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In Mathematics / Middle School | 2014-04-30

What property is shown in the equation? \(-53 \div 1 = -53\)

A. Division into zero property
B. Identity property of division
C. Negative one property of division
D. Reciprocal property


What property is shown in the equation? \(5ac = 5ca\)

A. Identity property of multiplication
B. Reciprocal property of multiplication
C. Zero property of multiplication
D. Commutative property of multiplication

Asked by mjchey

Answer (3)

The first one is negative one property of division, I think. The second one is commutative property of multiplication.

Answered by Bharti | 2024-06-10

The equation 53 1 = 53 exemplifies the Identity Property of Division,.
The first equation 53 1 = 53 demonstrates the Identity Property of Division, which states that any number divided by one is the number itself. This aligns with option B; thus, the identity property is shown here. Regarding the second equation, 5ac = 5ca, it shows the Commutative Property of Multiplication. This property means that the order in which two numbers are multiplied does not change their product, which corresponds to option D.
Multiplication and division are inherently connected, as division is essentially multiplying by the reciprocal. This linkage is reinforced by the rules for the signs of products and quotients, which follow the same conventions and are based on the operators' properties

Answered by SumeraAshfaq | 2024-06-24

The first equation demonstrates the Identity Property of Division, where dividing a number by 1 does not change its value. The second equation shows the Commutative Property of Multiplication, which states that the order of factors does not affect the product. Therefore, the answers are B and D respectively.
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Answered by Bharti | 2025-01-12