Ask a New Question
Menu

Amanda evaluates the following expression on a math quiz.

- 3 7/8 x 6 + 4.36

3 answers

To evaluate the expression \(- 3 \frac{7}{8} \times 6 + 4.36\), we will first convert the mixed number into an improper fraction, perform the multiplication, and then add the decimal.

  1. Convert \(3 \frac{7}{8}\) to an improper fraction: \[ 3 \frac{7}{8} = \frac{3 \times 8 + 7}{8} = \frac{24 + 7}{8} = \frac{31}{8} \]

  2. Now multiply \(\frac{31}{8}\) by \(6\): \[ \frac{31}{8} \times 6 = \frac{31 \times 6}{8} = \frac{186}{8} \] To simplify \(\frac{186}{8}\): \[ \frac{186 \div 2}{8 \div 2} = \frac{93}{4} \]

  3. Now we convert \(\frac{93}{4}\) to a decimal for easier addition with \(4.36\): \[ \frac{93}{4} = 23.25 \]

  4. Finally, add \(23.25\) and \(4.36\): \[ 23.25 + 4.36 = 27.61 \]

Thus, the final answer is: \[ \boxed{27.61} \]

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 is not equal to -20. So, it is not reasonable.

B.
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.

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 -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.

To determine if Amanda’s answer of -19.14 is reasonable, we should first appropriately round the components of the expression:

  1. The value of \(-3 \frac{7}{8}\) is approximately \(-4\) when rounded.
  2. The value of \(4.36\) rounds to \(4\).

Now, calculate what these rounded values would yield when considered in the multiplication and addition of the original expression:

  1. Multiply \(-4\) by \(6\): \[ -4 \times 6 = -24 \]

  2. Add \(4\): \[ -24 + 4 = -20 \]

Now, we can examine Amanda’s answer of -19.14 in comparison to our calculated value of -20.

  1. According to the distracting options provided:
    • If considering option A, Amanda's answer of -19.14 rounds to -20, making it reasonable.
    • According to option B, it states her answer does round to -20, which is also correct.

However, options C and D provide incorrect reasoning based on the rounding of the values (specifically rounding \(4.63\) instead of \(4.36\)).

Given the calculations and reasoning, the best choice according to what we deduced is:

B. Since -4 rounds to -4 and 4.36 rounds to 4, the final answer rounds to -20. Her answer of -19.14 rounds to -20. So, it is reasonable.