To solve the expression \(-972.18 - (-452.76)\) using the concept of additive inverses, we can rewrite the double negative:
\[ -972.18 - (-452.76) = -972.18 + 452.76 \]
Now we need to perform the addition:
To do this, we can align the numbers:
-972.18
+ 452.76
-----------
To perform this calculation, we can consider it as adding the absolute values and taking care of the signs.
- Add the absolute values: \(972.18 + 452.76\).
- Start with the hundredths: \(0.18 + 0.76 = 0.94\) (which we carry over 1 to the tenths).
- Next, the tenths: \(7 + 5 = 12\) (including carry 1 from hundredths) gives us \(2\) with a carry of \(1\) to the units.
- Now for units: \(2 + 2 + 1 = 5\).
- Next, the tens: \(9 + 4 = 13\) gives us \(3\) with a carry of \(1\) to the hundreds.
- And lastly, the hundreds: \(9 + 0 + 1 = 10\).
So, we get \( 452.76 + 972.18 = 1424.94\).
- Now, we know that \(-972.18\) is negative, and \(452.76\) is positive, so we confirm the resulting sign:
- The larger absolute value is that of \(-972.18\).
Next, we compute the difference of absolute values since the sum is negative. Thus, \(972.18 - 452.76 = 519.42\) is also a straightforward calculation:
972.18
- 452.76
-----------
Going across, we have:
- For hundredths: \(8 - 6 = 2\)
- For tenths: \(1 - 7\) (borrow) becomes \(11 - 7 = 4\)
- For units: \(2 - 2 = 0\)
- For tens: \(7 - 5 = 2\)
- For hundreds: \(9 - 4 = 5\)
Finally, we find that:
\(-972.18 + 452.76 = -519.42\).
Thus, the result of the original expression is:
\[ \boxed{-519.42} \]