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Order of Operations: Simplifying Expressions with Negative Numbers

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Order of Operations: Simplifying Expressions with Negative Numbers

In mathematics, the order of operations is a set of rules that dictate the sequence in which operations should be performed in a mathematical expression. This ensures that everyone arrives at the same answer when solving the same expression.

The Order of Operations: PEMDAS/BODMAS

The most common acronym used to remember the order of operations is PEMDAS, which stands for:

  • Parentheses (or Brackets)
  • Exponents (or Orders)
  • Multiplication and Division (performed from left to right)
  • Addition and Subtraction (performed from left to right)

Another common acronym is BODMAS, which stands for:

  • Brackets
  • Orders
  • Division and Multiplication (performed from left to right)
  • Addition and Subtraction (performed from left to right)

Simplifying Expressions with Negative Numbers

When working with negative numbers, it's crucial to follow the order of operations meticulously. Let's look at some examples:

Example 1:

Simplify the expression: -5 + 3 * 2

1. **Multiplication:** 3 * 2 = 6

2. **Addition:** -5 + 6 = 1

Therefore, -5 + 3 * 2 = 1

Example 2:

Simplify the expression: ( -4 - 2 ) * 3

1. **Parentheses:** -4 - 2 = -6

2. **Multiplication:** -6 * 3 = -18

Therefore, (-4 - 2) * 3 = -18

Example 3:

Simplify the expression: -2^2 + 5

1. **Exponent:** -2^2 = -4 (Remember that squaring a negative number results in a positive number)

2. **Addition:** -4 + 5 = 1

Therefore, -2^2 + 5 = 1

Key Points to Remember

  • Always follow the order of operations (PEMDAS/BODMAS) to avoid errors.
  • Parentheses/Brackets take precedence over all other operations.
  • When performing multiplication and division or addition and subtraction at the same level of priority, work from left to right.
  • Pay close attention to the signs of negative numbers.

Practice Makes Perfect

The best way to master the order of operations is to practice solving various expressions. Start with simple examples and gradually increase the complexity. You can find numerous practice problems online and in textbooks.

By understanding and applying the order of operations correctly, you'll be able to simplify expressions involving negative numbers with confidence and accuracy.

Negative Numbers