Question

Consider this expression:



− 0.5 +


− 0.25 +


+ 0.4
Question 1
You are asked to find the sum by using fractions. Which expression could you use?
Responses
A

−

+

−

+

+

1 4 − 1 2 + 1 2 − 1 4 + 3 5 + 2 5
B

−

+

−

+

+

1 4 − 1 4 + 1 2 − 1 4 + 3 5 + 2 5
C

−

+

−

+

+

1 4 − 1 2 + 1 2 − 1 4 + 4 5 + 2 5
D

−

−

−

+

+

1 4 − 1 2 − 1 2 − 1 4 + 3 5 + 2 5
Question 2
Find the sum.
Responses
A 00
B 11
C 1

1 1 2
D

1 2
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Answer 1

To solve the first question, we need to convert the decimals in the original expression \(-0.5 + (-0.25) + 0.4\) into fractions and see which response matches those fractions.

1. Convert the decimals to fractions:
- \(-0.5\) is \(-\frac{1}{2}\)
- \(-0.25\) is \(-\frac{1}{4}\)
- \(0.4\) is \(\frac{2}{5}\)

So the original expression in fraction form is:
\[
-\frac{1}{2} - \frac{1}{4} + \frac{2}{5}
\]

Now, let's compare this with the provided options:

A
\(- \frac{1}{4} - \frac{1}{2} + \frac{1}{2} - \frac{1}{4} + \frac{3}{5} + \frac{2}{5}\)

B
\(- \frac{1}{4} - \frac{1}{4} + \frac{1}{2} - \frac{1}{4} + \frac{3}{5} + \frac{2}{5}\)

C
\(- \frac{1}{4} - \frac{1}{2} + \frac{1}{2} - \frac{1}{4} + \frac{4}{5} + \frac{2}{5}\)

D
\(- \frac{1}{4} - \frac{1}{2} - \frac{1}{2} - \frac{1}{4} + \frac{3}{5} + \frac{2}{5}\)

After comparison, the correct choice must accurately translate the fractions \(-\frac{1}{2}\), \(-\frac{1}{4}\), and \(\frac{2}{5}\).

None of the provided choices match exactly, as \(-\frac{1}{2}\) is present in multiple options but the associated fractional parts do not conform to the given operation.

Now moving on to question 2:
To find the sum of \(-0.5 + (-0.25) + 0.4\):
- Calculate:
\[
-0.5 = -\frac{1}{2}, \quad -0.25 = -\frac{1}{4}, \quad 0.4 = \frac{2}{5}.
\]
Converting all of these to a common denominator (which is 20):
\[
-\frac{1}{2} = -\frac{10}{20}, \quad -\frac{1}{4} = -\frac{5}{20}, \quad \frac{2}{5} = \frac{8}{20}.
\]
Adding them:
\[
-\frac{10}{20} - \frac{5}{20} + \frac{8}{20} = \frac{-10 - 5 + 8}{20} = \frac{-7}{20}.
\]

Now the question is to find the overall sum, which finalizes at \(-\frac{7}{20}\).

None of the options given (A, B, C, D) directly reflect the sum, indicating there might be a misunderstanding or mis-calculation with respect to the fractions provided initially or perhaps the final answers.

If examining those responses:
- A: \(0\)
- B: \(1\)
- C: \(1\)
- D: \(\frac{1}{2}\)

None of those options correspond to any clear matches from our findings of \(-0.5 - 0.25 + 0.4\).

If any of the options present the negative fractions, these would be miscalibrated, necessitating a closer resolve or review on the fractional calculations or options originally proposed.

Thus:
- **Final Choice from Question 1**: Neither but closest match, perhaps A with a review, but factor-wise doesn't tally.
- **Final Choice from Question 2**: Also none match the processed findings. Review needed.