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Chapter 10: Problem 71

Simplify. $$ -5-(-30)+30+40-(-12) $$

Short Answer

Expert verified
107

Step by step solution

01

- Rewrite Subtraction of Negative Numbers

Rewrite the expression by changing the subtraction of negative numbers into addition: \(-5 - (-30) + 30 + 40 - (-12)\) becomes \(-5 + 30 + 30 + 40 + 12\).
02

- Combine Positive Numbers

Add all the positive numbers together: \(30 + 30 + 40 + 12 = 112\).
03

- Subtract the Remaining Number

Subtract the remaining number from the sum of positives: \(112 - 5 = 107\).

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Key Concepts

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

Subtraction of Negative Numbers
When you see a subtraction of a negative number, it's a little bit different than regular subtraction. Think of it this way: subtracting a negative is like adding a positive. For example, in our exercise, we see
  • -(-30)
  • -(-12)
This can be rewritten as
  • +30
  • +12
So, o(-5 - (-30) + 30 + 40 - (-12)) becomes o(-5 + 30 + 30 + 40 + 12).
Addition of Integers
After rewriting the subtraction of negatives, we can focus on adding the integers. In the expression
  • (-5 + 30 + 30 + 40 + 12)
we see both positive and negative integers. When adding integers: First, combine all positive numbers. You have
  • 30 + 30 + 40 + 12 = 112
Then combine this with the remaining negative integer. So you end up with
  • 112 - 5 = 107
.
Combining Like Terms
Combining like terms means grouping together terms that have the same variables or constants and then simplifying them. In this exercise, we are dealing with integer constants. When simplifying, rearrange the expression and group all positive and negative numbers separately.
  • First, handle the subtraction of negative numbers:
    • -5 + 30
    • + 30
    • + 40
    • + 12
  • Then, combine all positive terms:
    • 30 + 30 + 40 + 12 = 112
Finally, subtract any remaining negative terms from the combined positive result
  • 112 - 5 = 107
.And there you have it! The final simplified expression is 107.

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