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Chapter 1: Problem 100

Simplify. $$ 25-(-12)-7-(-2)+9 $$

Short Answer

Expert verified
41

Step by step solution

01

- Identify the negative signs

Rewrite each term clearly, paying special attention to the negative signs. The expression is: 25 - (-12) - 7 - (-2) + 9
02

- Simplify double negatives

Double negatives become positives. Therefore, 25 - (-12) becomes 25 + 12 and -(-2) becomes +2. So, the expression now reads: 25 + 12 - 7 + 2 + 9
03

- Perform addition and subtraction

Now add and subtract the terms in the expression from left to right: 25 + 12 = 37 37 - 7 = 30 30 + 2 = 32 32 + 9 = 41.

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Key Concepts

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

Negative Numbers
In arithmetic, a negative number is a number that is less than zero. Negative numbers are often used to represent values such as debts or temperature below freezing. They have a minus sign (-) in front of them to show that they are less than zero.

Understanding negative numbers is crucial when simplifying expressions. For example, if you owe someone money, you can think of it as having a negative amount of money. So, if you owe $7, it's like having -7 dollars.

When negative numbers appear in an expression, pay close attention to the minus signs. A single negative sign means you owe or subtract, and this changes your total value depending on if you are adding or subtracting.
Double Negatives
Double negatives can seem tricky at first, but they follow a simple rule: two negatives make a positive. This happens because subtracting a negative is like adding.

For example, in the expression 25 - (-12), the two negatives next to each other (the subtraction sign and the negative sign in -12) become a positive. So it becomes 25 + 12.

Another example is -(-2). The two negative signs turn into a positive, resulting in +2. This rule helps simplify expressions that initially seem complicated by turning them into straightforward addition or subtraction tasks.
Addition and Subtraction
When simplifying expressions, adding and subtracting correctly is key. Follow these steps to ensure accuracy:

1. Write down the original expression.
2. Convert any double negatives to positives.
3. Add and subtract the numbers from left to right.

Consider the expression 25 - (-12) - 7 - (-2) + 9. First, turn double negatives into positives:
25 + 12 - 7 + 2 + 9. Then follow the operations from left to right:

  • 25 + 12 = 37
  • 37 - 7 = 30
  • 30 + 2 = 32
  • 32 + 9 = 41

This method ensures you don't miss any steps and simplifies the process of solving complex expressions.

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