Which equation shows the identity property of multiplication? $\newline$ Choices: $\newline$ (A) $(p + q) \cdot r = p \cdot r + q \cdot r$ $\newline$ (B) $p = p \cdot 1$ $\newline$ (C) $p + r = p \cdot q$ $\newline$ (D) $q \cdot p = p \cdot q$

Full solution

Q. Which equation shows the identity property of multiplication?

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Choices:

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(A)

(p + q) \cdot r = p \cdot r + q \cdot r

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(B)

p = p \cdot 1

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(C)

p + r = p \cdot q

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(D)

q \cdot p = p \cdot q

Understand Identity Property: Understand the identity property of multiplication. The identity property of multiplication states that any number multiplied by $1$ gives the number itself. This means that if we have a number ' $p$ ', then $p$ multiplied by $1$ should give us ' $p$ '.
Analyze Choices: Analyze each choice to see which one represents the identity property of multiplication. $\newline$ (A) $(p + q) \cdot r = p \cdot r + q \cdot r$ - This is the distributive property, not the identity property.
Check Remaining Choices: Continue analyzing the choices. $\newline$ (B) $p = p \cdot 1$ - This choice shows that $p$ multiplied by $1$ gives us $p$ , which is exactly the identity property of multiplication.
Check Remaining Choices: Continue analyzing the choices. $\newline$ (B) $p = p \cdot 1$ - This choice shows that $p$ multiplied by $1$ gives us $p$ , which is exactly the identity property of multiplication.Check the remaining choices for completeness. $\newline$ (C) $p + r = p \cdot q$ - This does not represent any property of multiplication related to the identity property. $\newline$ (D) $q \cdot p = p \cdot q$ - This is the commutative property of multiplication, not the identity property.