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Chapter 1: Problem 82

Perform the operations. $$ -33-(-22)-44 $$

Short Answer

Expert verified
The result is -55.

Step by step solution

01

Rewrite the Expression

Identify and rewrite the expression so it is clear to perform operations on it: \(-33 - (-22) - 44\)
02

Simplify the Double Negative

When you have a negative sign in front of a negative number, it turns into a positive. Thus, \(-33 - (-22)\) becomes \(-33 + 22\).
03

Perform Addition and Subtraction

Perform the operation from left to right. Start with \(-33 + 22 = -11\) and then perform \(-11 - 44 = -55\).

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Key Concepts

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

Working with Integer Operations
Integer operations involve basic arithmetic with whole numbers, both positive and negative. When working with integers, it's important to remember some key concepts to make calculations easier.
  • Addition and Subtraction: Treat these operations as finding the difference on a number line.
  • Same Sign: When adding two numbers with the same sign, add their absolute values and keep the common sign.
  • Different Signs: When adding numbers with different signs, subtract their absolute values and keep the sign of the number with the largest absolute value.
  • Subtraction as Addition: Remember, subtracting a number is the same as adding its negative, which can simplify operations.
In problems like \( -33 + 22 - 44 \), first simplify by tackling pairs of values, then perform the operations left to right.
Understanding Negative Numbers
Negative numbers can seem a bit tricky at first, but with practice, they become second nature. A negative number represents a value less than zero. Think of them as counting backwards from zero.
  • Negative Sign: The "-" before a number indicates it's negative.
  • Visualizing on a Number Line: If you are subtracting a negative number, like \(-(-22)\), move to the right, turning it into addition.
  • Applications: In real life, negative numbers can indicate losses or temperatures below freezing.
  • Example: To work through \(-33 - (-22)\), think of it as taking away debt, simplifying into addition.
Getting comfortable with these can help in performing calculations correctly in problems involving both subtraction and addition.
Order of Operations Simplified
The order of operations is essential when performing complex mathematical problems to ensure you get the correct answer. This set of rules dictates the sequence in which operations are performed.
  • PEMDAS/BODMAS: Parentheses/Brackets first, then Exponents/Orders, followed by Multiplication and Division (left to right), and finally Addition and Subtraction (left to right).
  • Simplifying Expressions: For the example \(-33 - (-22) - 44\), you prioritize simplifying any double negatives first before proceeding.
  • Evaluating Expressions: Work sequentially from left to right, ensuring to revisit the steps if unsure and avoid skipping operations.
  • Real-world Example: Incorrect order of operations in engineering or baking can lead to mishaps, so precision is key.
By mastering the order of operations, complex math problems become easier and less prone to error.

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