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Chapter 2: Problem 43

simplify. $$4-8+12-(-1)$$

Short Answer

Expert verified
9

Step by step solution

01

Identify all terms in the expression

Look at each number and sign in the expression. The expression is: 4 - 8 + 12 - (-1)
02

Combine first two terms

Start by combining the first two terms: 4 - 8 = -4
03

Combine the result with the next term

Add the next term to the result: -4 + 12 = 8
04

Simplify the last term

Remember that subtracting a negative number is the same as adding its positive: -(-1) = +1
05

Combine with the simplified last term

Add the simplified last term to the result: 8 + 1 = 9

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Key Concepts

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

Arithmetic Operations
Understanding arithmetic operations is crucial for simplifying expressions. These operations include addition, subtraction, multiplication, and division.
In our example, we will focus on addition and subtraction.

To simplify the expression, we follow a specific sequence:
  • Combine the first two terms: 4 - 8 = -4
  • Add the next term to the result: -4 + 12 = 8
  • Handle the negative sign in the last term and add it to the result: -(-1) = +1
Applying these operations correctly ensures an accurate result.
Negative Numbers
Working with negative numbers can be tricky, but it鈥檚 essential for solving many math problems.
When you see a negative number, pay attention to how it interacts with other numbers in the problem.

In our example for the term -(-1), we've used an important rule:
  • Subtracting a negative number is the same as adding its positive counterpart. So, -(-1) becomes +1.
This rule helps you handle negative numbers effectively and simplifies expressions accurately.
Combining Like Terms
Combining like terms involves adding or subtracting terms that have the same variable or are of the same type.
In our expression 4 - 8 + 12 - (-1), we simplify by combining the constants step-by-step.

The process is straightforward:
  • Combine the first two constants: 4 - 8 = -4
  • Add the next constant: -4 + 12 = 8
  • Handle the last constant: 8 + 1 = 9
By combining like terms efficiently, we simplify the expression to its final result.

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