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## 4th grade foundations (Eureka Math/EngageNY)

### Course: 4th grade foundations (Eureka Math/EngageNY) > Unit 3

Lesson 2: Topic B & C: Foundations- Properties and patterns for multiplication
- Intro to associative property of multiplication
- Intro to commutative property of multiplication
- Distributive property
- Basic multiplication
- Multiplying 1-digit numbers by multiples of 10, 100, and 1000
- Multiply 1-digit numbers by a multiple of 10, 100, and 1000
- Multiplying by tens word problem
- Multiply by tens word problems

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# Intro to commutative property of multiplication

Practice changing the order of factors in a multiplication problem and see how it affects the product.

## Comparing totals

This array shows start color #1fab54, 2, end color #1fab54 rows of dots with start color #7854ab, 4, end color #7854ab dots in each row. We can use the expression start color #1fab54, 2, end color #1fab54, times, start color #7854ab, 4, end color #7854ab, equals, start color #e07d10, 8, end color #e07d10 to represent the array.

This array shows start color #7854ab, 4, end color #7854ab rows of dots with start color #1fab54, 2, end color #1fab54 dots in each row. We can use the expression start color #7854ab, 4, end color #7854ab, times, start color #1fab54, 2, end color #1fab54, equals, start color #e07d10, 8, end color #e07d10 to represent the array.

In both examples we get a total of start color #e07d10, 8, end color #e07d10 dots.

start color #1fab54, 4, end color #1fab54, times, start color #7854ab, 2, end color #7854ab, equals, start color #e07d10, 8, end color #e07d10 and start color #7854ab, 2, end color #7854ab, times, start color #1fab54, 4, end color #1fab54, equals, start color #e07d10, 8, end color #e07d10

When we change the order of the numbers that we are multiplying the product stays the same.

start color #1fab54, 5, end color #1fab54, times, start color #7854ab, 4, end color #7854ab, equals, start color #e07d10, 20, end color #e07d10

start color #7854ab, 4, end color #7854ab, times, start color #1fab54, 5, end color #1fab54, equals, start color #e07d10, 20, end color #e07d10

start color #1fab54, 5, end color #1fab54, times, start color #7854ab, 4, end color #7854ab, equals, start color #7854ab, 4, end color #7854ab, times, start color #1fab54, 5, end color #1fab54

start color #7854ab, 4, end color #7854ab, times, start color #1fab54, 5, end color #1fab54, equals, start color #e07d10, 20, end color #e07d10

start color #1fab54, 5, end color #1fab54, times, start color #7854ab, 4, end color #7854ab, equals, start color #7854ab, 4, end color #7854ab, times, start color #1fab54, 5, end color #1fab54

start color #1fab54, 7, end color #1fab54, times, start color #7854ab, 10, end color #7854ab, equals, start color #e07d10, 70, end color #e07d10

start color #7854ab, 10, end color #7854ab, times, start color #1fab54, 7, end color #1fab54, equals, start color #e07d10, 70, end color #e07d10

start color #1fab54, 7, end color #1fab54, times, start color #7854ab, 10, end color #7854ab, equals, start color #7854ab, 10, end color #7854ab, times, start color #1fab54, 7, end color #1fab54

start color #7854ab, 10, end color #7854ab, times, start color #1fab54, 7, end color #1fab54, equals, start color #e07d10, 70, end color #e07d10

start color #1fab54, 7, end color #1fab54, times, start color #7854ab, 10, end color #7854ab, equals, start color #7854ab, 10, end color #7854ab, times, start color #1fab54, 7, end color #1fab54

## Commutative property

The math rule that says the order in which we multiply the factors does not change the product is the commutative property.

Let's use an array to help explain why this works. This array shows start color #e07d10, 5, end color #e07d10 rows with start color #11accd, 2, end color #11accd dots in each row.

We can find the total number of dots by multiplying the number of rows by the number of dots in each row.

If we turned the array on its side we have an array that shows start color #11accd, 2, end color #11accd rows with start color #e07d10, 5, end color #e07d10 dots in each row.

All we did was tip the array over. The total number of dots did not change.

If we multiply the number of rows by the number of dots in each row we get:

The order in which we multiply the numbers start color #11accd, 2, end color #11accd and start color #e07d10, 5, end color #e07d10 does not matter.

### Let's try a few problems

This array shows 8 rows with 4 dots in each row.

## Using the commutative property

### Describing an array

The commutative property says that the order of the numbers doesn't matter in multiplication.

So the order of the numbers doesn't matter when describing an array.

We can use the expression 5, times, 3 to show 5 groups of 3.

Or the expression 3, times, 5 to show 3 groups of 5.

Both expressions equal 15.

### Another problem

## Why is the commutative property helpful?

The commutative property can make multiplying more than two numbers easier.

Let's look at an example:

We can multiply 7, times, 2, times, 5 in two steps:

7, times, 2, equals, 14

14, times, 5, equals, 70

14, times, 5, equals, 70

We got the right answer, but 14, times, 5 is a little tricky to multiply!

Remember that the commutative property lets us change the order of the numbers without changing the answer.

We can switch the 7 and 5 and change the problem to 5, times, 2, times, 7. Let's see how this makes it easier to multiply:

5, times, 2, equals, 10

10, times, 7, equals, 70

10, times, 7, equals, 70

Multiplying by 10 in the second step made it easier to find the product.

## Want to join the conversation?

- if there was 6 rows and 8 dots do I have to multiply 6 AND 8(7 votes)
- so example if you properties of multiplication problem like 3x4 it will equal 4x3(4 votes)
- Yes when you multiply it doesn't matter what order you have the numbers is. 1*2 and 2*1 will be the same thing. The same goes for addition (1+2 is the same as 2+1) , however, this does not apply when you are calculating minus or division. 1-2=-1 while 2-1=1.(7 votes)

- did you know that subtraction i basically a negative right?(5 votes)
- we just started learning and its so easy(5 votes)
- I keep rearranging my correct answers on this site, yet it keeps stating I'm incorrect. I think a sample of all that is needed would truly help. It seems to be to specific and what specificity your site desires is not user friendly.The format you desire would be great, up to now I know or have the answer, the site doesn't recognize it.(5 votes)
- i confoose

last question is...

questionable ( ͡° ͜ʖ ͡°)(5 votes) - how do you answer the first question?(4 votes)
- It would help you alot if you watch the video(2 votes)

- how can I put mult sine n a laptop?(4 votes)
- This is just to easy. It is fun though.(3 votes)
- it's kind of hard for me(3 votes)