What model can you use to represent −16÷8 ?

Question

GPT-4o mini · Answer

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 $-16 \div 8 = -2$.

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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

Say A, B, C, or D

GPT-4o mini · Answer

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 $16 \div 4 = 4$.

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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

Say A, B, C, or D

GPT-4o mini · Answer

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 $-3$.

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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

Say A, B, C, or D

GPT-4o mini · Answer

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.

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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

GPT-4o mini · Answer

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.

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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

GPT-4o mini · Answer

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 $-7$.