What model can you use to represent −30÷−6?(1 point)
Responses
(−6)+(−6)+(−6)+(−6)+(−6)=5(−6)=−30
left parenthesis negative 6 right parenthesis plus left parenthesis negative 6 right parenthesis plus left parenthesis negative 6 right parenthesis plus left parenthesis negative 6 right parenthesis plus left parenthesis negative 6 right parenthesis plus left parenthesis negative 6 right parenthesis equals 5 left parenthesis negative 6 right parenthesis equals negative 30
(−5)+(−5)+(−5)+(−5)+(−5)+(−5)=6(−5)=−30
negative 5 plus negative 5 plus negative 5 plus negative 5 plus negative 5 plus negative 5 equals 6 left parenthesis negative 5 right parenthesis equals negative 30
30−6−6−6−6−6=30−5(6)
30 minus 6 minus 6 minus 6 minus 6 minus 6 equals 30 minus 5 left parenthesis 6 right parenthesis
−30−(−6)−(−6)−(−6)−(−6)−(−6)=−30−5(−6)=0
negative 30 minus left parenthesis negative 6 right parenthesis minus left parenthesis negative 6 right parenthesis minus left parenthesis negative 6 right parenthesis minus left parenthesis negative 6 right parenthesis minus left parenthesis negative 6 right parenthesis equals negative 30 minus 5 left parenthesis negative 6 right parenthesis equals 0
What is the result of dividing −245÷35?(1 point)
The result of dividing −245÷35 is -7.
What is the result of the division modeled by −108−(−18)−(−18)−(−18)−(−18)−(−18)−(−18)=0?(1 point)
The result of the division modeled by −108−(−18)−(−18)−(−18)−(−18)−(−18)−(−18)=0 is -108÷(-18) = 6.
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.(2 points)
To represent the expression −17−(−3) using a two-color counter model, we start with 17 black counters to represent -17. Then, we subtract 3 white counters to represent the subtraction of -3.
If Elaine's answer of -14 is correct, then the final count of the two-color counters should be -14. We can count the total number of counters in the model and observe if it matches -14.
If the result is indeed -14, it confirms that Elaine's answer is correct. However, if the count of the counters does not match -14, then Elaine's answer is incorrect.
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.
To represent the expression −17−(−3) using a two-color counter model, we can start with 17 red counters to represent -17 and subtract 3 blue counters to represent the subtraction of -3.
If Elaine's answer of -14 is correct, then the final count of the two-color counters should be -14. We can count the total number of counters in the model and observe if it matches -14.
In the two-color counter model, each red counter represents a negative value and each blue counter represents a positive value. Adding or removing blue counters represents increasing or decreasing the overall value, while adding or removing red counters represents decreasing or increasing the overall value.
By counting the total number of counters in the model and evaluating their colors, we can determine the final result. If the count of red and blue counters matches -14, then Elaine's answer is correct. However, if the count does not match -14, then Elaine's answer is incorrect and further calculation or double-checking is needed.
To represent −30÷−6, you can use the model of repeated subtraction.
Here's how you can use the model to solve this problem:
1. Start with the dividend, which is −30.
2. Divide the dividend by the divisor, which is −6.
3. Subtract the divisor −6 from the dividend −30. You get −24.
4. Repeat the subtraction process: subtract −6 from −24. You get −18.
5. Repeat this process until you have subtracted −6 a total of 5 times.
- Subtract −6 from −18 to get −12.
- Subtract −6 from −12 to get −6.
- Subtract −6 from −6 to get 0.
6. After 5 repetitions, you reach a result of 0.
Therefore, using the repeated subtraction model, you can see that −30÷−6 is equal to 5.