Introduction to algebra:
Algebra is the branch of mathematics concerning the study of the rules of operations and relations, and the constructions and concepts arising from them, including terms, polynomials, equations and algebraic structures. Together with geometry, analysis, topology, combinatorics, and number theory, algebra is one of the main branches of pure mathematics. Please express your views of this topic Factor Polynomial Calculator by commenting on blog.
Source: Wikipedia
Concept of associative property in algebra:
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.
Associative property for addition in algebra:
First, add any two of the numbers and then add the third.
(p+q)+r=p+(q+r)
The parentheses group numbers together. Suppose you want to add 1+2+3. You could first add 1 and 2 to get 3, and then add 3 and 3 to get 6. Or you could first add 3 and 2 to get 5, and then add 5 and 1 to get 6. The results are the same in algebra addition.
If you replace p with 1, q with 2 and r with 3, the associative property in algebra of addition looks like this:
(a+b)+c=a+(b+c)
(1+2)+3=1+(2+3)
3+3=1+5
6=6
Associative property for multiplication in algebra:
First, multiply two numbers and then multiply that product by the third number.
(p*q)*r=p*(q*r) or (pq)r=p(qr)
Again, the parentheses group numbers together. Suppose you want to solve the multiplication problem 1x2x3. You could first multiply 1x2 to get 2, and then multiply 2x3 to get 6. Or you could first multiply 2x3 to get 6, and then multiply 6x1 to get 6. The results are the same.
If you replace p with 1, q with 2, and r with 3, the associative property in algebra of multiplication looks like this:
(pq)r=p(qr)
(1*2)*3=1*(2*3)
2*3=1*6
6=6
Example for associative property in 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
5x2+5x3
3(5x2)
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. Is this topic algebra 2 homework solver hard for you? Watch out for my coming posts.
Practice problem for associative:
Problem 1:
Which of the following is the same as (8+2)+5?
8(2+5)
(8+2)5
8+5+2+5
8+(2+5)
Answer: 4.
Problem 2:
Which of the following is the same as (5+2)*6?
5(2+6)
(5+6)2
(5*6)+(2*6)
(5+6)+2+15
Answer: 3.
Problem 3:
Which of the following is the same as (5*2)+6?
6+(2*5)
(5+6)2
(5*6)+(2*6)
(5+6)+2
Answer: 1.
Algebra is the branch of mathematics concerning the study of the rules of operations and relations, and the constructions and concepts arising from them, including terms, polynomials, equations and algebraic structures. Together with geometry, analysis, topology, combinatorics, and number theory, algebra is one of the main branches of pure mathematics. Please express your views of this topic Factor Polynomial Calculator by commenting on blog.
Source: Wikipedia
Concept of associative property in algebra:
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.
Associative property for addition in algebra:
First, add any two of the numbers and then add the third.
(p+q)+r=p+(q+r)
The parentheses group numbers together. Suppose you want to add 1+2+3. You could first add 1 and 2 to get 3, and then add 3 and 3 to get 6. Or you could first add 3 and 2 to get 5, and then add 5 and 1 to get 6. The results are the same in algebra addition.
If you replace p with 1, q with 2 and r with 3, the associative property in algebra of addition looks like this:
(a+b)+c=a+(b+c)
(1+2)+3=1+(2+3)
3+3=1+5
6=6
Associative property for multiplication in algebra:
First, multiply two numbers and then multiply that product by the third number.
(p*q)*r=p*(q*r) or (pq)r=p(qr)
Again, the parentheses group numbers together. Suppose you want to solve the multiplication problem 1x2x3. You could first multiply 1x2 to get 2, and then multiply 2x3 to get 6. Or you could first multiply 2x3 to get 6, and then multiply 6x1 to get 6. The results are the same.
If you replace p with 1, q with 2, and r with 3, the associative property in algebra of multiplication looks like this:
(pq)r=p(qr)
(1*2)*3=1*(2*3)
2*3=1*6
6=6
Example for associative property in 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
5x2+5x3
3(5x2)
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. Is this topic algebra 2 homework solver hard for you? Watch out for my coming posts.
Practice problem for associative:
Problem 1:
Which of the following is the same as (8+2)+5?
8(2+5)
(8+2)5
8+5+2+5
8+(2+5)
Answer: 4.
Problem 2:
Which of the following is the same as (5+2)*6?
5(2+6)
(5+6)2
(5*6)+(2*6)
(5+6)+2+15
Answer: 3.
Problem 3:
Which of the following is the same as (5*2)+6?
6+(2*5)
(5+6)2
(5*6)+(2*6)
(5+6)+2
Answer: 1.
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