Elaine used the subtraction algorithm to subtract −17−(−3)
. She got the answer −14
, but she does not feel confident that she is correct. Connect the expression −17−(−3)
to a two-color counter model. Explain how the two-color counter model can be used to confirm whether Elaine’s answer is correct.
In a two-color counter model, each color represents a positive or negative value. Let's say one color represents positive values, and the other color represents negative values.
To represent the subtraction expression −17−(−3) using two-color counters, we start with 17 counters of the positive color (to represent −17) and add 3 counters of the negative color (to represent −(−3)).
Now, we need to subtract the negative value. To do so, we remove 3 counters of the negative color from the model. The result of this subtraction should be the same as Elaine's answer, which is −14.
By physically manipulating the counters in the two-color counter model, we can visually confirm whether Elaine's answer is correct. If, after removing the 3 counters, we are left with 14 counters of the positive color, then Elaine's answer is confirmed to be correct. However, if we have a different number of counters remaining, then Elaine's answer is incorrect.
how do you show how to solve this problem
Apologies for the confusion. Let me provide a step-by-step explanation on how to solve the problem using the subtraction algorithm.
The given expression is −17−(−3).
To solve this, we can rewrite the subtraction of a negative number as an addition of a positive number. So, −17−(−3) is equivalent to −17+3.
To confirm Elaine's answer, which is −14, we can use the following steps:
1. Start with the value −17.
2. Add 3, which represents the positive value in the subtraction: −17+3.
3. Perform the addition: -17 + 3 = -14.
Based on Elaine's answer, the result is −14.
We can use a two-color counter model to visually represent this process as well. By starting with 17 counters of one color to represent −17 and adding 3 counters of the other color to represent +3, we would end up with 14 of the first color, confirming Elaine's answer of −14.
I apologize for the previous confusion and hope this explanation helps clarify the solution process.
To connect the expression −17−(−3) to a two-color counter model, we can represent the negative numbers using one color (let's say red) and the positive numbers using another color (let's say blue).
First, start with 17 blue counters to represent the absolute value of 17 (|−17|). Then, arrange them in a vertical line or stack.
Next, to subtract −3, we need to remove 3 red counters from the stack. Since subtracting a negative is equivalent to adding, we can think of it as adding 3 blue counters instead.
After removing the 3 red counters, we are left with 14 blue counters. This represents the result of the subtraction operation, which is 14.
By visually representing the expression using a two-color counter model, we can confirm whether Elaine's answer of −14 is correct. If the model shows that we are left with 14 blue counters, then Elaine's answer is indeed correct.
To connect the expression −17−(−3) to a two-color counter model, we first need to understand what each number represents in the context of the counters.
In a two-color counter model, each color represents a positive or negative value. For example, let's say red counters represent positive values and blue counters represent negative values.
With that in mind, let's represent the expression −17−(−3) using two-color counters.
1. Start with 17 red counters representing the absolute value of 17 (-17).
2. Subtract by taking away 3 blue counters representing the absolute value of (-3).
3. Remove 3 red counters.
Now, let's analyze the model to confirm Elaine's answer of -14.
- The remaining red counters represent the positive value (17 - 3 = 14), which is correct based on Elaine's answer.
- The presence or absence of the blue counters represents the negative value. In this case, since we have removed 3 blue counters, it means we took away a negative value (-3).
Based on the model, there are no blue counters remaining, indicating that -14 is a valid result.
To confirm Elaine's answer further, we can also use a number line. Starting from -17, if we move 3 units to the right (opposite of the negative direction), we arrive at -14, which aligns with the answer she obtained.
Therefore, both the two-color counter model and the number line confirm Elaine's answer of -14.