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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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# Strategies for multiplying multi-digit decimals by whole numbers

Learn how to multiply decimals and whole numbers. The video presents two strategies: converting decimals to tenths and multiplying, then converting back, and using estimation to determine where the decimal should go in the answer. Both methods reinforce understanding of place value. Created by Sal Khan.

## Want to join the conversation?

- i watched every video and i still don't get it i still need help(36 votes)
- you take the decimal away and multiply.then,you put the decimal point the number of places to the left of the number by the number of places to the left of the numbers you're multiplying by. make sense?(24 votes)

- What do you do if the decimal is a number like 7475.92? That would definitely be hard to multiply, right? I really hate doing really long multi-digit multiplication problems. 😥😥😥 It takes A LOT of time to solve, and I want to use the most less time.

I know that was really long, but somehow, I got it out of me.(7 votes)- You just multiply it like you usually would. The only difference is that your adding a decimal in with your equation. Though, its important that you don't forget to add the decimal when your multiplying because that can change your answer dramatically, and sadly can mess you up on your answers. Be sure to also check your work step-by-step once your finished to make sure you didnt forget any steps or make errors. I know this is a lot of steps, but they are important so that you get these things correct. Its also not a good option to forget any of these things. Im in 7th grade and I still to this day use long digit multiplication for more subjects than just math, even science.(13 votes)

- there is an easier way to figure out how many decimal places will be in your answer. let's say you have one decimal place in the question, then the answer will have 1 decimal place b/c there's one decimal in the question.

ex.

45.3 times 6 = 271.8

this is more helpful when you have two decimals tho(7 votes)- that and you have to count total decimals in both numbers, so 45.3^.6=27.18.(7 votes)

- why do you take the hard way just move the decimal(7 votes)
- how can i divide by decimels ?(5 votes)
- decamals are kinda hard for me i still need help....(2 votes)
- https://www.khanacademy.org/math/arithmetic/x18ca194a:multiply-and-divide-decimals/x18ca194a:multiplying-decimals-and-whole-numbers/v/multiplying-decimals-and-whole-numbers-with-visuals. https://www.khanacademy.org/math/arithmetic/x18ca194a:multiply-and-divide-decimals/x18ca194a:multiplying-decimals-and-whole-numbers/v/multiplying-decimals-and-whole-numbers-with-visuals. Hope this helps.(6 votes)

- How do I know where I put the decimal? What if I think that I had only a place for a tenth, ones, tenths, and hundreths? Get what I mean?(4 votes)
- You can find out where to put the decimal with this simple example!:

0.02 X 0.3

0.02-------> 2

0.3--------> 3

2*3 =6

OG Problem: 0.02 x 0.3

Altogether there is 3 spaces to the right of the decimal point so you would start behind the 6, like so: 6. After this you would move it 3 spaces: 0.0.0.6.

<- <- <-

This answer would be .006(1 vote)

- i watched multiple video of decimals and i didn't get it until this video(2 votes)
- basically u move the decimal point back until u get a whole number. then u multiply it like normal. Once u get ur answer, move the decimal point back. (if it was 83.4 x 8, u would move the point backward so it's 834 x 8. then when u get the answer, 6,672, u would move the decimal point forward 1 place bc it was orignally in front of one number. So in conclusion, ur answer would be 667.2)(1 vote)

- I still don’t get it why would you make it a whole number, and how to put the number back in its place value(2 votes)
- I dond know vhat yur saying beta(1 vote)

## Video transcript

- [Instructor] So in this
video, we're gonna try to think of ways to compute
what 31.2 times 19 is. And there's multiple
ways to approach this, but like always, try to pause this video and see if you can work
through this on your own. All right, now let's do this together. Now one way to think about this is you could view 31.2 as a
certain number of tenths. And how many tenths would this be? Well, you could view
this, 31.2, as 312 tenths. And so, this is the same
thing as 312 tenths times 19. And so, what we could do
is we could figure out what is 312 of something times
19, or what's 312 times 19. It's gonna be that many tenths, and then we could convert
it back to a decimal. I'll also show another strategy,
but let's just do that. So if we were to just
multiply 312 times 19, times 19, this is going to be, let's see, two, obviously, another color. Two times nine is 18. One times nine is nine. Plus one is 10. Three times nine is 27, plus one is 28. If what I just did looks unfamiliar, we have videos that explain
how this process works. And then, we go to the tens
place, right over here. And so, we'd say one times two is two. One times one is one. One times is three is three. And then we add everything together. We get eight. Zero plus two is two. Eight plus one is nine. Two plus three is five. So we get five, nine, two, eight, or 5928. Now that's not going
to be the answer here. The answer is going to be 5928 tenths. So this is going to be
equal to 5928 tenths. Now, how can we express this as a decimal? Well, we could think of it this way. If that's the decimal,
this is the tenths place, this is the ones place, which is the same, this is the same thing as 10 tenths place, which is the ones place. This is the tens place, and
this is the hundreds place. Well, you have eight tenths. We could put that in the tenths place. You have these 20 tenths. That's the same thing as two ones. You have the 900 tenths. Do that in a different color. 900 tenths is the same thing as nine tens. And then, your 5000 tenths is the same thing as five hundreds. Another way to think about it is we wrote all the places out, and we wrote it in terms of tenths. So the eight went there,
and then every place to the left of that went to
the place to the left of that. So this is going to be
592 and eight tenths. So we could write it like that. 592 and eight tenths. Now another way to approach this is to just think about the digits, not the actual numbers, to figure out, well, the answer will
have what digits in it. And then try to estimate to think about where the decimal place should go. So, for example, you
could do 312 times 19. So since you remove the
decimal, do the computation, and say, okay, the answer
should have the digits five, nine, two, eight in that order. Now where should I put the decimal in order for that to
be a reasonable answer? And that's where estimation comes in. You could say, hey, 31.2 times 19, that's going to be approximately equal to, in fact, if I were to estimate these with numbers that are easy to multiply, that's going to be roughly equal to 30 times 20, which is equal to 600. So that tells me that my product here should be roughly equal to 600. And so where would I put the decimal here for it to be roughly equal to 600? So I know the answer has the
digits five, nine, two, eight. Where do I put a decimal for
it to be roughly equal to 600? Well, if I were to put the decimal there, that's not roughly equal to 600. If I were to put the decimal there, that's not roughly equal to 600. That's close to 60. If I put the decimal
there, that's close to six. If I wanna be close to 600, I'd have to put the decimal right over there. And so that's also a good way to test the reasonableness of what's going on. This should be roughly equal to 600, if we were to estimate it. And so, we like that our process got an answer that is
roughly equal to 600.