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Chapter 3: Problem 45

Evaluate each of the following: $$8-5(-3)$$

Short Answer

Expert verified
23

Step by step solution

01

Understand the Expression

The given expression is: 8 - 5(-3).
02

Apply the Multiplication inside the Parentheses

First, perform the multiplication inside the parentheses: Multiply -5 by -3 to get 15. The expression now becomes: 8 - (-15).
03

Simplify the Expression

Simplify the expression by noting that subtracting a negative is the same as adding: 8 - (-15) is the same as 8 + 15. Perform the addition: 8 + 15 = 23.

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Key Concepts

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

Order of Operations
When evaluating algebraic expressions, one of the most critical concepts is the order of operations. This ensures that everyone solves mathematical expressions consistently and correctly. The order is often remembered by the acronym PEMDAS, which stands for:
  • Parentheses first
  • Exponents (ie. powers and square roots, etc.)
  • Multiplication and Division (left-to-right)
  • Addition and Subtraction (left-to-right)
So, in our exercise 8 - 5(-3), we first deal with the multiplication inside the parentheses (following PEMDAS) before performing subtraction. Because parentheses are a form of grouping, they take precedence. Always approach the expression step by step and keep the rule of PEMDAS in mind!
Multiplication
Multiplication is the next key step in our example. The given expression 8 - 5(-3) has parentheses indicating that -3 should be multiplied by -5. To multiply these two numbers:
  • Multiply the absolute values: 5 * 3 = 15
  • Determine the sign: A negative times a negative gives a positive
So, -5 multiplied by -3 equals 15. The expression now updates to 8 - (-15). Notice how important it is to understand the rules for multiplying positive and negative numbers.
Addition
Finally, let's dive into the addition part of our expression. After performing the multiplication, the updated expression is 8 - (-15). Subtracting a negative number can seem tricky, but it's simpler than it looks. When you subtract a negative, you essentially add the absolute value of that number.
  • Subtracting -15 is the same as adding 15
  • So, 8 - (-15) transforms into 8 + 15
Adding these two numbers, 8 + 15, gives us 23. Hence, the final evaluated expression is 23. This demonstrates the importance of understanding both subtraction and addition when negative numbers are involved.

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