(−61)−(+442)=
To solve this problem, we'll follow these steps:
- Step 1: Convert the mixed number to an improper fraction.
- Step 2: Simplify the improper fraction, if possible.
- Step 3: Find a common denominator for the fractions.
- Step 4: Subtract the fractions by rewriting them with a common denominator.
- Step 5: Simplify the result, if needed.
Now, let's work through each step:
Step 1: +442 is first converted to an improper fraction:
442=4+42. Since 42 can be simplified to 21, it becomes 4+21=28+21=29. Thus, +442=29.
Step 2: Simplification has already been done in the conversion.
Step 3: Determine a common denominator for −61 and 29. The least common denominator between 6 and 2 is 6.
Step 4: Rewrite each fraction with the common denominator:
- −61 remains as −61.
- 29 needs to be converted to have a denominator of 6: 29=2×39×3=627.
Now, perform the subtraction:
−61−627=6−1−27=6−28.
Step 5: Simplify the result: 6−28=3−14. This can be expressed as a mixed number −432.
Therefore, the solution to the problem is −432, which matches the correct choice: −432.