Question
Amanda evaluates the following expression on a math quiz.
-3 7/8 x 6 + 4.63
She gets an answer of -19.14. Is this a reasonable answer?
A.
Since rounds to -4 and 4.63 rounds to 4, the final answer rounds to -20.
Her answer of -19.14 rounds to -20. So, it is reasonable.
B.
Since rounds to -3 and 4.63 rounds to 5, the final answer rounds to -13.
Her answer of -19.14 rounds to -19. So, it is not reasonable.
C.
Since rounds to -4 and 4.63 rounds to 5, the final answer rounds to -19.
Her answer of -19.14 rounds to -19. So, it is reasonable.
D.
Since rounds to -4 and 4.63 rounds to 4, the final answer rounds to -20.
Her answer of -19.14 is not equal to -20. So, it is not reasonable.
-3 7/8 x 6 + 4.63
She gets an answer of -19.14. Is this a reasonable answer?
A.
Since rounds to -4 and 4.63 rounds to 4, the final answer rounds to -20.
Her answer of -19.14 rounds to -20. So, it is reasonable.
B.
Since rounds to -3 and 4.63 rounds to 5, the final answer rounds to -13.
Her answer of -19.14 rounds to -19. So, it is not reasonable.
C.
Since rounds to -4 and 4.63 rounds to 5, the final answer rounds to -19.
Her answer of -19.14 rounds to -19. So, it is reasonable.
D.
Since rounds to -4 and 4.63 rounds to 4, the final answer rounds to -20.
Her answer of -19.14 is not equal to -20. So, it is not reasonable.
Answers
Answered by
GPT-4o mini
To evaluate whether Amanda's answer of -19.14 is reasonable, we can first convert the numbers in the expression to a more manageable form.
1. Convert \(-3 \frac{7}{8}\) to a decimal:
\[
-3 \frac{7}{8} = -3 - \frac{7}{8} = -3 - 0.875 = -3.875
\]
2. Evaluate the expression:
\[
-3.875 \times 6 + 4.63
\]
Calculating \(-3.875 \times 6\):
\[
-3.875 \times 6 = -23.25
\]
3. Now, add \(4.63\):
\[
-23.25 + 4.63 = -23.25 + 4.63 = -18.62
\]
So the actual value of the expression \( -3 \frac{7}{8} \times 6 + 4.63\) is \(-18.62\).
Now let's evaluate Amanda's answer of -19.14 against the options given:
A. \(-4\) and \(4.63\) round to \(-20\). Her answer of -19.14 rounds to -20. So, it is reasonable.
- This interpretation is somewhat misleading because it tries to analyze rounding but doesn't consider the actual calculated result.
B. \(-3\) rounds to \(-3\) and \(4.63\) rounds to \(5\), so the calculation is off here, and going by raw rounding leads to misleading conclusions.
C. This is also incorrect because it states rounding logic that does not reflect the transformation of the numbers or the ultimate output.
D. \(-4\) doesn't correctly reflect \(-3 \frac{7}{8}\) rounded; \(4.63\) to \(4\) is not correct usage, and concluding her answer isn't equal disregards the fact that \( -18.62 \) is what should lead us to evaluate reasonable outputs.
Considering we calculated the overall value to be around \(-18.62\), her answer of \(-19.14\) rounds off relatively close by about half (compared to rounding -18.62 to -19. However, it doesn't match the expectation of rounding up to -18 being reasonable.
To clarify, \(-19.14\) rounds to -19 which isn't the nearest possible around -18.62.
Thus, Option C and A can be termed reasonable, as they approve without any radical mismatches; nevertheless, your calculated value leads into more critical avenues measuring risk considering correctness of operation outcomes over abstract rounding premises.
If I simplify:
Amanda's answer of \(-19.14\): closer but logically marking nor resultant checks put it on the line mathematically from outputs showcase an unequivocal failing for expected round normalization.
So, Amanda has concluded reasonably; however, further evaluations could expand dimensions or refine discrepancies under analytical reviews.
1. Convert \(-3 \frac{7}{8}\) to a decimal:
\[
-3 \frac{7}{8} = -3 - \frac{7}{8} = -3 - 0.875 = -3.875
\]
2. Evaluate the expression:
\[
-3.875 \times 6 + 4.63
\]
Calculating \(-3.875 \times 6\):
\[
-3.875 \times 6 = -23.25
\]
3. Now, add \(4.63\):
\[
-23.25 + 4.63 = -23.25 + 4.63 = -18.62
\]
So the actual value of the expression \( -3 \frac{7}{8} \times 6 + 4.63\) is \(-18.62\).
Now let's evaluate Amanda's answer of -19.14 against the options given:
A. \(-4\) and \(4.63\) round to \(-20\). Her answer of -19.14 rounds to -20. So, it is reasonable.
- This interpretation is somewhat misleading because it tries to analyze rounding but doesn't consider the actual calculated result.
B. \(-3\) rounds to \(-3\) and \(4.63\) rounds to \(5\), so the calculation is off here, and going by raw rounding leads to misleading conclusions.
C. This is also incorrect because it states rounding logic that does not reflect the transformation of the numbers or the ultimate output.
D. \(-4\) doesn't correctly reflect \(-3 \frac{7}{8}\) rounded; \(4.63\) to \(4\) is not correct usage, and concluding her answer isn't equal disregards the fact that \( -18.62 \) is what should lead us to evaluate reasonable outputs.
Considering we calculated the overall value to be around \(-18.62\), her answer of \(-19.14\) rounds off relatively close by about half (compared to rounding -18.62 to -19. However, it doesn't match the expectation of rounding up to -18 being reasonable.
To clarify, \(-19.14\) rounds to -19 which isn't the nearest possible around -18.62.
Thus, Option C and A can be termed reasonable, as they approve without any radical mismatches; nevertheless, your calculated value leads into more critical avenues measuring risk considering correctness of operation outcomes over abstract rounding premises.
If I simplify:
Amanda's answer of \(-19.14\): closer but logically marking nor resultant checks put it on the line mathematically from outputs showcase an unequivocal failing for expected round normalization.
So, Amanda has concluded reasonably; however, further evaluations could expand dimensions or refine discrepancies under analytical reviews.