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Operations on Integers

Guillermo Bautista, Feb 16, 2022

1. Addition of Integers on the Number Line
2. Addition of Integers Practice Exercise
3. Subtraction of Integers Practice Exercise
4. Multiplication of Integers Practice Exercise
5. Division of Integers Practice Exercise

1.

Addition of Integers on the Number Line

I. Number as Movement

Move the slider and observe what happens.

1.) On the number line, the point 0 is called the [b]origin[/b]. In terms of movement, what does 5 mean?

A movement from the origin to the point 5 units to the RIGHT of 0. A movement from the point 5 units to the RIGHT of 0 to the origin. A movement from the origin to the point 5 units to the LEFT of 0. A movement from the point 5 units to the LEFT of 0 to the origin.

2.) In terms of movement, what does -3 mean?

A movement from the point 3 units to the RIGHT of 0 to the origin. A movement from the origin to the point 3 units to the right of 0. A movement from the point 3 units to the LEFT of 0 to the origin. A movement from the origin to the point 3 units to the left of 0.

II. Addition of Integers

Move the two sliders and observe what happens.

1.) Use the sliders above to add 2 and 3. In terms of movement, what does 2 + 3 mean?

From the origin, move [b]2 units to the left[/b], and then [b]3 units to the right[/b]. From the origin, move [b]2 units to the right[/b], and then [b]3 units to the right[/b]. From the origin, move [b]2 units to the left[/b], and then [b]3 units to the left.[/b] From the origin, move [b]2 units to the right[/b], and then [b]3 units to the left[/b].

2.) Use the sliders above to add -3 and -4. In terms of movement, what does (-3) + (-4) mean?

From the origin, move [b]3 units to the left[/b], and then [b]4 units to the left.[/b] From the origin, move [b]3 units to the right[/b], and then [b]4 units to the right[/b]. From the origin, move [b]3 units to the left[/b], and then [b]4 units to the right[/b]. From the origin, move [b]3 units to the right[/b], and then [b]4 units to the left[/b].

3.) Based on your answer above, what is the sum (-3) + (-4)?

-7

4.) Use the sliders above to add -6 and 3. In terms of movement, what does (-6) + (3) mean?

From the origin, move [b]6 units to the left[/b], and then [b]3 units to the left.[/b] From the origin, move [b]6 units to the left[/b], and then [b]3 units to the right[/b]. From the origin, move [b]6 units to the right[/b], and then [b]3 units to the right[/b]. From the origin, move [b]6 units to the right[/b], and then [b]3 units to the left[/b].

5.) Based on your answer above, what is the sum (-6) + (3)?

-3

6.) Using the sliders above to add 6 and -3. In terms of movement, what does 6 + (-3) mean?

From the origin, move [b]6 units to the right[/b], and then [b]3 units to the right[/b]. From the origin, move [b]6 units to the left[/b], and then [b]3 units to the left.[/b] From the origin, move [b]6 units to the left[/b], and then [b]3 units to the right[/b]. From the origin, move [b]6 units to the right[/b], and then [b]3 units to the left[/b].

7.) Based on your answer above, what is the sum (6) + (-3)?

8.) Based on your observation above, write your thoughts about adding integers that are[br][br](1) both positive[br](2) both negative[br](3) positive and negative

– Guillermo Bautista

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