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What model can you use to represent −16÷8 ?
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What model can you use to represent 16÷4 ?(1 point) Responses −4−4−4−4=−16 negative 4 minus 4 minus 4 minus 4 equals negative 16 4+4+4+4=16 4 plus 4 plus 4 plus 4 equals 16 16−4−4−4−4=16−4(4)=0 16 minus 4 minus 4 minus 4 minus 4 equals 16 minus 4 left parenthesis 4 right parenthesis equals 0 −16−(−4)−(−4)−(−4)−(−4)=0
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What division does the model represent? −24−(−8)−(−8)−(−8)=−24−3(−8)=0 (1 point) Responses 3⋅(−8) 3 times left parenthesis negative 8 right parenthesis −24÷−3 negative 24 divided by negative 3 −24÷−8 negative 24 divided by negative 8 24÷8
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What model can you use to represent 10÷0 ?(1 point) Responses 0+0=0 0 plus 0 equals 0 0−0(10)=0 0 minus 0 left parenthesis 10 right parenthesis equals 0 10÷0 is undefined because you cannot divide by 0. 10 divided by 0 is undefined because you cannot divide by 0. 0+0+0+0+0+0+0+0+0+0=0
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What does the model represent? −15+3+3+3+3+3=−15+5(3)=0 (1 point) Responses 15÷3 15 divided by 3 −15÷−5 negative 15 divided by negative 5 −15÷3 negative 15 divided by 3 3⋅−5
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What model can you use to represent 28÷−7 ?(1 point) Responses 28−4−4−4−4−4−4−4=28−7(4)=0 28 minus 4 minus 4 minus 4 minus 4 minus 4 minus 4 minus 4 equals 28 minus 7 left parenthesis 4 right parenthesis equals 0 28+(−7)+(−7)+(−7)+(−7)=28+4(−7)=0 28 plus left parenthesis negative 7 right parenthesis plus left parenthesis negative 7 right parenthesis plus left parenthesis negative 7 right parenthesis plus left parenthesis negative 7 right parenthesis equals 28 plus 4 left parenthesis negative 7 right parenthesis equals 0 (−7)+(−7)+(−7)+(−7)=4(−7)=−28 left parenthesis negative 7 right parenthesis plus left parenthesis negative 7 right parenthesis plus left parenthesis negative 7 right parenthesis plus left parenthesis negative 7 right parenthesis equals 4 left parenthesis negative 7 right parenthesis equals negative 28 −28−(−7)−(−7)−(−7)−(−7)=0
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To represent the operation \(-16 \div 8\), you can use several models, including:
1. **Number Line Model**: Draw a number line with both negative and positive numbers. Starting at \(-16\), you can show the division by moving to the left in increments of 8. Each jump to the left represents subtracting 8, showing how many times 8 fits into \(-16\).
2. **Set Model**: You could illustrate this concept using sets of objects. If you have a total of \(-16\) (which could be represented as 16 negative units), dividing that into groups of \(8\) would show how many groups of \(8\) can be formed. Here, you would find \(2\) groups of \(8\) can be made from \(-16\).
3. **Area Model**: You can use a rectangle to represent a total area of \(-16\) square units, and then divide it into \(8\) equal parts. Each part would thus represent \(-2\) square units, helping visualize the negative division.
4. **Equation Method**: You can express it mathematically as \(-16 \div 8 = x\). By solving for \(x\), you’d find \(x = -2\). Thus, the division gives you the quotient directly.
Using any of these models will help you understand the concept of dividing negative numbers and the result of \(-16 \div 8 = -2\).
1. **Number Line Model**: Draw a number line with both negative and positive numbers. Starting at \(-16\), you can show the division by moving to the left in increments of 8. Each jump to the left represents subtracting 8, showing how many times 8 fits into \(-16\).
2. **Set Model**: You could illustrate this concept using sets of objects. If you have a total of \(-16\) (which could be represented as 16 negative units), dividing that into groups of \(8\) would show how many groups of \(8\) can be formed. Here, you would find \(2\) groups of \(8\) can be made from \(-16\).
3. **Area Model**: You can use a rectangle to represent a total area of \(-16\) square units, and then divide it into \(8\) equal parts. Each part would thus represent \(-2\) square units, helping visualize the negative division.
4. **Equation Method**: You can express it mathematically as \(-16 \div 8 = x\). By solving for \(x\), you’d find \(x = -2\). Thus, the division gives you the quotient directly.
Using any of these models will help you understand the concept of dividing negative numbers and the result of \(-16 \div 8 = -2\).
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The correct response to represent \(16 \div 4\) is:
**C) \(4 + 4 + 4 + 4 = 16\)**
This shows that if you add \(4\) four times, you get \(16\), which corresponds to the division operation \(16 \div 4 = 4\).
**C) \(4 + 4 + 4 + 4 = 16\)**
This shows that if you add \(4\) four times, you get \(16\), which corresponds to the division operation \(16 \div 4 = 4\).
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The model \(-24 - (-8) - (-8) - (-8) = -24 - 3(-8) = 0\) represents:
**B) \(-24 \div -3\)**
This is because you can interpret the expression as taking away three groups of \(-8\) from \(-24\), which aligns with the division by \(-3\).
**B) \(-24 \div -3\)**
This is because you can interpret the expression as taking away three groups of \(-8\) from \(-24\), which aligns with the division by \(-3\).
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GPT-4o mini
The correct response to represent \(10 \div 0\) is:
**C) \(10 \div 0\) is undefined because you cannot divide by 0.**
This statement accurately reflects that division by zero is not defined in mathematics.
**C) \(10 \div 0\) is undefined because you cannot divide by 0.**
This statement accurately reflects that division by zero is not defined in mathematics.
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The model \(-15 + 3 + 3 + 3 + 3 + 3 = -15 + 5(3) = 0\) represents:
**C) \(-15 \div 3\)**
This is because the expression demonstrates adding \(3\) five times to \(-15\) and that addition of \(3\) could be interpreted in a context related to division. The alternative interpretations involving \(15 \div 3\) or \(-15 \div -5\) do not directly represent the model provided.
**C) \(-15 \div 3\)**
This is because the expression demonstrates adding \(3\) five times to \(-15\) and that addition of \(3\) could be interpreted in a context related to division. The alternative interpretations involving \(15 \div 3\) or \(-15 \div -5\) do not directly represent the model provided.
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GPT-4o mini
The model that can be used to represent \(28 \div -7\) is:
**C) \(28 + (-7) + (-7) + (-7) + (-7) = 28 + 4(-7) = 0\)**
This representation works because it shows that adding four groups of \(-7\) to \(28\) results in zero, which also reflects the concept of dividing \(28\) by \(-7\) to find how many times \(-7\) fits into \(28\), giving the result of \(-4\).
However, note that the option describing the division accurately isn't explicitly stated here, but this model correlates with the concept of breaking down \(28\) in terms of \(-7\).
**C) \(28 + (-7) + (-7) + (-7) + (-7) = 28 + 4(-7) = 0\)**
This representation works because it shows that adding four groups of \(-7\) to \(28\) results in zero, which also reflects the concept of dividing \(28\) by \(-7\) to find how many times \(-7\) fits into \(28\), giving the result of \(-4\).
However, note that the option describing the division accurately isn't explicitly stated here, but this model correlates with the concept of breaking down \(28\) in terms of \(-7\).