What is the difference between associative and commutative property? Also is there a way I can easily tell the difference and remember all 3 properties?
a commuter is a person who drives back and forth to work.
Addition and multiplication commute because you can reverse the order and still get the same answer
a+b = b+a
ab = ba
The associative property says that you can associate the operations differently but still get the same answer
(a+b)+c = a+(b+c)
(ab)c = a(bc)
The distributive property says that multiplication distributes over addition. That is, take the multiplier and distribute it across each o f the parts of the sum
a(b+c) = ab + bc
3(2-5+8) = 3*2 - 3*5 + 3*8 = 6-15+24 = 15
this is the same as
3(2-5+8) = 3(5) = 15
As with most things, repetition helps your memory. Do a dozen problems for each property (many available online) and you'll never have to worry about it again.
Thank you this helped a lot!
Also if you can can you give me a online site to work out some problems?
The associative property and the commutative property are both mathematical principles that apply to different operations.
The associative property states that the grouping of numbers in an operation does not affect the result. For addition and multiplication, it can be expressed as (a + b) + c = a + (b + c) or (a * b) * c = a * (b * c). This means that when you are adding or multiplying three or more numbers together, you can group them in any way you want and still get the same result.
On the other hand, the commutative property states that the order of the numbers in an operation does not affect the result. For addition and multiplication, it can be expressed as a + b = b + a or a * b = b * a. This means that when you are adding or multiplying two numbers together, you can swap their places and still get the same result.
To easily remember the difference between these two properties, you can think of the wordings:
- Associative sounds like "associate," which means to group or combine things. So, the associative property deals with grouping numbers in an operation.
- Commutative sounds like "commute," which means to change or switch. So, the commutative property deals with changing the order of numbers in an operation.
Now, as for remembering all three properties, the third property you might be referring to is the distributive property. The distributive property states that multiplying a number by a sum is the same as multiplying the number by each addend individually and then adding the products. It is commonly expressed as a * (b + c) = (a * b) + (a * c).
To remember all three properties, you can use the mnemonic device "AACD," which stands for Associative, Commutative, Distributive. This acronym can help you recall the order of these properties.
I hope this explanation helps you understand the difference between the associative and commutative properties and provides you with a simple way to remember all three properties.