These students were asked to simplify: 2⋅3(−4)/5(−2)

Question

Adam wrote: 2⋅5(2)/3(4)

Nick wrote: 5(2)/2⋅3(4)

Shane wrote: 2⋅3(4)/5(2)

(1 point)
Responses

None of these are correct because the students did not add the exponents in the numerator and then subtract exponents since there is division.
None of these are correct because the students did not add the exponents in the numerator and then subtract exponents since there is division.

Adam is correct because the negative exponent moves the base to the other side of the fraction bar and makes the exponent positive.
Adam is correct because the negative exponent moves the base to the other side of the fraction bar and makes the exponent positive.

Nick is correct because the negative exponent in the numerator moves the whole numerator into the denominator and makes the exponent positive.
Nick is correct because the negative exponent in the numerator moves the whole numerator into the denominator and makes the exponent positive.

Shane is correct because all that needs to be done is to make the negative exponents positive.

Answer 1

To simplify the expression \( \frac{2 \cdot 3 \cdot (-4)}{5 \cdot (-2)} \), we can first rewrite it without the negative signs affecting the clarity, then we can proceed with the calculation.

1. Rewrite the expression without sign confusion: \[ \frac{2 \cdot 3 \cdot 4}{5 \cdot 2} = \frac{6 \cdot 4}{5 \cdot (-2)} \]

2. Calculate the numerator and denominator: \[ \text{Numerator: } 2 \cdot 3 \cdot 4 = 24 \] \[ \text{Denominator: } 5 \cdot (-2) = -10 \]

So, we can express the division: \[ \frac{24}{-10} = -\frac{12}{5}\text{ if simplified.} \]

Now let's evaluate the students' answers to check who is correct:

• Adam: \[ \frac{2 \cdot 5(2)}{3 \cdot 4} \quad \text{This is incorrect.} \]

• Nick: \[ \frac{5(2)}{2 \cdot 3(4)} \quad \text{This is incorrect.} \]

• Shane: \[ \frac{2 \cdot 3(4)}{5(2)} \quad \text{This is also incorrect.} \]

As none of the students produced the equivalent simplified expression of \( -\frac{12}{5} \), the correct response to choose would be:

None of these are correct because the students did not add the exponents in the numerator and then subtract exponents since there is division.