To find \( 8.76 - 26.54 \) using the additive inverse, we can rewrite the expression. The additive inverse of a number \( a \) is \( -a \).
So, we can express the subtraction as:
\[ 8.76 - 26.54 = 8.76 + (-26.54) \]
Now, we can add the two numbers:
\[ 8.76 + (-26.54) = 8.76 - 26.54 \]
Now let's perform the calculation:
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Align the numbers for addition: \[ \begin{array}{r} 8.76 \ -26.54 \ \hline \end{array} \]
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Subtract each column from right to left:
- In the hundredths place: \( 6 - 4 = 2 \)
- In the tenths place: \( 7 - 5 = 2 \)
- In the units place: \( 8 - 6 = 2 \) (We can’t do this directly, since 8 is less than 6, so we carry over)
- From the tens: We borrow 1 from the 0 in front of the 8, making it a 7. This means we are subtracting \( 26 - 27 = -1 \)
This gives us: \[ 8.76 - 26.54 = -17.78 \]
Thus, the result is:
\[ \boxed{-17.78} \]