Compute -7.23 - 32.4 and 32.7 + (-51.82).

Understand the Problem

The question is asking us to perform the arithmetic operations involving negative and positive decimals. We need to calculate the result of these expressions step by step.

Answer

The results are $-39.63$ and $-19.12$.

Steps to Solve

Compute the first expression: $-7.23 - 32.4$

To subtract a positive number from a negative number, add their absolute values and keep the negative sign.

$$ -7.23 - 32.4 = - (7.23 + 32.4) $$

Calculating the absolute values:

$$ 7.23 + 32.4 = 39.63 $$

So,

$$ -7.23 - 32.4 = -39.63 $$

Compute the second expression: $32.7 + (-51.82)$

Adding a negative number is the same as subtracting its positive counterpart.

$$ 32.7 + (-51.82) = 32.7 - 51.82 $$

Again, subtracting the absolute values:

$$ 51.82 - 32.7 = 19.12 $$

Since the larger absolute value (51.82) is negative, the result is:

$$ 32.7 + (-51.82) = -19.12 $$

The results are:

For $-7.23 - 32.4$: $-39.63$
For $32.7 + (-51.82)$: $-19.12$

More Information

This problem involves adding and subtracting negative and positive decimals, highlighting how to deal with signs when performing arithmetic operations. The cumulative effects of combining negative and positive numbers are essential for learning basic arithmetic.

Tips

Confusing the operation with adding when subtracting a negative number. Remember that subtraction of a negative is the same as addition.
Misplacing the negative signs when performing calculations.

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