is literally
viewing it as 2/3 six times. And this way is we're taking
a fraction of the number 6. We're going 2/3 of the way to
6, which would get us to 4.