Question
pick one of the choices
Simplify: 32×3−15−2×20
Adam wrote: 3−2×522
Nick wrote: 3×52
Shane wrote: 3−352
Who was correct and why?
(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.
Nick is correct because the negative exponent in the numerator can combine with the like base and the denominator negative exponent goes to the numerator.
Nick is correct because the negative exponent in the numerator can combine with the like base and the denominator negative exponent goes to the numerator.
Adam is correct because the negative exponent combines with the base and the denominator moves to the numerator.
Adam is correct because the negative exponent combines with the base and the denominator moves to the numerator.
Shane is correct because all that needs to be done is to make the negative exponents positive.
Simplify: 32×3−15−2×20
Adam wrote: 3−2×522
Nick wrote: 3×52
Shane wrote: 3−352
Who was correct and why?
(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.
Nick is correct because the negative exponent in the numerator can combine with the like base and the denominator negative exponent goes to the numerator.
Nick is correct because the negative exponent in the numerator can combine with the like base and the denominator negative exponent goes to the numerator.
Adam is correct because the negative exponent combines with the base and the denominator moves to the numerator.
Adam is correct because the negative exponent combines with the base and the denominator moves to the numerator.
Shane is correct because all that needs to be done is to make the negative exponents positive.
Answers
GPT-4o mini
To simplify \(32 \times 3 - 15 - 2 \times 20\):
1. Calculate \(32 \times 3 = 96\).
2. Calculate \(2 \times 20 = 40\).
3. Now substitute back into the expression: \(96 - 15 - 40\).
4. Simplify step by step:
- \(96 - 15 = 81\)
- \(81 - 40 = 41\)
Thus the simplified result is \(41\).
Now, looking at the students' work:
- Adam wrote: \(3 - 2 \times 522\)
- Nick wrote: \(3 \times 52\)
- Shane wrote: \(3 - 352\)
None of the options presented by Adam, Nick, or Shane correctly reflect the simplification of the original expression \(32 \times 3 - 15 - 2 \times 20\).
Therefore, the correct response is:
**None of these are correct because the students did not add the exponents in the numerator and then subtract exponents since there is division.**
However, none of the statements provided directly relate to the arithmetic simplification shown earlier, indicating a possible mismatch in the question context regarding exponents and the initial calculations. The focus here should be strictly on the arithmetic performed above, which leads to the conclusion that none of the students were correct.
1. Calculate \(32 \times 3 = 96\).
2. Calculate \(2 \times 20 = 40\).
3. Now substitute back into the expression: \(96 - 15 - 40\).
4. Simplify step by step:
- \(96 - 15 = 81\)
- \(81 - 40 = 41\)
Thus the simplified result is \(41\).
Now, looking at the students' work:
- Adam wrote: \(3 - 2 \times 522\)
- Nick wrote: \(3 \times 52\)
- Shane wrote: \(3 - 352\)
None of the options presented by Adam, Nick, or Shane correctly reflect the simplification of the original expression \(32 \times 3 - 15 - 2 \times 20\).
Therefore, the correct response is:
**None of these are correct because the students did not add the exponents in the numerator and then subtract exponents since there is division.**
However, none of the statements provided directly relate to the arithmetic simplification shown earlier, indicating a possible mismatch in the question context regarding exponents and the initial calculations. The focus here should be strictly on the arithmetic performed above, which leads to the conclusion that none of the students were correct.