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## 4th grade

### Course: 4th grade > Unit 9

Lesson 1: Multiplying fractions and whole numbers visually# Multiplying fractions and whole numbers visually

Learn the concept of multiplying fractions and whole numbers. Watch how to visually represent this process and practice understanding the relationship between fractions and whole numbers in multiplication. Created by Sal Khan.

## Want to join the conversation?

- I'm just wanting to confirm and understand why:

2/5 = 2 x 1/5

and why isn't it like before with mixed numerals where this is done:

2 x 1/5 = ((2 x 5)+1)/5 = 11/5 ?

is there a conceptual difference i am missing? thanks in advance !! :)(56 votes)- Yes there's a conceptual difference.

I believe you are confusing multiplication of a whole number and a fraction, with addition of a whole number and a fraction. Many students have difficulty in math, including higher levels such as algebra, ultimately because they confuse the fundamental concepts of addition and multiplication.

((2 x 5)+1)/5 is equivalent to the mixed number 2 and 1/5. This mixed number means 2 + 1/5, not 2 x 1/5.

2 x 1/5 can be thought of as the repeated addition 1/5 + 1/5, which is clearly 2/5.(59 votes)

- Sal explained it in a simple way, but it is confusing for me. I am here to know whether to do reciprocal in the multiplication of fractions. Can someone pls clarify my question?(22 votes)
- You do not have to use reciprocals when multiplying fractions, only when dividing.(6 votes)

- pls upvote. I am in gr 5 an i really want a badge(21 votes)
- If you promise you will let me eat all your (hologram) blueberries, then I will upvote. Also, the badge works only as an answer.(2 votes)

- *
*why can't we just add it the normal way.like 1/5+3/4=4/9**(14 votes)- You cant just add the denominators as well as adding the numerators, you need to find a common factor.(10 votes)

- 3 X 2/5= (Can be written as) 3/1 X 2/5 = 3x2 and 5x1 That equals : 6 fifths or 6/5

Am i right? I'm sorry if you dint understand.. I am only in grade five(9 votes)- Yes, I believe that your calculations are correct. 6/5 can also be written as 1 1/5.(6 votes)

- good luck everyone [:(10 votes)
- How do you multiply by 1000000(3 votes)
- Any time you're multiplying by a number that is a 1 followed by some number of 0's, you can simply add on that amount of 0's. If I were to multiply 37 by 10, my answer would be 370. Multiplying 42 by 100 results in 4200. Multiplying 13 by 1 million (1000000) results in 13 million (13000000)(14 votes)

- pls upvote. I am in gr 5 an i really want a badge(10 votes)
- Im bored don't uo vote me(9 votes)

## Video transcript

We've already seen that the
fraction 2/5, or fractions like the fraction 2/5, can
be literally represented as 2 times 1/5, which
is the same thing, which is equal to literally
having two 1/5s. So 1/5 plus 1/5. And if we wanted
to visualize it, let me make a hole
here and divide it into five equal sections. And so this represents
two of those fifths. This is the first of the
fifths, and then this is the second of the fifths,
Literally 2/5, 2/5, 2/5. Now let's think about something
a little bit more interesting. What would 3 times
2/5 represent? 3 times 2/5. And I encourage you
to pause this video and, based on what
we just did here, think about what you think
this would be equivalent to. Well, we just saw that 2/5
would be the same thing as-- so let me just
rewrite this as instead of 3 times 2/5
written like this, let me write 2/5
like that-- so this is the same thing as
3 times 2 times 1/5. And multiplication, we can
multiply the 2 times the 1/5 first and then
multiply by the 3, or we can multiply the 3
times the 2 first and then multiply by the 1/5. So you could view this literally
as being equal to 3 times 2 is, of course, 6, so this is
the same thing as 6 times 1/5. And if we were to try
to visualize that again, so that's a whole. That's another whole. Each of those wholes
have been divided into five equal sections. And so we're going to
color in six of them. So that's the first 1/5, second
1/5, third 1/5, fourth 1/5, fifth 1/5-- and that
gets us to a whole-- and then we have
6/5 just like that. So literally 3 times 2/5
can be viewed as 6/5. And of course, 6
times 1/5, or 6/5, can be written as--
so this is equal to, literally-- let me do the
same color-- 6/5, 6 over 5. Now you might have said, well,
what if we, instead of viewing 2/5 as this, as we just
did in this example, we view 2/5 as 1/5 plus
1/5, what would happen then? Well, let's try it out. So 3 times 2/5-- I'll rewrite
it-- 3 times 2/5, 2 over 5, is the same thing as
3 times 1/5 plus 1/5. 2/5 is the same thing
as 1/5 plus 1/5. So 3 times 1/5 plus
1/5 which would be equal to-- well, I just
have to have literally three of these added together. So it's going to be
1/5 plus 1/5 plus 1/5 plus 1/5 plus-- I think
you get the idea here-- plus 1/5 plus 1/5. Well, what's this going to be? Well, we literally
have 6/5 here. We can ignore the parentheses
and just add all of these together. We, once again, have
1, 2, 3, 4, 5, 6/5. So once again, this
is equal to 6/5. So hopefully this
shows that when you multiply-- The 2/5 we saw
already represents two 1/5s. We already saw that,
or 2 times 1/5. And 3 times 2/5 is literally
the same thing as 3 times 2 times 1/5. In this case, that would be 6/5.