Miki is trying to help her younger brother understand why 12−(−5) is equal to 17. She draws a number line to help. Explain how a number line could help to show that 12−(−5) is equal to 17. (1 point)
Responses
Starting at 12 on the number line, you must move 5 units in the negative direction to get to 7.
Starting at 12 on the number line, you must move 5 units in the negative direction to get to 7.
Starting at −5 on the number line, you must move 17 units in the positive direction to get to 12.
Starting at negative 5 on the number line, you must move 17 units in the positive direction to get to 12.
Starting at −5 on a number line, you must move 12 units in the positive direction to get to 17.
Starting at negative 5 on a number line, you must move 12 units in the positive direction to get to 17.
Starting at 12 on the number line, you must move 17 units in the negative direction to get to −5.
Starting at 12 on the number line, you must move 17 units in the negative direction to get to −5.
This explanation is incorrect. The correct explanation is: Starting at 12 on the number line, you must move 5 units in the negative direction to get to 7.
Connect the model −(7+7+7+7+7+7) to the algorithm for solving the multiplication problem it models.(1 point)
Responses
The model represents 7⋅(−6), which is solved by multiplying 7 times 6 and changing the sign to get −42.
The model represents 7 times left parenthesis negative 6 right parenthesis , which is solved by multiplying 7 times 6 and changing the sign to get negative 42 .
The model represents 6⋅(−7), which is solved by multiplying 6 times 7 and changing the sign to get −42.
The model represents 6 times left parenthesis negative 7 right parenthesis , which is solved by multiplying 6 times 7 and changing the sign to get negative 42 .
The model represents −7⋅6, which is solved by multiplying 7 times 6 and changing the sign to get −42.
The model represents negative 7 times 6 , which is solved by multiplying 7 times 6 and changing the sign to get negative 42 .
The model represents −6⋅7, which is solved by multiplying 6 times 7 and changing the sign to get −42.
The model represents 7⋅(−6), which is solved by multiplying 7 times 6 and changing the sign to get −42.
What model can you use to represent −30÷−6?(1 point)
Responses
(−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)=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
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
(−6)+(−6)+(−6)+(−6)+(−6)=5(−6)=−30
(−6)+(−6)+(−6)+(−6)+(−6)=5(−6)=−30
Starting at 12 on the number line, you must move 17 units in the negative direction to get to -5.
The correct explanation is: Starting at 12 on the number line, you must move 5 units in the negative direction to get to 7.
To understand why 12 - (-5) is equal to 17, Miki drew a number line. On this number line, she marked the number 12. Subtracting a negative number means moving in the opposite direction (positive). So, to subtract -5 from 12, Miki started at 12 and moved 5 units in the negative (left) direction. This brought her to the number 7 on the number line.
Therefore, starting at 12 on the number line and moving 5 units in the negative direction, she arrived at 7. And since 7 is less than 17, the original expression 12 - (-5) is not equal to 17.