Associative property is an important part of mathematics, which is used to solve the problems of Algebra. In a proper definition, real numbers are those numbers that are not imaginary numbers. The Real Numbers did not have a name before Imaginary numbers, that‘s why they were known as a real numbers. Associative properties holds true under two operations which are addition and multiplication.
1. Associative Property of Addition
a + (b + c) = (a +b) + c
In the above given equation, it shows the associative property of real numbers by addition. The Associative Property of Addition states that altering the arrangement of brackets between the operators does not make any modification in the final result i.e, we can sum up numbers in any order but it does not affect the final result. Here are some examples through which we can easily describe the Associative property of addition.
e.g, 3 + (4 + 5) = (3 + 4) + 5 = 12
2. Commutative Property of Multiplication
a * (b * c) = (a * b) * cIn the above given equation, it shows the associative property of real numbers by multiplication. The Associative Property of multiplication states that altering the arrangement of brackets between the operators does not make any modification in the final result i.e, we can multiply numbers in any arrangement it wont affect the concluding result. Here are some examples through which we can easily describe the Associative property of multiplication.
In order to solve the given problem we can use the Associative Property of the real number. Where, property states that (a + b) + c=a+(b+c), so according to property answer is (5 + 2) + 3.
Let's see how to approach this type of problems: In this changing the grouping of sum don't make any effect on the final value.
=> 5 +(2 +3) =(5 +2) +3,
=> 5 + 5 = 7 + 3,
=> 10 = 10.
Write the equivalent expression for the given expression (5x +7y) +4a, using the associative property?
In this question, given expression is a Combination of real Numbers in which we are using different operators. Now, we use Associative Property to change the Position of the brackets, which doesn't make any change in the final answer.
Suppose x=1,y =2, a=3 then,
=> 5(1) +(7*2 + 4*3) =(5(1) + 7*2) + 4*3,
=> 31 = 31.
So answer is 5x +(7y +4a).
Here we follow the Associative Property of the real number to solve the expression by changing the bracket’s Position, but here we have to remember that it doesn’t make any change in the expressions value to solve the problem. Let’s show you how to solve this using associative property.
Suppose p =1 , q =2, r=3 then,
=> (1 + 2*2) -6* 3 =1+(2*2 – 6*3),
=> 5 -18 = 1-14,
=> - 13 = -13.
In the given expression we use the multiplication with Associative Property. As we know, in associative property we change the brackets without affecting the final answer. Let's see how to approach this type of problems, here we take the value of a=2 , b=3 then:
=> (4.3 *2) * 3 =4.3* (2*3),
=> 8.6 * 3 = 4.3 * 6,
=> 25.8 = 25.8.
Then the final value is 4.3(ab).
As we know that Associative Property is nothing it’s just changing the Position of brackets without affecting the final answer. Let’s show you that how associative property works by supposing the value of y =1 ,x =2 then:
=> (8(1)) * 5*2 =8(1) *(5*2),
=> 8 * 10 =8 *10,
=> 18 = 18.
So final value is 8y4(5x).
Write the equivalent expression using the associative property for given expression (24a + 53b) + 45c?
Here we use the additive Associative Property of the real number. Here we change the order group of sum in the given expression, which doesn't change the value. Additive associative property states that a + (b+c) =(a+b) +c .
Suppose value of a=1, b=2, c=3 then,
=> 24(1) + (53(2) +45(3)) = (24(1) + 53(2)) + 45 (3),
=> 24+(106 + 135) = (24 + 106) +135,
=> 24 +241 =130 +135,
=> 265 = 265.
In above we see that by changing the Position of brackets final answer doesn’t get affect. So answer is 24a + (53b +45c).
Here, we are solving this question by using Associative Property but final answer don’t get affected
=> (5+4) + 10 =5+(4 + 10),
=> 9 +10 =5 + 14,
=>19 = 19.
In above example we can see that by changing the Position of brackets we can perform the calculation without affecting the final answer.