Select all of the equations below that are equivalent to: $\newline$ $rs = 22$ $\newline$ Use properties of equality. $\newline$ Multi-select Choices: $\newline$ (A) $\frac{rs}{11} = 2$ $\newline$ (B) $\frac{rs}{11} = 4$ $\newline$ (C) $\frac{rs}{-11} = -3$ $\newline$ (D) $\frac{rs}{2} = 11$

Full solution

Q. Select all of the equations below that are equivalent to:

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rs = 22

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Use properties of equality.

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Multi-select Choices:

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(A)

\frac{rs}{11} = 2

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(B)

\frac{rs}{11} = 4

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(C)

\frac{rs}{-11} = -3

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(D)

\frac{rs}{2} = 11

Analyze Equation and Properties: Analyze the given equation $rs = 22$ and the properties of equality to determine which of the multi-select choices are equivalent. $\newline$ We will use the property of equality that allows us to divide both sides of an equation by the same nonzero number to maintain equality.
Check Choice (A): Check choice (A) $\frac{rs}{11} = 2$ . $\newline$ Divide both sides of the original equation $rs = 22$ by $11$ . $\newline$ $\frac{rs}{11} = \frac{22}{11}$ $\newline$ $\frac{rs}{11} = 2$ $\newline$ This matches choice (A), so (A) is equivalent.
Check Choice (B): Check choice (B) $\frac{r}{s}=\frac{11}{4}$ . $\newline$ Divide both sides of the original equation $rs = 22$ by $11$ . $\newline$ $\frac{rs}{11} = \frac{22}{11}$ $\newline$ $\frac{rs}{11} = 2$ $\newline$ This does not match choice (B), so (B) is not equivalent.
Check Choice (C): Check choice (C) $\frac{rs}{-11} = -3$ . $\newline$ Divide both sides of the original equation $rs = 22$ by $-11$ . $\newline$ $\frac{rs}{(-11)} = \frac{22}{(-11)}$ $\newline$ $\frac{rs}{(-11)} = -2$ $\newline$ This does not match choice (C), so (C) is not equivalent.
Check Choice (D): Check choice (D) $\frac{rs}{2} = 11$ . $\newline$ Divide both sides of the original equation $rs = 22$ by $2$ . $\newline$ $\frac{rs}{2} = \frac{22}{2}$ $\newline$ $\frac{rs}{2} = 11$ $\newline$ This matches choice (D), so (D) is equivalent.