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### Course: 5th grade (Eureka Math/EngageNY) > Unit 1

Lesson 5: Topic E: Multiplying decimals- Estimating with multiplying decimals and whole numbers
- Estimating with multiplying decimals and whole numbers
- Strategies for multiplying decimals and whole numbers
- Multiply whole numbers by 0.1 and 0.01
- Multiplying decimals and whole numbers with visuals
- Multiply decimals and whole numbers visually
- Strategies for multiplying multi-digit decimals by whole numbers
- Multiply whole numbers and decimals
- Estimating decimal multiplication
- Estimating with multiplying decimals
- Represent decimal multiplication with grids and area models
- Understanding decimal multiplication
- Multiplying decimals using estimation
- Understand multiplying decimals
- Developing strategies for multiplying decimals
- Multiply decimals tenths
- Multiplying decimals (no standard algorithm)
- Multiply decimals (up to 4-digit factors)

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# Multiplying decimals and whole numbers with visuals

Multiplying whole numbers and decimals can be fun. It starts with simple examples, such as multiplying 3/10 by 4, and then moves on to more complex examples, such as multiplying 52/100 by 3. In each case, we demonstrate how to use a number line or model to visualize the process and find the product. Created by Sal Khan.

## Want to join the conversation?

- the dude is awesome(40 votes)
- cap such a lie(0 votes)

- i don't get it or any math for that matter but i'm trying as hard as i pssibly can(25 votes)
- and also couldn't you just do a fraction problem?

ok so say we have 52 hundredths right? we put a 1 under the 3 as 3 over 1 to make it a fraction.

then we do 52/100 *3/1

the answer is 156 over 100 or 156/100.

then divide. 156 divided by 100 is 1.56! 52*3 is 156!

so couldn't you just do a a fraction problem to make it easier?

I just do those to make it easy :D(7 votes)- Good thinking. Yes, that is possible. Yet we are basically doing the same thing as decimal multiplication with the same number of steps as fraction multiplication. Actually, there are fewer steps as you have to convert it to a fraction (Though this step is very quick and easy to do in your head.) Both ways are perfectly fine and will always give you the same answer with no significant difference in difficulty or speed.(3 votes)

- i love number lines!!

they make math easier to understand, especially when first learning something.(8 votes)- I hate number lines they are so annoying i have to use them in math class for no reason(3 votes)

- can't you just do 3x4 and then just move the decimal to the left in your answer and the same with 3x0.2 just do 3x2 and move the decimal to the left in your answer and it would make it easier or would be harder or the same.(4 votes)
- how would this apply to like say, 0.05 X 70?(1 vote)
- Hi,

Well, like shown in the video:

0.05 x 70:

5 x 70 = 350

Then, add up the number of place values after the decimal point, which is in this case 2.

3.50

You can ignore all the zeroes after a nonzero digit (after the decimal point, that is).

0.05 x 70 = 3.5(7 votes)

- how do i do dividing demials . Do you do that(2 votes)
- Hi million 4577! To divide decimals, you have to set it up just like regular division. Once you have that set up, you have to make sure both the divisor and dividend are both whole numbers. To get the dividend to a whole number, you have to move the decimal point up. So, however many places to the left it was in your dividend, you will have it that many places left in your answer. Then, you just have to divided normally. If you had 12.3 divided by 3, you would move up the decimal point and then divide to get 4.1. It would be 41 if this was normal division, but since we moved the decimal point up, it's 4.1. Hope this helps. Have a great day! 😄(4 votes)

- Are there variables such as x or y in decimals?(1 vote)
- thanks this is very usefull for me because i used to struggle with this but now i just fly right through this(1 vote)
- what would be a fast way?(1 vote)

## Video transcript

- [Instructor] So what we
have here on this number line that we've now marked off with the tenths and you can see that this
is three tenths here. We can think about this as a
multiplication of a decimal. And so what is this representing? And I'll give you a hint. It's representing something
times three tenths. So pause the video and
try to think about that. Well, let's see. We are going one times three tenths, two times three tenths,
three times three tenths, and then four times three tenths. So what's represented here
is four times three tenths, and so what is this going to be equal to? Well you can see you go from three tenths, to six tenths, to nine tenths, and then you could view
this as twelve tenths, but twelve tenths is the same thing as one, one and two tenths. So you could view this as 1.2. One and two tenths. Let's do another example. No, actually I'll do it
on the same number line. If we wanted to represent three times 0.2 What would that look
like on this number line? And what would this be equal to? So I'll put a little equal sign here. Pause this video and see
if you an figure that out. All right, so let's think
about where two tenths is this is one tenth, two
tenths is right over there. This is 0.2, and we're gonna
multiply it times three. So, we're gonna multiply it times one, then we're gonna multiply it times two, that takes us to four tenths and then we're gonna
multiply it times three to get us to six tenths, 0.6. So it's six tenths just like that. Now you could also visualize two tenths as parts of a whole. So for example, this
represents two tenths. I have this whole, this square is a whole it's split into ten equal columns here and we have two of them filled in. So this represents two tenths. So if you have three times two tenths, Well this is one times two tenths, this is two times two tenths, and this is three times two tenths. And so how many tenths do we now have? Well we have one, two, three,
four, five, six tenths. Which is exactly what we
have here, six tenths. Let's do one more example, that gets a little bit more involved. So here we're told to multiply. It says you many use the models shown to help find the product. And this is a screen
shot from the exercise on Khan Academy. So pause this video and see if you can
figure out what this is. All right, so they're saying 52 hundredths times three, and they have 52 hundredths depicted right over here and then they have it
depicted three times. So the total number of
hundredths depicted here that is 52 hundredths times three, because we have 52 hundredths here, another 52 hundredths, and
then another 52 hundredths. So how many hundredths
is that going to be? Well, you could view
this as 52 times three and that will give you the
number of hundredths we have. So let's think about this. So if we were to just say 52 times three, well this is going to be two times three is equal to six and then
five tens times three is 15 tens, which is the same thing. We either just write it as 15 tens, or that's 100 and five tens. But either way if I have 52 of something and I multiply that by three, I now have 156 of that something. And here the something is hundredths. So if I say 52 hundredths times three that's going to be 156 hundredths. And how do we represent 156 hundredths. Well there is a couple
of ways to think about it if this is the ones place,
this is the tenths place, this is the hundredths place. Well we would write the
six there, the five there, and the one there. So you could recognize this as hey look, a hundred hundredths,
let me color code it, a hundred hundredths is
the same thing as a whole and I'll circle that in
red, and fifty hundredths is the same thing as five tenths, and of course six
hundredths is the same thing as six hundredths. So this is going to be equal to 1.56, or you could view this as 156 hundredths, or you could view this as a whole, which is a hundred
hundredths, and five tenths, which is fifty hundredths,
and six hundredths.