Question

The given series \[38 + 83 = 83 + 38\] is an example of
A. Commutative Property
B. Associative Property
C. Closure Property
D. Distributive Property

Answer 1

Hint: We assign variables to each number on the left hand side of the equation and form an equation for the right hand side of the equation in terms of the variables.
* For any two elements ‘a’ and ‘b’ and ‘c’, we can write the properties as:
Commutative Property: \[a + b = b + a\]
Associative Property: \[(a + b) + c = a + (b + c)\]
Closure Property: \[a,b\]belong to the set then \[a + b\]belongs to the set
Distributive Property: \[a(b + c) = ab + bc\]

Complete step-by-step solution:
We have to find the equation \[38 + 83 = 83 + 38\] is an example of which of the given properties.
We look at the left hand side of the equation i.e.\[38 + 83\]
Let us assign different variables to different numbers on left hand side of the equation
Put \[a = 38\] and \[b = 83\]...............… (1)
Then left hand side of the equation becomes \[a + b\]...............… (2)
Now we have to write the right hand side of the equation in terms of ‘a’ and ‘b’.
We know right hand side of the equation is\[83 + 38\]
Substitute the values of ‘a’ and ‘b’ in right hand side of the equation from the equation (1)
Then right hand side of the equation becomes \[b + a\]..................… (3)
Now we write left hand side equal to right hand side using equation (2) and equation (3)
\[ \Rightarrow a + b = b + a\]...................… (4)
Now we know the equation (4) represents a basic equation for commutative property.
\[\therefore \]\[38 + 83 = 83 + 38\] is an example of commutative property.

\[\therefore \]Option A is the correct option.

Note: Students are likely to make mistake commutative property and associative property with each other, keep in mind commutative property always has two elements in it whereas associative property always has three elements to deal with.