Let's break down the original problem 55.72 - 24.31 into its components:
- Whole numbers: 55 - 24 = 31
- Tenths: 0.7 - 0.3 = 0.4
- Hundredths: 0.02 - 0.01 = 0.01
Now, combining these, we express the original subtraction as:
\[ (50 + 5 + 0.7 + 0.02) - (20 + 4 + 0.3 + 0.01) \]
To ensure that we analyze the answer options thoroughly, we can rewrite 55.72 and 24.31 to fit into the structure of the answer choices presented:
Let's evaluate each option:
A. \[ (50 - 20) + (5 - 4) + (0.7 - 0.3) + (0.02 - 0.01) \] Calculating this:
- \(50 - 20 = 30\)
- \(5 - 4 = 1\)
- \(0.7 - 0.3 = 0.4\)
- \(0.02 - 0.01 = 0.01\)
Adding these results together gives: \[ 30 + 1 + 0.4 + 0.01 = 31 + 0.4 + 0.01 = 31.41 \] This does not match 55.72 - 24.31.
B. \[ (50 - 20) - (5 - 4) - (0.7 - 0.3) - (0.02 - 0.01) \] Calculating this:
- \(50 - 20 = 30\)
- \(- (5 - 4) = -1\)
- \(- (0.7 - 0.3) = -0.4\)
- \(- (0.02 - 0.01) = -0.01\)
So we have: \[ 30 - 1 - 0.4 - 0.01 = 30 - 1 = 29 \quad (subtracting 0.4 and 0.01) \] This also does not match.
C. \[ (50 + 20) + (5 + 4) + (0.7 + 0.3) + (0.02 + 0.01) \] Calculating this:
- \(50 + 20 = 70\)
- \(5 + 4 = 9\)
- \(0.7 + 0.3 = 1\)
- \(0.02 + 0.01 = 0.03\)
Adding these gives: \[ 70 + 9 + 1 + 0.03 = 80.03 \] This is also not correct.
D. \[ (50 + 20) - (5 + 4) - (0.7 + 0.3) - (0.02 + 0.01) \] Calculating this:
- \(50 + 20 = 70\)
- \((5 + 4) = 9\)
- \((0.7 + 0.3) = 1\)
- \((0.02 + 0.01) = 0.03\)
Putting it all together gives: \[ 70 - 9 - 1 - 0.03 = 70 - 9 = 61 \quad (then subtracting 1) = 60 \quad (subtracting 0.03 gives 59.97) \] Not correct either.
Conclusion:
None of the options seem to yield a valid equivalent to the original subtraction problem of 55.72 - 24.31. If we need an expression equivalent to the original subtraction formula, we should be looking for ways that directly derive from the composition of the terms leading to 55.72 and 24.31.
The best representation in this context is Option A but adjusted for accuracy to demonstrate that these segments when calculated properly give closer understanding of the magnitude of value calculated if within a representative scope with a full carry-over functioning or proper attacking the numerical place values from further ranges.