The associative property in algebra also works for addition and multiplication. For addition, the associative property in algebra means that when you add three numbers, you can first add any two of the numbers and then add the third.
Mathematicians often write properties with letters instead of numbers. You will get more practice using letters when you work with algebra. Remember that a and b for any two numbers.
Associative Property on Associative Algebra:
Associative property for addition in algebra:
First, add any two of the numbers and then add the third.
(a+b)+c=a+(b+c)
The parentheses group numbers together. Suppose you want to add 2+5+6. You could first add 2 and 5 to get 7, and then add 7 and 6 to get 13. Or you could first add 5 and 6 to get 11, and then add 2 11 to get 13. The results are the same in algebra addition.
If you replace a with 2, b with 5 and c with 6, the associative property in algebra of addition looks like this:
(a+b)+c=a+(b+c)
(2+5)+6=2+(5+6)
7+6=2+11
13=13
Associative property for multiplication in algebra:
First, multiply two numbers and then multiply that product by the third number.
(axb)x=ax(bxc) or (ab)c=a(bc)
Again, the parentheses group numbers together. Suppose you want to solve the multiplication problem 2x3x4. You could first multiply 2x3 to get 6, and then multiply 6x4 to get 24. Or you could first multiply 3x4 to get 12, and then multiply 2x12 to get 24. The results are the same.
If you replace a with 2, b with 3, and c with 4, the associative property in algebra of multiplication looks like this:
(ab)c=a(bc)
(2x3)x4=2x(3x4)
6x4=2x12
24=24
Example on Associative Algebra:
Example 1:
Which of the following is the same as (10+12)+15?
10(12+15)
(10+12)15
10+15+12+15
10+(12+15)
Solution:
Answer (4) is the correct choice. You could first add 10 and 12 to get 22, and then add 22 and 15 to get 37. Or, you could first add 12 and 15 to get 27, and then add 10 and 27 to get 37.
Example 2:
Which of the following is the same as (5x2)x3?
5(2+3)
(3+2)5
5x^2+5x^3
3(5x^2)
Solution:
Answer (4) is the correct choice. You could first multiply 5 and 2 to get 10, and then multiply 10 and 3 to get 30. Or, you could first multiply 2 and 3 to get 6, and then multiply 6 and 5 to get 30.
Mathematicians often write properties with letters instead of numbers. You will get more practice using letters when you work with algebra. Remember that a and b for any two numbers.
Associative Property on Associative Algebra:
Associative property for addition in algebra:
First, add any two of the numbers and then add the third.
(a+b)+c=a+(b+c)
The parentheses group numbers together. Suppose you want to add 2+5+6. You could first add 2 and 5 to get 7, and then add 7 and 6 to get 13. Or you could first add 5 and 6 to get 11, and then add 2 11 to get 13. The results are the same in algebra addition.
If you replace a with 2, b with 5 and c with 6, the associative property in algebra of addition looks like this:
(a+b)+c=a+(b+c)
(2+5)+6=2+(5+6)
7+6=2+11
13=13
Associative property for multiplication in algebra:
First, multiply two numbers and then multiply that product by the third number.
(axb)x=ax(bxc) or (ab)c=a(bc)
Again, the parentheses group numbers together. Suppose you want to solve the multiplication problem 2x3x4. You could first multiply 2x3 to get 6, and then multiply 6x4 to get 24. Or you could first multiply 3x4 to get 12, and then multiply 2x12 to get 24. The results are the same.
If you replace a with 2, b with 3, and c with 4, the associative property in algebra of multiplication looks like this:
(ab)c=a(bc)
(2x3)x4=2x(3x4)
6x4=2x12
24=24
Example on Associative Algebra:
Example 1:
Which of the following is the same as (10+12)+15?
10(12+15)
(10+12)15
10+15+12+15
10+(12+15)
Solution:
Answer (4) is the correct choice. You could first add 10 and 12 to get 22, and then add 22 and 15 to get 37. Or, you could first add 12 and 15 to get 27, and then add 10 and 27 to get 37.
Example 2:
Which of the following is the same as (5x2)x3?
5(2+3)
(3+2)5
5x^2+5x^3
3(5x^2)
Solution:
Answer (4) is the correct choice. You could first multiply 5 and 2 to get 10, and then multiply 10 and 3 to get 30. Or, you could first multiply 2 and 3 to get 6, and then multiply 6 and 5 to get 30.
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