To find the product of -2 and 5 using addition, we can use integer tiles and a number line to visually represent the multiplication. Here's how we can approach this:
Step 1: Understanding the Product
Multiplying -2 by 5 means we are essentially adding -2 to itself a total of 5 times. In mathematical terms: \[ -2 \times 5 = -2 + -2 + -2 + -2 + -2 \]
Step 2: Using Integer Tiles
Imagine we have tiles that represent positive and negative integers:
- A red tile represents -1 (negative).
- A yellow tile represents +1 (positive).
To represent -2, we would use two red tiles (since -2 is equal to -1 + -1).
For the product of -2 and 5, we need to perform the addition of -2 five times:
- Add two red tiles (for the first -2).
- Add two more red tiles (for the second -2).
- Keep adding until you have a total of five sets of two red tiles.
Counting all the red tiles:
- First set: 2 red tiles (representing the first -2)
- Second set: 2 red tiles (representing the second -2)
- Third set: 2 red tiles (representing the third -2)
- Fourth set: 2 red tiles (representing the fourth -2)
- Fifth set: 2 red tiles (representing the fifth -2)
Total:
We would have a total of 10 red tiles, which represents -10.
Step 3: Using the Number Line
Using a number line helps to visualize the process as well:
- Start at 0.
- The first step: move 2 units to the left (to -2).
- The second step: move another 2 units to the left (to -4).
- The third step: move another 2 units to the left (to -6).
- The fourth step: move another 2 units to the left (to -8).
- The fifth step: move another 2 units to the left (to -10).
Result:
After five steps of moving 2 units left, you end up at -10.
Therefore, the product of -2 and 5 is: \[ -2 \times 5 = -10 \]
Summary:
Both methods—using integer tiles and the number line—demonstrate that multiplying -2 by 5 results in -10.