Which property is illustrated by the equation 7×9=9×7?
A. Commutative Property of Multiplication
B. Inverse Property of Multiplication
C. Associate Property of Multiplication
D. Identity Property of Multiplication
The Correct Answer and Explanation is:
The correct answer is A. Commutative Property of Multiplication.
Explanation:
The Commutative Property of Multiplication states that the order in which two numbers are multiplied does not affect the product. In other words, for any two numbers ( a ) and ( b ), the equation ( a \times b = b \times a ) holds true. This is exactly what is being illustrated by the equation:
[
7 \times 9 = 9 \times 7
]
In this case, the numbers 7 and 9 are multiplied, and regardless of whether 7 is multiplied by 9 or 9 is multiplied by 7, the result remains the same, which is 63. This demonstrates the commutative property of multiplication because the factors are switched (commuted), but the product remains unchanged.
Other Properties Explained:
- B. Inverse Property of Multiplication: This property refers to the concept that for any non-zero number ( a ), there exists a number ( b ) such that ( a \times b = 1 ). In other words, ( b ) is the multiplicative inverse of ( a ). For example, the multiplicative inverse of 7 is ( \frac{1}{7} ), because ( 7 \times \frac{1}{7} = 1 ). The equation ( 7 \times 9 = 9 \times 7 ) does not demonstrate the inverse property.
- C. Associative Property of Multiplication: The associative property states that when multiplying three or more numbers, the grouping of the numbers does not affect the product. It is expressed as ( (a \times b) \times c = a \times (b \times c) ). The given equation does not show the grouping of numbers; it only switches the order of two numbers, so it does not illustrate the associative property.
- D. Identity Property of Multiplication: The identity property of multiplication states that any number multiplied by 1 remains unchanged. For example, ( 7 \times 1 = 7 ). The given equation does not involve multiplying by 1, so it does not demonstrate the identity property.
Thus, the equation ( 7 \times 9 = 9 \times 7 ) clearly illustrates the Commutative Property of Multiplication, where the order of multiplication does not affect the result.