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## 4th grade

### Course: 4th grade > Unit 3

Lesson 4: Estimate products# Estimating with multiplication

Sal estimates to find reasonable products to 1-digit by 2, 3, and 4-digit multiplication expressions.

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- Question: How do you know what number is a friendly number or not?

And how do you know when you are supposed to round a single-digit or ten-digit number up or down?

It looks like sometimes when estimating what to round up or down you sometimes have to round both numbers down like 16 to 15 and 1111 to 1000. I have trouble knowing what to round up or down if it's not asking for a friendly number.

This is a similar problem I had when estimating was first introduced in the 3rd-grade segments of Khan Academy. Those questions weren't fully mentioned besides rounding by 10s 100s, and 1000s.(12 votes) - Let's multiply 6 times 7,981. And the way we're going to do it right now is just to represent or expand out 7,981 as 7,000 plus 900 plus 80 plus 1. And so multiplying 6 times 7,981 is the same thing as multiplying 6 times 7,000 plus 6 times 900 plus 6 times 80 plus 6 times 1. You'd essentially distribute the 6. And to help us keep track of things, let me draw a little grid right over here. So this is the 6, and we're going to have to think about what 6 times 7,000 is, 6 times 900, 6 times 80, and 6 times 1. So I'll make a little square for our rectangle for each of them. Let me do that. So here we go. And so we just need to think about, what is 6 times 7,000? Well 6 times 7 is 42. So 6 times 7,000 is 42,000. 6 times 900, well once again, 6 times 9 is 54. So 6 times 900 is 5,400. 6 times 80, well 80 is eight 10s. So 6 times 8 is 48, but since it's six times 80 or eight 10s, this is going to be 48 10s, or 480. And then finally, 6 times 1, of course, is equal to 6. So to find what this product is, we just have to take the sum of each of these numbers. What 6 times 7,000 is plus 6 times 900 plus 6 times 80 plus 6 times 1. So let's do that right over here. So it's going to be 42,000 plus 5,400 plus 480 plus 6. And we get, let's see, in the ones place, we just have a 6. In the tens place, we just have an 8. In the hundreds place, 4 plus 4 is 8. In the thousands place, 2 plus 5 is 7. And then finally, the ten thousandths place, we still have a 4. So we get 47,886. So this Is equal to 47,886. And what I encourage you to do is to think about how this is really underlining what we're doing here. It's not that different than what you might have done with the traditional multiplication techniques. And this is a useful way of thinking about it because now you really understand what's going on. And actually, when you start doing things like this in your head, at least for myself, this is actually how I try to tackle the multiplication problem. When someone says 6 times 7,981, if I was just looking at this and I didn't have any paper, I would say, OK, what's 6 times 7,000? I'd say, OK, that's 42,000. I'll try to remember that. What's 6 times 900? Oh that's 5,400. Well if I add that to the 42,000, I get 47,400. Then, what's 6 times 80? 480. Have to add that to the 47,400 to get to 47,880. And then, what's 6 times 1? Well that's 6. Well add that to the 47,880, which I've been keeping in my brain, and that's going to be 47,886. So this helps you understand what's really going on when you multiply multiple digits, and it's a useful technique for doing mental multiplication. did you read this all?(12 votes)
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## Video transcript

- [Instructor] In this video,
we're gonna get a little bit of practice estimating
with multiplication. So over here it says question
mark is, and then you have this squiggly equal sign. And so you can view that
squiggly equal sign as being what does this roughly equal to? It doesn't have to be exactly right. So what is roughly equal to 58 times six? And so which of these
choices would you pick? Pause the video and see
if you can answer that. So once again, we don't have
to get this exactly we just need to estimate what 58 times six is. And the way that I would
tackle it is hey, can I rewrite 58 as a number that is easy
to multiply by six or easy to multiply in general? And the easiest thing I can think of is 58 is awfully close to 60. So if you say that that is
close to 60 if we're just estimating it, well what
would 60 times six be? Well 60 times six is the same
thing as, actually let me just write it this way. You can view 60 times six
as six times 10 times six, which you could also view
as six times six times 10. And what's six times six? That's 36. And then 36 times 10 is 360. So I would go with that
choice right over there. Notice, these other choices
aren't anywhere close to that so we feel pretty good
about our estimation. Let's do another example. So here we're asked
what's three times 2,890? What's that roughly equal to? How would you estimate this? Pause the video and see if
you can figure that out. Alright, so 2,890 is not an
easy thing to maybe multiply in our heads, but I can say
hey, that's kinda close to 3,000 so I'm gonna say that this
is going to be approximately equal to, or roughly equal
to, three times 3,000. Now what's three times three? That's nine. So what's three times 3,000? We'll it's gonna be nine thousands. So it would be this
choice right over here. If what I just did was a little
bit confusing, you can view three times 3,000 as three
times three times 1,000. This part right over there is 3,000. Three times three is the nine, and you have nine thousands, 9,000. Let's do one more example. This is going to involve
fairly large numbers. So what is, if you had to
estimate 5,111 times nine. Which of these would you pick? Pause the video and answer that. Alright, so I would view
this, this is roughly, I would estimate it, as 5,000 times 9. And so 5,000 times nine, that's
the same thing as five times 1,000 times nine, which is
the same thing as five times nine times 1,000. Five times nine is 45, so
it's gonna be 45 thousands, or 45,000 which is this
choice right over there.