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Chapter 1: Problem 81

Simplify each expression. $$-4+(-3+2)+(-3)$$

Short Answer

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Step by step solution

01

Parentheses First

According to the rule of order of operations, or BIDMAS/PEDMAS (Brackets/parentheses, Indices/Exponents, Division and Multiplication (from left to right), Addition and Subtraction (from left to right)), you should solve any operation enclosed in parentheses first. Here, you have \(-3 + 2\) in parentheses. Solve this: \(-3 + 2 = -1\). So now the expression becomes \(-4 + -1 + -3\).
02

Add Together

Now add the numbers together from left to right: adding \(-4\) and \(-1\) gives \(-5\), and then adding \(-3\) to \(-5\) gives \(-8\).

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Key Concepts

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

Order of Operations
Understanding the order of operations is crucial in algebra. It ensures that everyone calculates expressions the same way and gets the correct result. The acronym BIDMAS or PEDMAS can help you remember the sequence:
  • B/P: Brackets, or Parentheses, come first. Always perform operations inside them before anything else.
  • I/E: Indices, or Exponents, follow next.
  • D/M: Division and Multiplication are next. These are performed from left to right.
  • A/S: Addition and Subtraction come last, also done from left to right.
In the exercise given, the parentheses contain the operation \(-3 + 2\). You solve this before proceeding with other operations. After calculation, the expression inside the parentheses is replaced with the result, simplifying your expression to be evaluated in the next steps.
Simplification
Simplification makes algebraic expressions easier to handle and understand. By breaking down complex problems into smaller parts, you make them more manageable. In the provided exercise, simplification was achieved by first dealing with the operation inside the parentheses: \(-3 + 2 = -1\).
After handling the parentheses, you are left with \(-4 + -1 + -3\). Process these from left to right:
  • Add \(-4\) and \(-1\) to get \(-5\).
  • Next, add \(-3\) to \(-5\), resulting in \(-8\).
Each step reduces the complexity until you have a single, simplified number. The result is \(-8\), a straightforward answer to the original, more complex expression.
Negative Numbers
Working with negative numbers is a fundamental skill in algebra. It involves understanding how these numbers interact with each other through addition and subtraction.
Negative numbers are those less than zero, often found on the left side of the number line. In arithmetic operations, consider the following:
  • Adding negative numbers: When you add a negative number, you're essentially subtracting its absolute value. For instance, \(-4 + -1\) is the same as \(-4 - 1\).
  • Combining negatives: Adding two negative numbers gives a more negative number. Like in the exercise, where adding \(-4\), \(-1\), and \(-3\) consecutively gives \(-8\).
By understanding these principles, you'll be more comfortable solving expressions that involve negative numbers and accurately perform calculations leading to the correct solutions.

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Most popular questions from this chapter

A plumber cuts a pipe that is 12 feet long into \(x\) equal pieces. Find an expression for the length of each piece.

Suppose there were no numbers other than the odd integers. \(\cdot\) Would the closure property for addition still be true? \(\cdot\) Would the closure property for multiplication still be true? \(\cdot\) Would there still be an identity for addition? \(\cdot\) Would there still be an identity for multiplication?

Graph each set of numbers on a number line. Use brackets or parentheses where applicable. The real numbers greater than -2 and less than 3

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Use the given property to rewrite the expression in a different form. SEE EXAMPLE \(6 .\) (OBJECTIVE 5 ) \(1 x ;\) multiplicative identity property.
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