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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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# Estimating decimal multiplication

This video is all about using estimation to simplify the process of multiplying decimals. It emphasizes the idea that rounding numbers to their nearest whole can make multiplication easier and quicker, especially when you're trying to do it in your head!

## Want to join the conversation?

- Hi this video helped me enough but I am still confused how to do your estimate problems can you tell me some more information?(23 votes)
- You round your numbers to the nearest tenths, hundredths,and ones, then you do your old buddy thing: Multiply(7 votes)

- whats 450x24 and how do you do it?(9 votes)
- 450*24=10800

I got this answer by using the normal algorithm method.

Step 1: You jot down the numerals like so:

450

24

----

----

(You might wonder what the dotted lines under the equation are for, it's for writing down the answer)

Step 2: You multiply the units digits in both numbers like so:

0*4=0

(So after step 2 the equation would be like:

450

24

----

0

----

So far you've got 1 number under your equation, which is your answer so far)

Step 3: You multiply the tens digit of the first numeral with the units digit of the second numeral.

Step 4: I guess you've caught the sequence by now. All you have to do this time is multiply the hundreds digit of the first numeral by the units digit of the second numeral.

Your equation would look like this so far:

450

24

----

1800

----

You might be wondering about the tens digit in the second numeral because we haven't even used it once yet right?

Don't worry I'll teach you in the next few steps:

(Hot Tip: Write down a plus sign underneath the units digit of your new answer so far)

Step 5: Now we come back to the units digit of the first numeral and multiply that by the tens digit of the first numeral.

Step 6: And the pattern starts all along again, but this time with the tens digit of the second numeral. This time you multiply the tens digit of the first numeral by the tens digit of the second numeral.

Step 7: Again, you multiply the hundreds digit of the first numeral by the tens digit of the second numeral.

Your equation will look like this so far:

450

24

----

1800

900+

----

Step 8: It's pretty obvious by now that all we have to do now is add the new answers we have acquired.

The new equation will look like this:

450

24

----

1800

900+

------

10800

------

Now you've got the answer!

Hope this helps :)(10 votes)

- I don't understand this whole video. Can someone help me?(7 votes)
- ok what he is doing is estimating so for EX 199 x 7.8 it is approximately equal to 1600 because 199 is equal to 200 and 7.8 is equal to 8.0 or just 8 because there's a zero next to it not a 1,2,3,4or any other number. Then multiply the 8 and the 200 you would get 1600(7 votes)

- Hi Sal, is there a specific strategy that will help solve multiplication with decimals for the exact sum?(7 votes)
- There is a few strategies. One is to use long multiplication, and just make sure that you have the correct amount of decimals. Example would be 0.25 x 1.23, you would first do 3 times 25, gives 75, then 20 times 25 for 500. and then 100 times 25 for 2500. Then add up for 3075, then you say first number had 2 decimal spaces, second also had 2, 2 plus 2 is 4, so you have 4 decimal places and get 0.3075.

Of course, this isn't the only way, you could also turn one or both decimals into fractions. For the example you could say 123/100 * 1/4 then multiply fractions to get 123/400. If you wanted to then turn that fraction into a decimal to get your answer you once again have different options but I would do long division.(6 votes)

- hi i need help at2:35(9 votes)
- Ok, so is turning a fraction into a decimal and estimating then turning it into a fraction an option? Can you do it the other way around.(5 votes)
- I just cannot get this lol(1 vote)
- When we do decimal multiplication, it might be difficult for us to compute by hand (or mentally).

Therefore, we usually round the decimal to the nearest**integer**.

3.14 ≈ 3

For others, it depends on how many digits it have.

But to be honest, I think this really isn't that necessary to learn, since estimation depends on situation, and should be based on intuition and not under a set of procedures with definite answer.(3 votes)

- I got the first two of the questions correct, but couldn't complete the last question, which involved two decimals. I am trying to get an exact answer. Could someone help me out please?(1 vote)
- Hi there, have you tried rounding? I’ll provide an example. 12.6 x 5.2, in this case you round to get the problem 13 x 5. You are given 4 choices, (most of the time they are not exact) 70, 300, 1020 and 2340. To fine the answer you round your decimals to create a whole number and then multiply. In this case, 13 x 5 = 65, now you have to pick which one of your options is correct. We know that 70 is the correct option because it is the closest to 65.(2 votes)

## Video transcript

- [Instructor] Let's
now get some practice. Estimating multiplying with decimals. So first here, we have 7.8 times 307, is approximately equal to what? When you see the squiggly equal sign, that means approximately equal to what. So pause this video, and
see if you can figure it out on your own. Alright, so the way that I
would think about doing it, even if I was trying to do this in my head at the supermarket or something, I'd say, well, okay,
I'd probably need paper to do this properly, but gee, 7.8 is awfully close to eight, and 307 is pretty close to 300, so maybe I can estimate
this by multiplying eight times 300. Now, this isn't going to be exact, it's definitely going to be off, but it's gonna give me a good sense of roughly what 7.8 times 307 is. So what is eight times 300? Well, eight times three is 24, and so eight times 300 would be 2,400, we got these two more
zeros, two more zeros. And so there you have it, and luckily, the people who wrote this question estimated in a very similar way. Two people when they
estimate might not get the exact same answer, but
in this case, we happen to. Let's do another example. So here, we're trying to
estimate 99.87 times 19. So pause the video again
and see if you can come up with a good estimation. Alright, so once again, not
easy to do this in your head, but this, 99 and 87/100 is pretty close, let me do this in a new color, this is pretty close to 100 times, and I could multiply 100 times 19, that's actually not so difficult, so for example, I could say 100 times 19 is equal to 1,900, but notice, we don't see that choice here, we could say, look, 1,900 is definitely much closer to 2,000
than any of these other, so that might be a good approximation. Now, how did they get 2,000? Well, they rounded both of these numbers, they said, this is
approximately 100 times 20. So, it's not that it's
the right thing to do, to round this 19 up to 20, if you could do 100 times 19, this is actually gonna give you a slightly more accurate result than doing 100 times 20, but 100 times 20 is even easier
to estimate in your head. But either way, the closest choice here, and that's why, I guess, these had to be multiple choice questions, is 2,000. Let's do another example. So here, we are asked to
multiply 2.21 times 5.1, and we wanna know what
it approximately equals, so once again, we are estimating, so pause this video and
try to figure it out. Well, we're just gonna do the same thing we did in the last two examples. 2.21, and, well, first of all, this is hard to do in my head, and so 2.21, well, that's approximately, if I round to the nearest two, or to the nearest one, I should say, this is gonna be two times five, which is equal to 10, so this would be approximately equal to
10, and that is a choice. Now, some of you might say, "Whoa, there's ways to
get better estimations "that you could still do with your head," so for example, you could say
that this is pretty close to, this is approximate,
let me do it over here, this is approximately
equal to two times 5.1, this is still pretty
straightforward to do in your head, this would be 10.2. And so, but you'd still
say that this is by far the closest one. Or you could even say something like, this is approximately
equal to 2.2 times five. What is this going to be equal to? Well, two times five is 10, and 2/10 times five is another whole, and so this is going to be equal to 11, so all of these might be
things that you could estimate that you might be able to do in your head, but the important thing to
realize is however you do it, by far, 10 is going to
be the closest response to what you're getting at, and 10 would be a very natural estimation if you try to simplify
both of these numbers when making that estimate.