Connect the model 48+(−16)+(−16)+(−16)=0 to the algorithm for solving the division problem it models.
The model 48+(−16)+(−16)+(−16)=0 can be connected to the algorithm for solving the division problem it models by using the concept of balancing equations.
In this model, the equation is balanced by adding three negative numbers (-16, -16, -16) to the positive number 48, resulting in a sum of 0. This reflects the idea that when dividing a number by a certain value, if we subtract the same value repeatedly until we reach 0, we have effectively divided the number.
Let's say we want to divide 48 by a value x. We can apply the same operation repeatedly until we reach 0:
48 - x = 32
32 - x = 16
16 - x = 0
In this case, the value of x would be 16. Thus, the model represents the algorithm for solving the division problem as follows:
48 ÷ x = 0,
where x = 16.
To connect the model 48 + (-16) + (-16) + (-16) = 0 to the algorithm for solving the division problem it models, you need to understand that this equation represents a balance model. Dividing a quantity into equal parts can be seen as a subtraction operation in this context.
Here's how to use the algorithm to solve the division problem represented by this model step-by-step:
Step 1: Start with the total value on the left side of the equation, which is 48.
Step 2: Subtract the first equal part from this total. In this case, the first equal part is -16.
48 - 16 = 32
Step 3: Subtract the second equal part from the new total calculated in the previous step. Again, the equal part is -16.
32 - 16 = 16
Step 4: Subtract the third equal part from the current total. The third equal part is also -16.
16 - 16 = 0
Consequently, the algorithm shows that dividing the quantity represented by the equation 48 + (-16) + (-16) + (-16) = 0 into equal parts of -16 gives a final result of 0.
So, the connection between the model and the algorithm is that the subtraction operation in the algorithm represents dividing the total quantity into equal parts.
To connect the model 48 + (-16) + (-16) + (-16) = 0 to the algorithm for solving the division problem it models, we need to follow these steps:
Step 1: Understand the Model:
The equation 48 + (-16) + (-16) + (-16) = 0 represents a subtraction problem where 48 is being divided by -16. The result of the division is 0, indicating that -16 can be subtracted from 48 three times until there is nothing left.
Step 2: Define the Algorithm:
The algorithm for division can be stated as follows: "Divide the dividend by the divisor while subtracting the divisor from the dividend until there is nothing left."
Step 3: Apply the Algorithm to the Model:
In this case, we can start with the dividend (48) and the divisor (-16). We repeatedly subtract the divisor from the dividend while keeping track of the number of times the subtraction is performed until the dividend becomes zero.
Step 4: Perform the Subtractions:
Subtracting -16 from 48, we get:
48 - (-16) = 48 + 16 = 64
We still have a non-zero remainder, so we continue subtracting:
64 - (-16) = 64 + 16 = 80
Again, there is a non-zero remainder, so we continue:
80 - (-16) = 80 + 16 = 96
At this point, the dividend (96) is greater than zero, but smaller than the divisor (-16). So, we cannot subtract -16 from 96 anymore without getting a negative number.
Since the dividend has not reached zero, but we cannot perform any further subtractions, we conclude that the result of dividing 48 by -16 is 0, and there is a remainder of 96.
Therefore, the model 48 + (-16) + (-16) + (-16) = 0 is connected to the algorithm for solving the division problem it models.