Verified Answer :

  • To solve \(-7.23 - 32.4\), treat it as the negative sum of absolute values: \(-(7.23 + 32.4) = -39.63\).
  • To solve \(25.6 + (-53.93)\), calculate the difference between the absolute values and apply the negative sign: \(-(53.93 - 25.6) = -28.33\).
  • The final results are \(-7.23 - 32.4 = \boxed{-39.63}\) and \(25.6 + (-53.93) = \boxed{-28.33}\).

Explanation

  1. Problem Analysis

The objective is to compute the values of two arithmetic expressions involving decimal numbers: \(-7.23 - 32.4\) and \(25.6 + (-53.93)\). These expressions involve negative numbers and addition/subtraction. To solve them, we will apply the rules for adding and subtracting signed numbers. For the first expression, since both numbers are negative, we can factor out the negative sign and add their absolute values. For the second expression, we have a positive number added to a negative number, which is equivalent to finding the difference between their absolute values and prefixing the sign of the number with the larger magnitude.

  1. Calculating the First Expression

For the first expression, \(-7.23 - 32.4\), both values are negative. This is equivalent to finding the negative of the sum of their absolute values:
\[ -7.23 - 32.4 = -(7.23 + 32.4) \]
Aligning the decimals for addition:
\[ 7.23 + 32.40 = 39.63 \]
Applying the negative sign, we get:
\[ -39.63 \]

  1. Calculating the Second Expression

For the second expression, \(25.6 + (-53.93)\), this is equivalent to subtracting 53.93 from 25.6. Since \(53.93 > 25.6\), the result will be negative, and we find the magnitude by calculating the difference \(53.93 - 25.60\):
\[ 53.93 - 25.60 = 28.33 \]
Since we are calculating \(25.6 - 53.93\), we negate this result:
\[ 25.6 - 53.93 = -28.33 \]

  1. Final Results

The results of the two calculations are \(-39.63\) and \(-28.33\). Therefore, the values are \(-7.23 - 32.4 = \boxed{-39.63}\) and \(25.6 + (-53.93) = \boxed{-28.33}\).

Examples

Imagine you have a small savings account for your hobby. If you owe \(\$7.23\) for supplies and then decide to purchase an additional item worth \(\$32.40\), your total debt becomes \(\$39.63\), which can be represented as \(-39.63\). Similarly, if you have \(\$25.60\) in your account but face a recurring charge of \(\$53.93\), your new balance would be \(25.60 - 53.93 = -28.33\), showing you are \(\$28.33\) overdrawn. Understanding these arithmetic operations helps in managing personal finances and keeping track of debts and balances.

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