Question

The product –2 • (–5) is shown on the number line. Use the drop-down menus to explain how the model on the number line could be used to find the answer. Number line from -10 to 10. Start at -10. Count up by 1. 2 black arrows are shown above the number line. First from -5 to 10 above which from -5 to 0 Starting at 0, move twice to the Choose... 5 spaces. 2 • –5= Choose... . Since –2 • (–5) is Choose... 2 • (–5), the number line shows the same distance to the Choose... of 0.

Answer 1

The procedure for representing the product $-2\cdot (-5)$ is described as following:

1) Draw the distance of the first negative number.

2) Extend the distance by the magnitude of the second negative number.

3) Draw the distance of the reflection of the result found in 2).

In the number line negative numbers represent leftward distances. The product of a negative number and a positive number is equal to the distance of the negative one by the number of times such distance is repeated. In addition, we know by algebra that the product of two negative numbers equals a positive number, so we know that distance becomes rightwards due to reflection on the former line segment.

The procedure is described as following:

1) Draw the distance of the first negative number.

2) Extend the distance by the magnitude of the second negative number.

3) Draw the distance of the reflection of the result found in 2).

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