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Chapter 3: Problem 158

In the following exercises, simplify each expression. $$-58-(-67)$$

Short Answer

Expert verified
9

Step by step solution

01

Identify the Operands and Operators

The expression is -58 - (-67). Notice there are two numbers, -58 and -67, and a subtraction operator in between. However, -67 is inside parentheses preceded by a negative sign.
02

Apply the Rule for Subtracting a Negative

Recall that subtracting a negative number is equivalent to adding the absolute value of that number. Therefore, we rewrite the expression as: -58 + 67.
03

Perform the Addition

Now, add -58 and 67. When adding a negative number and a positive number, subtract the smaller absolute value from the larger absolute value and keep the sign of the larger absolute value. Thus, 67 - 58 = 9.
04

Write the Final Simplified Expression

The simplified result of the expression -58 - (-67) is 9.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Subtracting Negative Numbers
In mathematics, subtracting a negative number is an important concept that often confuses students. When you subtract a negative number, you are effectively adding the positive equivalent of that number. For instance, if you have the expression \(-58 - (-67)\), notice the double negative sign. These double negatives turn into a positive, so the expression simplifies to \-58 + 67\. This rule can be visualized as reverse subtraction, which essentially means you move in the opposite direction on a number line.
Absolute Value
Absolute value refers to the distance of a number from zero on the number line, regardless of direction. For example, the absolute value of both -67 and 67 is 67. When dealing with negative numbers, it's essential to understand that the absolute value turns any negative into a positive. This is crucial when simplifying expressions like \(-58 - (-67)\) because you convert the subtraction of a negative to the addition of a positive. Once you know 67 is inherently positive, you can proceed with the simplification without confusion.
Adding Integers
Adding integers is a fundamental operation in math. When adding a positive integer to a negative integer, consider their absolute values. For example, in the expression \(-58 + 67\), you subtract the smaller absolute value from the larger absolute value: \ 67 - 58 = 9 \. Since the absolute value of 67 is larger than the absolute value of -58, the result takes the sign of 67, which is positive. Therefore, the final simplified expression results in 9. So, remember the rules for signs and absolute value to smoothly add integers, whether positive or negative.

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