Video: Understanding Subtraction of Integers as Adding the Inverse

A teacher asked his students to find an expression that can be used to find the difference between the height of the Empire State Building, 443.2 m, and the height of the Eiffel Tower, 324 m. The first student said the expression is 443.2 − (−324), while the second said that it is 443.2 + (−324). Who was correct?

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Video Transcript

A teacher asked his students to find an expression that can be used to find the difference between the height of the Empire State Building, 443.2 meters, and the height of the Eiffel Tower, 324 meters. The first student said the expression is 443.2 minus negative 324, while the second student said that it is 443.2 plus negative 324. Who was correct?

Let’s think about what we know. If we let this image represent the Empire State Building, that is, 443.2 meters tall, and this represent the Eiffel Tower, at 324 meters, this space will be the difference between the two heights. Student one says we could represent this space by saying 443.2 minus negative 324, while student two says it would be 443.2 plus negative 324.

We know that subtracting a negative is equal to adding. And that means student one is saying that the difference between the two heights is 443.2 plus 324. And student two has adding a negative. And we can rewrite adding a negative as subtracting, 443.2 minus 324.

If we follow student one’s expression, we will be adding the two heights together. But if we follow student two’s expression, we will be subtracting the height of the Eiffel Tower from that of the height of the Empire State Building, which would give us the difference in heights. And so the second student has found a correct expression to find the difference in height between the Empire State Building and the Eiffel Tower.

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