How can you represent -5 *-4 with a model?
-5 + -5 + -5 + -5
5*4
4+4+4+4+4
- (-4 + -4 +-4 +- 4 -4)
One way to represent -5 * -4 with a model is by using a number line. Start at 0 and move 5 units to the left to represent -5. Then, move 4 units to the left four times to represent -4. The total distance moved would be 20 units. Therefore, -5 * -4 equals 20.
Another way to represent -5 * -4 with a model is by using counters or objects. Take 5 red counters to represent -5 and 4 black counters to represent -4. Arrange them in a grid with 5 rows and 4 columns. Count the total number of counters, which would be 20. Therefore, -5 * -4 equals 20.
Additionally, you can represent -5 * -4 using the concept of repeated addition. Take -5 and add it to itself 4 times: -5 + -5 + -5 + -5. The sum of these additions would be -20. Therefore, -5 * -4 equals -20.
You can also represent -5 * -4 using the concept of additive inverse. This can be done by taking -4 and adding its additive inverse -4, four times: -4 + -4 + -4 + -4 + -4. The sum of these additions would be -20. Therefore, -5 * -4 equals -20.
To represent -5 * -4 with a model, you can imagine two concepts:
1. Using a number line:
Start at 0 on a number line and move 5 units to the left, representing -5. Then, move 4 units to the left from the point representing -5, which will show -5 multiplied by -4.
2. Using a set of chips or objects:
Take 5 identical objects and label them as -5. Then, take another 4 identical objects and label them as -4. Arrange them in a line or grid fashion, emphasizing that they are negatives. Counting the objects from left to right will show the result of -5 * -4.
Some possible models representing -5 * -4 could be:
-5 + -5 + -5 + -5 + -5
5*4
4 + 4 + 4 + 4 + 4
- (-4 + -4 + -4 + -4 + -4)
To represent -5 * -4 with a model, you can use the concept of repeated addition or a number line.
1. Repeated Addition:
You can represent -5 * -4 by using repeated addition with negative integers. Start with -5, and add it to itself for a total of -4 times.
-5 + -5 + -5 + -5 + -5 = -25
So, -5 * -4 = -25.
2. Number Line:
To represent -5 * -4 on a number line, start at 0 and count backwards in increments of -5 for a total of -4 iterations.
0 - 5 - 10 - 15 - 20 = -20
So, -5 * -4 = -20.
Both methods demonstrate that when you multiply a negative number (-5) by another negative number (-4), the result is a positive number (-25 or -20 in this case).