Solve Properties of Reals

There are four types of properties are present in algebra. Those properties are used to solve many of the mathematical problems. Commutative, associative, distributive, identity are the four types of properties present in the algebra. This article gives brief explanation about the properties of reals with the solved example problems.

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Explanation to Solve Properties of Reals

The explanation for the solve properties of reals is as follows,

Commutative property:

Addition: a + b = b + a
Multiplication: a * b = b * a

Associative property:

Addition: a + ( b + c) = (a + b) + c
Multiplication: a* (y *z) = (x * y) * z

Distributive property:

Multiplication: a (b + c) = ab + ac

Identity property:

Addition: a + 0 = 1
Multiplication: a * 0 =a

Example Problems to Solve Properties of Reals

Commutative Property:

Problem 1: Solve: 6 * 3  = 3 * 6.

Solution:

Given:

6* 3  = 3 * 6

18 = 18

Thus, this is the answer for solving the properties of reals.

Associative property:

Problem 2: Solve: 3 + ( 4 + 8) = (3 + 4) + 8.

Solution:

Step 1: Given:

3 + ( 4 + 8) = (3 + 4) + 8

Step 2: Simplify:

3 + ( 4 + 8) = (3 + 4) + 8

3 + (12) = (7) + 8

3 + 12 = 7 + 8

15 = 15

Result: 15 = 15

Thus, this is the answer for solving the properties of reals.

Distributive property:

Problem 3: 5 (4 + 3)

Solution:

Step 1: Given:

5 (4 + 3)

Step 2: Simplify:

5 (4 + 3) = (5)(4) + (5)(3)

= 20 + 15

= 35

Result: 5 (4 + 3) = 35

Thus, this is the answer for solving the properties of reals.

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Identity Property:

Problem 4: Solve: 57+ 0.

Solution:

Step 1: Given:

57 = 0

Step 2: Simplify:

57 + 0 = 57

Result: 57

Thus, this is the answer for solving the properties of reals.