Video: Describing Situations in Which Opposite Quantities Combine to Make Zero

One of addition’s properties is that the sum of a number and its opposite is always equal to zero. Which of the following situations does NOT demonstrate this property of addition? [A] The school’s football team lost 10 yards on their first down and lost 10 yards on the second down. [B] The school’s football team lost 5 yards on their first down and gained 5 yards on the second down. [C] On a Sunday, the temperature was −2°F outside and 2°F inside. [D] A ball was kicked 10 m upward in the air, and then it fell down 10 m. [E] A bucket descended 100 m down a well, and then it was lifted 100 m up the well.

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Video Transcript

One of addition’s properties is that the sum of a number and its opposite is always equal to zero. Which of the following situations does NOT demonstrate this property of addition? Is it A) the school’s football team lost 10 yards on their first down and lost 10 yards on the second down? Is it B) the school’s football team lost five yards on their first down and gained five yards on the second down? Is it C) on a Sunday, the temperature was negative two degrees Fahrenheit outside and two degrees Fahrenheit inside? D) A ball was kicked 10 metres upward in the air, and then it fell down 10 metres. Or (E) a bucket descended 100 metres down a well, and then it was lifted 100 metres up the well.

In order to answer this question, we need to decide which of the five situations does not demonstrate the property. We are looking for a situation where the sum is not equal to zero.

In situation, E the bucket initially descends 100 metres down the well. This is equal to negative 100. It was then lifted 100 metres up the well. This would be equal to positive 100. The sum of negative 100 and positive 100 is zero. Therefore, this is not the correct answer.

In situation D, the ball was kicked 10 metres upward in the air. This would be equal to positive 10. The ball then fell down 10 metres. This would be equal to negative 10. Once again, the sum of these is equal to zero. Positive 10 plus negative 10 equals zero. Situation D is not the correct answer.

In situation C, the temperature outside was negative two. The temperature inside was two degrees Fahrenheit, or positive two. Once again, the sum of these two values is equal to zero, as it is the number two and its opposite. We are now left with two possible correct answers, option B and option A.

In option B, the school’s football team lost five yards on their first down. This is equal to negative five. The team gained five yards on the second down. This is equal to positive five. The sum of negative five and positive five is zero. Therefore, we can also rule out option B.

In option A, the football team lost 10 yards on their first down. This is equal to negative 10. They also lost 10 yards on the their second down, which is also equal to negative 10. Negative 10 plus negative 10 is equal to negative 20. As this can also be written as negative 10 minus 10. As this answer is not equal to zero, situation A is the correct answer.

The situation that does not demonstrate the property of addition whereby the sum of a number and its opposite is always equal to zero is situation A. The school’s football team lost 10 yards on their first down and lost 10 yards on the second down.

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