Does these rules apply for subtraction and division?

Nice question! Subtraction and division are neither commutative nor associative. Rather than just memorizing this, let's look at some examples. Example 1: 5-3 = 2, but 3-5 = -2. Example 2: 7-(3-1) = 7-2 = 5, but (7-3)-1 = 4-1 = 3. Example 3: 6/2 = 3, but 2/6 = 1/3. Example 4: 8/(4/2) = 8/2 = 4, but (8/4)/2 = 2/2 = 1. Subtraction has a partial identity of 0, and division has a partial identity of 1, but this only works if the identity is *on the right*. x - 0 is always x, and x/1 is always x. However, 0 - x is usually not x, and 1/x is usually not x. Example 5: 0 - 2 = -2, not 2. Example 6: 1/2 is one-half, not 2. In math, it is very important to learn to distinguish properties from non-properties. Otherwise, you could end up using an invalid shortcut and getting a wrong answer, or end up failing to recognize an opportunity to use a valid shortcut.

I'm confused about this problem: -2(5 x 7) = (-2 x 5) x (-2 x 7) True or False? I know this is false but does the distributive property only apply to addition and subtraction and not multiplication?

The distributive property distributes multiplication across addition or subtraction. In your example, someone is trying to use it to distribute multiplication across multiplication. The distributive property does no do this. And, if you do the math on each side of the example, you can see that the steps are invalid because they don't create the same result.

What is this property? 1/8 * 8 = 1 or 1/3 * 3 = 1.

That is the inverse property of multiplication. Any number * its reciprocal = 1. Hope this helps.

2+2+2=3+3 Above said this was incorrect selection. Both sides equal 6. The one below has two different answers. Why wouldn’t it be this one.

Because in 2+2+2 you cant get 3 without breaking apart the numbers. It also doesn't follow the rules of any property.

What is the property of 4*(5+8)= (4*8)?

It isn't a property. The 2 sides are not equal. There is a distributive property that tells you: 4*(5+8) = 4*5+4*8 Hope this helps.

is 60x30x20= (30x20)x60 communiative or asscosiative

It could be both. Commutative means you can move things around which you did Associative means you can the order of which ones you multiply, so if you do it in order on the first one (60*30)*20 .

What about *Inverse* _property_?

The inverse property that I've heard of states that multiplication and division are inverse operations, so you multiply a number by another number and then divide it by that same other number, you'd get the first number back again. This is the same as when you add and then subtract the same number, and get what you started with. Is that what you're talking about?

For the question (a+c)+b=(a+b)+c what property is it

It is 2 properties. Apply commutative property: (a+c)+b = (c+a)+b Apply associative proeprty: (c+a)+b = c+(a+b) Apply commutative property again: c+(a+b) = (a+b)+c Hope this helps.

Main content

6th grade

Course: 6th grade > Unit 6

Lesson 1: Properties of numbers

Properties of multiplication

Google Classroom

Explore the commutative, associative, and identity properties of multiplication.

In this article, we'll learn the three main properties of multiplication. Here's a quick summary of these properties:

Commutative property of multiplication: Changing the order of factors does not change the product. For example, 4, times, 3, equals, 3, times, 4.

Associative property of multiplication: Changing the grouping of factors does not change the product. For example, left parenthesis, 2, times, 3, right parenthesis, times, 4, equals, 2, times, left parenthesis, 3, times, 4, right parenthesis.

Identity property of multiplication: The product of 1 and any number is that number. For example, 7, times, 1, equals, 7.

Commutative property of multiplication

The commutative property of multiplication says that changing the order of factors does not change the product. Here's an example:

4, times, 3, equals, 3, times, 4

Notice how both products are 12 even though the ordering is reversed.

Here's another example with more factors:

1, times, 2, times, 3, times, 4, equals, 4, times, 3, times, 2, times, 1

Notice that both products are 24.

Which of these is an example of the commutative property of multiplication?

Associative property of multiplication

The associative property of multiplication says that changing the grouping of the factors does not change the product. Here's an example:

start color #11accd, left parenthesis, 2, times, 3, right parenthesis, times, 4, end color #11accd, equals, start color #e07d10, 2, times, left parenthesis, 3, times, 4, right parenthesis, end color #e07d10

Remember that parentheses tell us to do something first. So here's how we evaluate the left-hand side:

empty space, start color #11accd, left parenthesis, 2, times, 3, right parenthesis, times, 4, end color #11accd

equals, 6, times, 4

equals, 24

And here's how we evaluate the right-hand side:

empty space, start color #e07d10, 2, times, left parenthesis, 3, times, 4, right parenthesis, end color #e07d10

equals, 2, times, 12

equals, 24

Notice that both sides equal 24 even though we multiplied the 2 and the 3 first on the left-hand side, and we multiplied the 3 and the 4 first on the right-hand side.

Which of these is an example of the associative property of multiplication?

(Choice A)
3, times, 5, times, 7, equals, 3, times, 5, times, 7
(Choice B)
3, times, left parenthesis, 7, times, 4, right parenthesis, equals, left parenthesis, 3, times, 7, right parenthesis, times, 4

Identity property of multiplication

The identity property of multiplication says that the product of 1 and any number is that number. Here's an example:

7, times, 1, equals, 7

The commutative property of multiplication tells us that it doesn't matter if the 1 comes before or after the number. Here's an example of the identity property of multiplication with the 1 before the number:

1, times, 6, equals, 6

Which of these is an example of the identity property of multiplication?

Want to join the conversation?

Sort by:

Giselle Superville
Posted 4 years ago. Direct link to Giselle Superville's post “Does these rules apply fo...”
Does these rules apply for subtraction and division?
Button navigates to signup pageComment on Giselle Superville's post “Does these rules apply fo...”
(31 votes)
Answer
- Ian Pulizzotto
  Posted 4 years ago. Direct link to Ian Pulizzotto's post “Nice question! Subtracti...”
  Nice question!
  
  Subtraction and division are neither commutative nor associative. Rather than just memorizing this, let's look at some examples.
  
  Example 1: 5-3 = 2, but 3-5 = -2.
  Example 2: 7-(3-1) = 7-2 = 5, but (7-3)-1 = 4-1 = 3.
  Example 3: 6/2 = 3, but 2/6 = 1/3.
  Example 4: 8/(4/2) = 8/2 = 4, but (8/4)/2 = 2/2 = 1.
  
  Subtraction has a partial identity of 0, and division has a partial identity of 1, but this only works if the identity is on the right.
  
  x - 0 is always x, and x/1 is always x.
  
  However, 0 - x is usually not x, and 1/x is usually not x.
  Example 5: 0 - 2 = -2, not 2.
  Example 6: 1/2 is one-half, not 2.
  
  In math, it is very important to learn to distinguish properties from non-properties. Otherwise, you could end up using an invalid shortcut and getting a wrong answer, or end up failing to recognize an opportunity to use a valid shortcut.
  Comment on Ian Pulizzotto's post “Nice question! Subtracti...”
  (44 votes)
Georgia Brasi
Posted 4 years ago. Direct link to Georgia Brasi's post “I'm confused about this p...”
I'm confused about this problem:
-2(5 x 7) = (-2 x 5) x (-2 x 7) True or False? I know this is false but does the distributive property only apply to addition and subtraction and not multiplication?
Button navigates to signup pageComment on Georgia Brasi's post “I'm confused about this p...”
(9 votes)
Answer
- Kim Seidel
  Posted 4 years ago. Direct link to Kim Seidel's post “The distributive property...”
  The distributive property distributes multiplication across addition or subtraction. In your example, someone is trying to use it to distribute multiplication across multiplication. The distributive property does no do this. And, if you do the math on each side of the example, you can see that the steps are invalid because they don't create the same result.
  Button navigates to signup page
  (7 votes)
:)
Posted 4 years ago. Direct link to :)'s post “What is this property? 1/...”
What is this property? 1/8 * 8 = 1 or 1/3 * 3 = 1.
Button navigates to signup pageButton navigates to signup page
(8 votes)
Answer
- Kim Seidel
  Posted 4 years ago. Direct link to Kim Seidel's post “That is the inverse prope...”
  That is the inverse property of multiplication.
  Any number * its reciprocal = 1.
  
  Hope this helps.
  Comment on Kim Seidel's post “That is the inverse prope...”
  (7 votes)
lauren.yang
Posted 3 years ago. Direct link to lauren.yang's post “What is the property of 4...”
What is the property of 4*(5+8)= (4*8)?
Button navigates to signup pageButton navigates to signup page
(5 votes)
Answer
- Kim Seidel
  Posted 3 years ago. Direct link to Kim Seidel's post “It isn't a property. The...”
  It isn't a property. The 2 sides are not equal.
  There is a distributive property that tells you:
  4*(5+8) = 4*5+4*8
  
  Hope this helps.
  Button navigates to signup page
  (8 votes)
em.coleman
Posted 5 months ago. Direct link to em.coleman's post “is 60x30x20= (30x20)x60 c...”
is 60x30x20= (30x20)x60 communiative or asscosiative
Button navigates to signup pageButton navigates to signup page
(5 votes)
Answer
- David Severin
  Posted 5 months ago. Direct link to David Severin's post “It could be both. Commuta...”
  It could be both.
  Commutative means you can move things around which you did
  Associative means you can the order of which ones you multiply, so if you do it in order on the first one (60*30)*20 .
  Button navigates to signup page
  (5 votes)
tehyam2
Posted 2 years ago. Direct link to tehyam2's post “2+2+2=3+3 Above said this...”
2+2+2=3+3 Above said this was incorrect selection. Both sides equal 6. The one below has two different answers. Why wouldn’t it be this one.
Button navigates to signup pageButton navigates to signup page
(6 votes)
Answer
- HARMANPREET
  Posted 2 months ago. Direct link to HARMANPREET's post “Because in 2+2+2 you cant...”
  Because in 2+2+2 you cant get 3 without breaking apart the numbers. It also doesn't follow the rules of any property.
  Button navigates to signup page
  (2 votes)
1972171308
Posted a month ago. Direct link to 1972171308's post “i eat rock sediments.”
i eat rock sediments.
Button navigates to signup pageComment on 1972171308's post “i eat rock sediments.”
(6 votes)
Answer
I make Games
Posted 2 years ago. Direct link to I make Games's post “What about *Inverse* _pro...”
What about Inverse property?
Button navigates to signup pageButton navigates to signup page
(4 votes)
Answer
- Hecretary Bird
  Posted 2 years ago. Direct link to Hecretary Bird's post “The inverse property that...”
  The inverse property that I've heard of states that multiplication and division are inverse operations, so you multiply a number by another number and then divide it by that same other number, you'd get the first number back again. This is the same as when you add and then subtract the same number, and get what you started with. Is that what you're talking about?
  Button navigates to signup page
  (5 votes)
arjunelati
Posted 3 years ago. Direct link to arjunelati's post “For the question (a+c)+b=...”
For the question (a+c)+b=(a+b)+c what property is it
Button navigates to signup pageButton navigates to signup page
(4 votes)
Answer
- Kim Seidel
  Posted 3 years ago. Direct link to Kim Seidel's post “It is 2 properties. Apply...”
  It is 2 properties.
  Apply commutative property: (a+c)+b = (c+a)+b
  Apply associative proeprty: (c+a)+b = c+(a+b)
  Apply commutative property again: c+(a+b) = (a+b)+c
  
  Hope this helps.
  Button navigates to signup page
  (5 votes)
Carson Carter
Posted 4 years ago. Direct link to Carson Carter's post “There is also the associa...”
There is also the associative property of multiplication over addition.
Button navigates to signup pageButton navigates to signup page
(6 votes)
Answer