# data[].attributes.attachment_link.description
When you visit any website, it may store or retrieve information on your browser, mostly in the form of cookies. This information might be about you, your preferences or your device and is mostly used to make the site work as you expect it to. The information does not usually directly identify you, but it can give you a more personalized web experience. Because we respect your right to privacy, you can choose not to allow some types of cookies. Click on the different category headings to find out more and change our default settings. However, blocking some types of cookies may impact your experience of the site and the services we are able to offer. More information

# data[].attributes.attachment_link.title
MyMath Ch 2 Lesson 10 Multiply 2 Digit Numbers

# data[].attributes.attachment_link.title
MyMath Ch 2 Lesson 9 Multiply by One-Digit Numbers

# data[].attributes.body
A prime number (or a prime) is a natural numbergreater than 1 that has no positive divisors other than1 and itself. ... For example, 5 is prime because 1 and 5 are its only positive integer factors, whereas 6 is composite because it has the divisors 2 and 3 in addition to 1 and 6.

# data[].attributes.body
2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97, 101, 103, 107, 109, 113, 127, 131, 137, 139, 149, 151, 157, 163, 167, 173, 179, 181, 191, 193, 197, 199

# data[].attributes.body
Basic Exponent Practice

# data[].attributes.attachment_link.description
Learn how to use exponents and bases. For example, writing 4 x 4 x 4 x 4 x 4 with an exponent.

# data[].attributes.body
Powers of 10 Practice

# data[].attributes.attachment_link.readable_text
If you're seeing this message, it means we're having trouble loading external resources on our website.

If you're behind a web filter, please make sure that the domains *.kastatic.org and *.kasandbox.org are unblocked.

# data[].attributes.attachment_link.title
Powers of ten (practice) | Powers of 10 | Khan Academy

# data[].attributes.attachment_link.description
If you're seeing this message, it means we're having trouble loading external resources on our website. If you're behind a web filter, please make sure that the domains *.kastatic.org and *.kasandbox.org are unblocked.

# data[].attributes.body
Multiplication by 10, 100, 1000 practice

# data[].attributes.attachment_link.title
5th Grade My Math Ch 2 Lesson 5 Making a Table

# data[].attributes.body
Distributive property explained

# data[].attributes.attachment_link.description
Read and learn for free about the following article: Distributive property explained

# data[].attributes.body
The Distributive Property is easy to remember, if you recall that "multiplication distributes over addition". Formally, they write this property as "a(b + c) = ab + ac". In numbers, this means, for example, that 2(3 + 4) = 2×3 + 2×4.

# data[].attributes.attachment_link.description
When you visit any website, it may store or retrieve information on your browser, mostly in the form of cookies. This information might be about you, your preferences or your device and is mostly used to make the site work as you expect it to. The information does not usually directly identify you, but it can give you a more personalized web experience. Because we respect your right to privacy, you can choose not to allow some types of cookies. Click on the different category headings to find out more and change our default settings. However, blocking some types of cookies may impact your experience of the site and the services we are able to offer. More information

# data[].attributes.attachment_link.readable_text
If you're seeing this message, it means we're having trouble loading external resources on our website.

If you're behind a web filter, please make sure that the domains *.kastatic.org and *.kasandbox.org are unblocked.

To log in and use all the features of Khan Academy, please enable JavaScript in your browser.

Video transcript

rewrite the expression four times than in parentheses we have eight plus three using the distributive law of multiplication over addition then simplify the expression so let's just try to solve this or evaluate this expression and then we'll talk a little bit about the distributive law of multiplication over addition usually just called the distributive law so we have 4 times 8 4 times 8 plus 8 plus 3 8 plus 3 now there's two ways to do it normally when you have parentheses your inclination is well let me just evaluate what's in the parentheses first and then worry about what's outside of the parentheses and we can do that fairly easily here we can evaluate what 8 plus 3 is 8 plus 3 is 11 so if we do that let me do that in this direction so if we do that we get 4 times we get 4 times and in parentheses we have an 1183 is 11 and then this is going to be equal to well 4 times 11 is just 44 so you can evaluate it that way but they want us to use the distributive law of multiplication we did not use the distributive law just now we just evaluated the expression maybe use the parentheses first then multiplied by 4 and the distributive law we multiply by 4 first and it's called the distributive law because you distribute the 4 and we're going to think about what that means so in the distributive law what this will become it'll become 4 times 8 plus 4 times 3 and we're going to think about why that is in a second so this is going to be equal to 4 times 8 4 times 8 plus 4 times 4 times 3 4 times 3 a lot of people's first instinct is just to multiply the 4 times the 8 but know you have to distribute the 4 you have to multiply it times times the 8 and times the 3 this is right here this is the distributive property in action right here distributive property in action and then when you evaluate I'm going to show you in kind of a visual way why this word but then when you evaluate it four times eight this in a different color 4 times 8 is 32 and then so we have 32 plus 4 times 3 4 times 3 is 12 and 32 plus 12 is equal to 44 that is also equal to 44 so you can get it either way but when they want us to use the distributive law you would multiply it you distribute the 4 first now let's think about why that happens let's let's visualize just what 8 plus 3 is so let me draw 8 of something so 1 2 3 4 5 6 let me draw it this well 6 7 8 right 1 2 3 4 5 6 7 8 and then we're going to add to that we're going to add to that 3 of something of them maybe the same thing 1 2 3 so you could imagine this is what we have inside of the parentheses we have 8 circles plus 3 circles now when we're multiplying this whole thing this whole thing times 4 what does that mean well that means we're just going to add this to itself 4 times so let me do that with the copy and paste copy and paste let me copy and then let me paste there you go that's 2 that's 1 2 3 and then we have 4 and we're going to add them all together so this is literally what 4 times right we have it let me go back to the drawing tool we have it 1 2 3 4 times this expression which is 8 plus 3 now what is this thing over here what is this thing over here what is this thing over here if you were to count all of this stuff you would get 44 but what is this thing over here well that's 8 add it to itself 4 times you could imagine you're adding all of these so what's 8 add it to itself 4 times that is 4 times 8 so this is 4 times 8 and what is this over here in the orange we have 1 2 3 4 times well each time we have three so it's got four times this right here this right here is four times three so you see why the distributive property works if you do four times eight plus three you have to multiply what when you I guess you could imagine duplicate the thing four times both the eight and the three is getting duplicated four times or it's being added to itself four times and that's why we distribute the four

# data[].attributes.attachment_link.title
Distributive property over addition (video) | Khan Academy

# data[].attributes.attachment_link.description
If you're seeing this message, it means we're having trouble loading external resources on our website. If you're behind a web filter, please make sure that the domains *.kastatic.org and *.kasandbox.org are unblocked. To log in and use all the features of Khan Academy, please enable JavaScript in your browser.

# data[].attributes.body
Distributive Property Song

# data[].attributes.attachment_link.title
5th Grade MyMath Ch 2 L7 Homework Helper

# data[].attributes.attachment_link.title
Practicing Fifth grade math: 'Estimate products'

# data[].attributes.attachment_link.description
Fun math practice! Improve your skills with free problems in 'Estimate products' and thousands of other practice lessons.

# data[].attributes.attachment_link.readable_text
Estimating products by rounding numbers to the nearest ten, hundred, thousand etc., we know how to estimate the sum, difference, etc., to the nearest 10, 100, 1000, etc. Now we have to estimate the products.

In order to estimate products, we round the given factors to the required place value. Estimating products help us to check the reasonableness of an answer.

1. Estimate the products of 34 and 86.

34 ⟶ 30 34 is rounded down to 30

86 ⟶ 90 86 rounded up to 90

Calculate mentally 30 × 90 = 2700

The estimated product is 2700.

2. Estimate the products of 331 and 267 by rounding to the nearest hundred.

300 × 300 = 90000

The estimated product is 90000.

Consider the following examples on estimating products:

1. Estimate the product: 42 × 57

Solution:
Thus estimated product = 2400

2. Estimate the product: 47 × 84

Solution:

4 7 × 8 4 47 is rounded up to 50

↓ ↓

5 0 × 8 0 84 is rounded down to 80

= 4 0 0 0

6300 is the estimated product

7 4 × 8 5 74 is rounded up to 80

↓ ↓

7 0 × 9 0 85 is rounded down to 90

= 6 3 0 0

4. Estimate the product: 358 × 326

Solution:

One number is rounded up and the other is rounded down. Here 358 is rounded up to the nearest hundred, i.e., 400 while 326 is rounded down to the nearest hundred, i.e., 300.

3 5 8 × 3 2 6 358 is rounded up to 400

↓ ↓

4 0 0 × 3 0 0 326 is rounded down to 300

= 1 2 0 0 0 0

120000 is the estimated product

5. Estimate the following product by rounding numbers to the nearest;

(i) Hundred

(ii) Ten '341 × 267'

Solution:

(i) 3 4 1 × 2 6 7 341 is rounded up to 300

↓ ↓

3 0 0 × 3 0 0 267 is rounded down to 300

= 90,000 & The estimated product is 90,000

Related Concept
(ii) 3 4 1 × 2 6 7 341 is rounded down to 340, the nearest ten

↓ ↓

3 4 0 × 2 7 0 267 is rounded up to 270, the nearest ten

= 91,800 The estimated product is 91,800

`

● Word Problems on Addition

● Check for Subtraction and Addition

● Word Problems Involving Addition and Subtraction

● Estimating Sums and Differences

● Find the Missing Digits

● Multiply a Number by a 2-Digit Number

● Multiplication of a Number by a 3-Digit Number

● Word Problems on Multiplication

● Multiplication and Division

● Terms Used in Division

● Division of Two-Digit by a One-Digit Numbers

● Division of Four-Digit by a One-Digit Numbers

● Division by 10 and 100 and 1000

● Estimating the Quotient

● Division by Two-Digit Numbers

● Word Problems on Division

# data[].attributes.attachment_link.title
Estimating Products | Rounding Numbers | Estimate the Sum | Examples

# data[].attributes.attachment_link.description
Estimating products by rounding numbers to the nearest ten, hundred, thousand etc., we know how to estimate the sum, difference, etc., to the nearest 10, 100, 1000, etc. Now we have to estimate the products. In order to estimate products, we round the given factors to the required place value.

# data[].attributes.attachment_link.readable_text
If you're seeing this message, it means we're having trouble loading external resources on our website.

If you're behind a web filter, please make sure that the domains *.kastatic.org and *.kasandbox.org are unblocked.

To log in and use all the features of Khan Academy, please enable JavaScript in your browser.

Video transcript

Let's multiply 7 times 253 and see what we get. So just like in the last example, what I like to do is I like to rewrite the largest number first. So that's 253. And then write the smaller number below it and align the place value, the 7. It only has a ones place, so I'll put the 7 right over here below the ones place in 253. And then put the multiplication symbol right over here. So you could read this as 253 times 7, which we know is the same thing as 7 times 253. And now we are ready to compute. And there are many ways of doing this, but this one you could call the standard way. So what I do is I start with my 7. And I multiply it times each of the numbers up here, and I carry appropriately. So first I start with 7 times 3. Well, 7 times 3 we know is 21. Let me write that down. 7 times 3 is equal to 21. You could do this part in your head, but I just want to make it clear where I'm getting these numbers from. What I would do in the standard method is I would write the 1 into 21 down here, but then carry the 2 to the tens place. Now I want to figure out what 7 times 5 is. We know from our multiplication tables that 7 times 5 is equal to 35. Now, we can't just somehow put the 35 down here. We still have to deal with this 2 that we carried. So we compute 7 times 5 is 35, but then we also add that 2. So it's 35 plus 2 is 37. Now, we write the 7 right over here in the tens place and carry the 3. Now we need to compute what 7 times 2 is. We know that 7 times 2 is 14 from our multiplication tables. We can't just put a 14 down here. We have this 3 to add. So 7 times 2 is 14, plus 3 is 17. So now we can write the 17 down here, because 2 is the last number that we had to deal with. And so we have our answer. 7 times 253 is 1,771.

# data[].attributes.attachment_link.title
Multiplying 3-digit by 1-digit (regrouping) (video) | Khan Academy

# data[].attributes.attachment_link.description
If you're seeing this message, it means we're having trouble loading external resources on our website. If you're behind a web filter, please make sure that the domains *.kastatic.org and *.kasandbox.org are unblocked. To log in and use all the features of Khan Academy, please enable JavaScript in your browser.

# data[].attributes.body
Multiply with Regrouping Practice

# data[].attributes.attachment_link.description
Multiply 3- or 4-digit numbers by 1-digit numbers. Regrouping (carrying) needed.

# data[].attributes.attachment_link.title
Multiplication - 2 Digits by 1 Digit | Math Playground

# data[].attributes.attachment_link.description
Practice multiplying large numbers at MathPlayground.com!

# data[].attributes.attachment_link.readable_text
In this video, we're going to multiply 36 times 27. So we're multiplying a two-digit number times another two-digit number. And the way that we're going to tackle it is we're going to first multiply 36 times 7, figure out what that is. Then we're going to multiply 36 times 20, figure out what that is, and then add those two numbers together. And what I want to do is first do this, just show you the process for how to multiply these two numbers. And then I'm going to do it again where we're going to think a little bit more about what the different numbers represent. So first let's start with the process. So I'm going to multiply 36 times 7 or 7 times 36. So I can start in the ones place. 7 times 6 is 42. Write the 2 down here. And then the 4, which represents 40, I can put in the tens place. 7 times 3 is 21, plus 4 is 25. So I could write the 25 right over here. There's no place to carry this 2, so I just wrote the 2 right over here in the hundreds place. Now let's move over. So let me clean this up so we don't get confused. So we just figured out what 7 times 36 is. It is 252. Now let's worry about what 36 times 20 is. And so what we're going to do is we're going to throw a 0 right over here, because we're now going to multiply 36 times something in the tens place. This isn't just a 2. This is a 20. So let's just go with the digits right now and then we'll think about it in terms of place value the second time around. 2 times 6 is 12. Write the 2 right over here. Carry the 1. 2 times 3 is 6, plus 1 is 7. So we just figured out that 36 times 20 is 720. And just think about what would've happened if we didn't put the 0 here. Then we would have figured out that 36 times 2 is 72, but this 2 isn't just a 2. This is a 20. So 36 times 20 is 720. And now we can add these two things because 36 times 27 is the same thing as 36 times 20 plus 36 times 7. So let's add these two numbers together. 2 plus 0 is 2. 5 plus 2 is 7. 2 plus 7 is 9. And we get 972. Now I'm going to do this exact same problem again. But this time, I'm going to really talk about what these digits represent. Hopefully the first pass, you kind of saw the process for doing it. Now we're going to think about what these digits actually represent. So we're going to multiply 36 times 7. So 7 times 6 is 42. We would write the 2 in the ones place, and then the 40 we can write in the tens place. This 4 represents 40. 7 times 30 is 210, plus 40 is 250. And we already had that 2 in the ones place, so we get 252. 36 times 7 is 252. Now let's clean this up. Now let's multiply-- 20 times 6 is going to give us 120. So let's write the 20 in the tens place, and then carry the 100, or carry the 1, which represents 100. Now, 2 times-- or I should say 20 times 30 is going to give you 600, plus one more 100 is going to give you 700. So we just figured out that 36 times 20 is 720. The 7 is in the hundreds place, 2 in the tens place. And then we can add again. And just like we did the last time, we got 972.

# data[].attributes.attachment_link.title
Multiplying 2-digit numbers (video) | Khan Academy

# data[].attributes.attachment_link.description
In this video, we're going to multiply 36 times 27. So we're multiplying a two-digit number times another two-digit number. And the way that we're going to tackle it is we're going to first multiply 36 times 7, figure out what that is.

# data[].attributes.headline
Multiply by Two-Digit by Two Digit Numbers Practice

# data[].attributes.subject
Multiply by Two-Digit by Two Digit Numbers Practice

# data[].attributes.attachment_link.description
Multiply 2-digit numbers by 2-digit numbers. Regrouping (carrying) needed.

# data[].attributes.attachment_link.title
IXL | Multiply a 2-digit number by a 2-digit number | 4th grade math

# data[].attributes.attachment_link.description
Improve your math knowledge with free questions in "Multiply a 2-digit number by a 2-digit number" and thousands of other math skills.