To add \(-27\) and \(45\), you can follow these steps:
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Understanding the Numbers: \(-27\) is a negative number, and \(45\) is a positive number. When adding a negative and a positive number, you're essentially finding the difference between their absolute values.
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Finding the Absolute Values: The absolute value of \(-27\) is \(27\), and the absolute value of \(45\) is \(45\).
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Subtract the Smaller Absolute Value from the Larger: Since \(45\) is larger than \(27\), we subtract \(27\) from \(45\): \[ 45 - 27 = 18 \]
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Determine the Sign of the Result: Because \(45\) (the positive number) is larger than \(-27\) (the negative number), the result will be positive.
Therefore, \( -27 + 45 = 18\).
So, the final answer is: \[ \boxed{18} \]