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### Course: 5th grade > Unit 5

Lesson 1: Multi-digit multiplication estimation# Estimating multi-digit multiplication

Learn the skill of estimating the product of multi-digit numbers. Watch a demonstration of the process. The video emphasizes the importance of estimation in simplifying complex multiplication problems.

## Want to join the conversation?

- I have a question. So for the first problem, where we are trying to estimate (29)(3198) = 92742, (I may be wrong) but I think it actually is a closer approximation to the real value if we use a rounded value of (30)(3000)=90,000 (which is an underestimation of -2742 from the real value) than if we use (3200)(30) = 96,000 (which is an overestimation of +3258). Similarly, for the second problem, for trying to find (137)(18)=2466, if we round it to (130)(20)=2600, we get the closest approximation, which is +134 from the actual value. If we use (140)(20)=2800, it is an overestimation of +334, and if we use (137)(20)=2740, it is an overestimation of +274, and if we use (100)(20)=2000, it is underestimation of -446. What I'd like to know is how do we go about determining or having a rule for when the values are a closer approximation, while still being able to calculate the values quickly in your head or on paper?(27 votes)
- dude wrote an entire book page (not a insult a compliment)(30 votes)

- what is estimating(4 votes)
- estimating is rounding to get an approximate answer for example 279*23 estimated would be 300*20 = 6000(30 votes)

- i don't understand? this fifth grade multi-digit ):(11 votes)
- For estimating multi-digit multiplication we first round the numbers that are being Multiplied Ex: 482 × 32 -> 500 × 30. Although we rounded the numbers it's still a bit hard. We can solve this by breaking up 30 into 3 and 10. Now the equation looks like this 500 × 3 × 10. Now we can just multiply at this point. 500 × 3 = 1500 × 10 = 15,000.(0 votes)

- I have a question. So for the first problem, where we are trying to estimate (29)(3198) = 92742, (I may be wrong) but I think it actually is a closer approximation to the real value if we use a rounded value of (30)(3000)=90,000 (which is an underestimation of -2742 from the real value) than if we use (3200)(30) = 96,000 (which is an overestimation of +3258). Similarly, for the second problem, for trying to find (137)(18)=2466, if we round it to (130)(20)=2600, we get the closest approximation, which is +134 from the actual value. If we use (140)(20)=2800, it is an overestimation of +334, and if we use (137)(20)=2740, it is an overestimation of +274, and if we use (100)(20)=2000, it is underestimation of -446. What I'd like to know is how do we go about determining or having a rule for when the values are a closer approximation, while still being able to calculate the values quickly in your head or on paper?(9 votes)
- another book page(9 votes)

- This is simple(8 votes)
- Thx for the vid it rlly helped []:(8 votes)
- how do you easly start knowing math in ur head?(3 votes)
- Just like anything, it goes through a progression starting from the simplest number sense. As you learn more number sense, you can do more and more in your head, I work with students at high school level on this.

One of the first concepts is compatible numbers, numbers that just go together well. Numbers that add to be 10 such as 3 and 7, 4 and 6, etc. as well as numbers ending in 5 times even numbers are important. Multiplying/dividing by powers of 10 are just decimal movers to left or right.

If you are adding 48 + 24, you see 49+2=50, so 48+2+24-2= 50+22 which is much easier to add. 536-288, you can subtract 12 and add 12 to get 536+12-288-12=548-300, much easier numbers to work with.

If you multiply 15*24, there is what is called the double and half trick, 15 *2*24*1/2=30*12 which is easier to do in your head.

There are other basic tricks such as multiplying by 11, add digits in pairs from right to left. So 11*1423 write the 3, add 3+2 to get 53, add 2+4 to get 653, add 4+1 to get 5653, then add 1 to front to get 15653.(4 votes)

- 92742 is the actual answer im not dumb(5 votes)
- maybe you are dumb(0 votes)

- It is a very good way if doing it(4 votes)
- im a little confused you made it tooo hard to understand for me atleast can you do another one that is easyer to undeerstand please! thanks(3 votes)
- He is saying that 29 can be estimated to 30, hence only one higher and that 3198 can be turned into 3000 (for estimation purposes). If you multiply 30 and 3000, you get 9000, which he got.(3 votes)

## Video transcript

- [Instructor] What I would like to do in this video is get some practice estimating the product
of multi-digit numbers and there's no better way of getting practice than just trying it ourselves. And so right over here, it says estimate 29 times 3,198. Why don't you pause this video
and try to estimate this? And of course you can do this by multiplying this out on
paper or using a calculator, but this is a useful skill,
try to do it in your head. See if you can estimate
what this is going to be. Well, before even
looking at these answers, I would say this is going to
be approximately equal to ... Let's see, 29 is awfully close to 30, and then I could multiply that times, I could either multiply
that times 32 hundred, which is awfully close to 3,198, or if I wanted an even
more rough approximation, I could say that's roughly equal to 30 times three thousand. So if I did 30 times three thousand, three times three is equal to nine, and then I have one,
two, three, four zeroes. One, two, three, four zeroes. And actually my
approximation, it turns out, is here, right over here, 90 thousand. Now if I wanted a slightly
better approximation, I could have said this is approximately equal to 30 times 3,200, and this you could also do in your head. You could say, well,
what is three times 32? Well, that is gonna be 96, and then you have one, two, three zeroes. One, two, three zeroes, so this would be a slightly better approximation, and if this is what you
got, the closest answer here is still going to
be equal to 90 thousand. Let's do another example. So here, we are asked to
estimate 137 times 18. So pause this video again and see if you can come up with an estimate. Try to do it in your head. Well, there's once again many
ways of trying to tackle it. The way I would tackle it, I would say, well, that's pretty close to 140 times 20, and then this would be
equal to 14 times two is 28, and then we have two zeroes here, so that would be roughly 28 hundred, but when I look over here,
there is no 28 hundred, and so maybe the closest
one right over here is two thousand, so that would be my, that could be an approximation. Another way, it looks actually the way that they did it, they even did a coarser approximation,
they rounded this to the nearest hundred, and so they said this is approximately
equal to one hundred times and they rounded this to the nearest ten, one hundred times 20
which is even easier to do in your head, which is
equal to two thousand, which is this choice that
they got right over here.