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Read this word problem. $\newline$ The overnight low temperature in Cassidy City was $-17 \, ^{\circ}\mathrm{F}$ . The overnight low temperature in Shakerville was $-6 \, ^{\circ}\mathrm{F}$ . How much warmer was Shakerville than Cassidy City? $\newline$ To solve the problem, Manny subtracted $-6 - (-17)$ and came up with an answer of $-11 \, ^{\circ}\mathrm{F}$ . Is Manny correct? Why or why not? $\newline$ Choices: $\newline$ (A) Yes, Manny is correct. $\newline$ (B) No. The answer should have been $11 \, ^{\circ}\mathrm{F}$ , not $-11 \, ^{\circ}\mathrm{F}$ , because Shakerville was warmer. $\newline$ (C) No. Manny should have added $-17 + -6$ because Shakerville was warmer.

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Add and subtract integers: word problems

Full solution

Q. Read this word problem.

\newline

The overnight low temperature in Cassidy City was

-17 \, ^{\circ}\mathrm{F}

. The overnight low temperature in Shakerville was

-6 \, ^{\circ}\mathrm{F}

. How much warmer was Shakerville than Cassidy City?

\newline

To solve the problem, Manny subtracted

-6 - (-17)

and came up with an answer of

-11 \, ^{\circ}\mathrm{F}

. Is Manny correct? Why or why not?

\newline

Choices:

\newline

(A) Yes, Manny is correct.

\newline

(B) No. The answer should have been

11 \, ^{\circ}\mathrm{F}

, not

-11 \, ^{\circ}\mathrm{F}

, because Shakerville was warmer.

\newline

(C) No. Manny should have added

-17 + -6

because Shakerville was warmer.

Calculate Temperature Difference: To find out how much warmer Shakerville was, we need to calculate the difference in temperature between Shakerville and Cassidy City.
Subtract Lower Temperature: Subtract the lower temperature ( $-17 \,\text{°F}$ ) from the higher temperature ( $-6 \,\text{°F}$ ): $-6 - (-17)$ .
Convert Negative Subtraction: When subtracting a negative, it's like adding a positive, so $-6 - (-17)$ becomes $-6 + 17$ .
Add Temperatures: Now, add $-6$ and $17$ : $-6 + 17 = 11$ °F.
Verify Correctness: Manny's answer of $-11 \, ^{\circ}\mathrm{F}$ is incorrect because the calculation should result in a positive difference, indicating that Shakerville was warmer.

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