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.
- 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.
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