Chapter 2: Q54. (page 117)

Which equation below illustrates the Commutative Property?
A $(3 x + 4 y) + 2 z = 3 x + (4 y + 2 z)$
B $7 (x + y) = 7 x + 7 y$
C $x y z = y x z$
D $x + 0 = x$

Short Answer

Expert verified

The equation representing the Commutative property is $x y z = y x z$ or option C.

Step by step solution

Step 1. Use the definition of the commutative property.

The commutative property is for addition and multiplication are given as shown:

$\begin{array}{l} a + b = b + a ......................... (1) \\ a b c = c b a = c a b ................... (2) \end{array}$

Step 2. Identify the expression having commutative property.

We are given the expressions:

A $(3 x + 4 y) + 2 z = 3 x + (4 y + 2 z)$

B $7 (x + y) = 7 x + 7 y$

C $x y z = y x z$

D $x + 0 = x$

Observe that in option A bracket is with the first two terms on the left-hand side and then on the right-hand side it is with the last two terms, we call such associations as associative property.

Similarly, option B is the distributive property

Option C is a commutative property by definition in step-1

Option D is an identity property.

Hence, the following equation represents the commutative property:

$x y z = y x z$

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Which equation below illustrates the Commutative Property?
A $(3 x + 4 y) + 2 z = 3 x + (4 y + 2 z)$
B $7 (x + y) = 7 x + 7 y$
C $x y z = y x z$
D $x + 0 = x$

Short Answer

Step by step solution

Step 1. Use the definition of the commutative property.

Step 2. Identify the expression having commutative property.

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Which equation below illustrates the Commutative Property?A (3x+4y)+2z=3x+(4y+2z)B 7(x+y)=7x+7yC xyz=yxzDx+0=x

Short Answer

Step by step solution

Step 1. Use the definition of the commutative property.

Step 2. Identify the expression having commutative property.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Probability and Statistics

Geometry

Decision Maths

Mechanics Maths

Logic and Functions

Applied Mathematics

Study anywhere. Anytime. Across all devices.

Which equation below illustrates the Commutative Property?
A $(3 x + 4 y) + 2 z = 3 x + (4 y + 2 z)$
B $7 (x + y) = 7 x + 7 y$
C $x y z = y x z$
D $x + 0 = x$