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1. What properties do the following expressions show?

i) [tex]23 + 45 = 45 + 23[/tex]

ii) [tex]13 \times 23 = 23 \times 13[/tex]

Sagot :

GinnyAnswer
Let's identify and explain the properties demonstrated by the given expressions:

### Expression i) [tex]\(23 + 45 = 45 + 23\)[/tex]
This expression shows the Commutative Property of Addition.

#### Explanation:
The Commutative Property of Addition states that when two numbers are added, the order in which they are added does not affect the sum. In mathematical terms, for any two numbers [tex]\(a\)[/tex] and [tex]\(b\)[/tex],
[tex]\[ a + b = b + a \][/tex]

In the given expression [tex]\(23 + 45 = 45 + 23\)[/tex], the numbers [tex]\(23\)[/tex] and [tex]\(45\)[/tex] are added in both sides of the equation, but their order is reversed. Despite the change in order, the sum remains the same, illustrating the commutative property.

### Expression ii) [tex]\(13 \times 23 = 23 \times 13\)[/tex]
This expression shows the Commutative Property of Multiplication.

#### Explanation:
The Commutative Property of Multiplication states that when two numbers are multiplied, the order in which they are multiplied does not affect the product. In mathematical terms, for any two numbers [tex]\(a\)[/tex] and [tex]\(b\)[/tex],
[tex]\[ a \times b = b \times a \][/tex]

In the given expression [tex]\(13 \times 23 = 23 \times 13\)[/tex], the numbers [tex]\(13\)[/tex] and [tex]\(23\)[/tex] are multiplied in both sides of the equation, but their order is reversed. Despite the change in order, the product remains the same, illustrating the commutative property of multiplication.

### Summary:
- i) [tex]\(23 + 45 = 45 + 23\)[/tex] shows the Commutative Property of Addition.
- ii) [tex]\(13 \times 23 = 23 \times 13\)[/tex] shows the Commutative Property of Multiplication.
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