Main content

## 5th grade

### Course: 5th grade > Unit 8

Lesson 2: Multiplying decimals strategies- Estimating decimal multiplication
- Estimating with multiplying decimals
- Developing strategies for multiplying decimals
- Decimal multiplication with grids
- Represent decimal multiplication with grids and area models
- Understanding decimal multiplication
- Multiplying decimals using estimation
- Understand multiplying decimals

© 2023 Khan AcademyTerms of usePrivacy PolicyCookie Notice

# Decimal multiplication with grids

Learn how to use a hundred grid to represent decimal multiplication. Use both vertical and horizontal tenths to represent each multiplier and then use the overlapping areas to find the product. Created by Sal Khan.

## Want to join the conversation?

- The correct answer was A, 0.21 = 0.3 x 0.7 and not 0.21 = 0.03 x 0.07.(3 votes)
- sal it would be A because 7 tenths = 0.7 + 3 tenths = 0.3 so 0.7 + 0.3 = 0.21(3 votes)
- So we're told the entire figure is one whole. So that is this entire square right over there. And then they ask us which multiplication equation best represents the figure. And so we're supposed to choose one of these four right over here. So pause this video, try it on your own before we work through it together. All right, now let's work through it together. So this whole square is a whole, and now let's first think about what's going on with this 3/10. So they've labeled the 3/10 as three of these vertical bars right over here. We could view the 3/10 as these three vertical bars. And then they also have this 7/10, which are seven of these horizontal bars. And notice each of those bars are 1/10 of the whole. So we have seven of these horizontal bars. If that doesn't look like seven bars, let me just draw it this way. So that's one, two, three, four, five, six, and seven. And of course we see something similar with these vertical bars. That's one, two, and three. Now what's going on here is we're looking at where these bars overlap. And one way to think about that is the overlap is going to be 3/10 times 7/10. You could view this overlap... Let me do this in another color right over here. This overlap right over here. You could view that as 7/10 of the 3/10 or 3/10 of the 7/10 or 7/10 times 3/10. So we immediately know it's going to be either this choice that has 0.3 times 0.7 or this choice that has 0.3 times 0.7. But let's see what this should be. Well, when we look at that overlap, we get 21 of these squares, because we have seven in this direction, three in this direction. I could count them, but we have 21 squares here. And each of those squares are what fraction of the whole? Well, each of those squares are now 1/100 of the whole because this is now a 10 by 10 grid, each of those is 1/100. So in the overlap we have 21 of these squares, that's 21/100. So 21/100 is 0.21. That's the same thing as 21/100, which is this choice right there. And we're done.(1 vote)

## Video transcript

- [Instructor] So we're told
the entire figure is one whole. So that is this entire
square right over there. And then they ask us which
multiplication equation best represents the figure. And so we're supposed to choose one of these four right over here. So pause this video, try it on your own before we work through it together. All right, now let's
work through it together. So this whole square is a
whole, and now let's first think about what's going on with this 3/10. So they've labeled the 3/10 as three of these vertical
bars right over here. We could view the 3/10 as
these three vertical bars. And then they also have this 7/10, which are seven of these horizontal bars. And notice each of those
bars are 1/10 of the whole. So we have seven of these horizontal bars. If that doesn't look like seven bars, let me just draw it this way. So that's one, two, three, four, five, six, and seven. And of course we see something similar with these vertical bars. That's one, two, and three. Now what's going on here is we're looking at where these bars overlap. And one way to think about that is the overlap is going
to be 3/10 times 7/10. You could view this overlap... Let me do this in another
color right over here. This overlap right over here. You could view that as 7/10 of the 3/10 or 3/10 of the 7/10 or 7/10 times 3/10. So we immediately know it's
going to be either this choice that has 0.3 times 0.7 or this choice that has 0.3 times 0.7. But let's see what this should be. Well, when we look at that overlap, we get 21 of these squares, because we have seven in this direction, three in this direction. I could count them, but
we have 21 squares here. And each of those squares are
what fraction of the whole? Well, each of those squares
are now 1/100 of the whole because this is now a 10 by 10 grid, each of those is 1/100. So in the overlap we
have 21 of these squares, that's 21/100. So 21/100 is 0.21. That's the same thing as 21/100, which is this choice right there. And we're done.