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Chapter 1: Problem 74

In Exercises \(73-84\), evaluate the given expression. $$7-3 \cdot 5-1$$

Short Answer

Expert verified
-9

Step by step solution

01

- Apply the Order of Operations

According to the order of operations (PEMDAS/BODMAS), multiplication and division should be performed before addition and subtraction. Identify the multiplication operation in the expression.
02

- Perform Multiplication

Evaluate the multiplication part of the expression first. \[7 - 3 \times 5 - 1 = 7 - 15 - 1\]
03

- Perform Subtraction

After completing the multiplication, perform the subtraction operations from left to right. \[7 - 15 - 1 = -8 - 1\]
04

- Final Subtraction

Finally, subtract 1 from -8. \[-8 - 1 = -9\]

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Key Concepts

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

PEMDAS
When solving mathematical expressions, it's important to follow the correct order of operations. The acronym PEMDAS helps remember this order:
  • P stands for Parentheses
  • E stands for Exponents
  • M stands for Multiplication
  • D stands for Division
  • A stands for Addition
  • S stands for Subtraction
In this exercise, we used PEMDAS to evaluate the expression ewline $$7-3 \times 5-1$$. Multiplication comes before subtraction. First, we assess the multiplication operation. This ensures the expression is simplified accurately.
Evaluating Expressions
To evaluate expressions like the given one, it's crucial to simplify step by step. Start by identifying and handling operations according to their precedence. In the expression $$7-3 \times 5-1$$, multiplication is performed first:
Step-by-Step:
  • First, calculate the multiplication part: $$3 \times 5 = 15$$
  • Replace the multiplication in the original expression: $$7-15-1$$
Then, move on to the subtraction, from left to right:
  • Calculate the first subtraction: $$7 - 15 = -8$$
  • Finish with the last subtraction: $$-8 - 1 = -9$$
This ordered approach ensures clarity and accuracy.
Multiplication and Subtraction
Let's dive deeper into multiplication and subtraction, as they are key operations in this problem.
  • Multiplication: This mathematical operation involves finding the product of two numbers. For example, $$3 \times 5$$ equals 15.
  • Subtraction: This operation involves finding the difference between two numbers. In the expression, we subtract left to right. For instance, $$7 - 15$$ results in -8.
Understanding these operations helps in evaluating expressions correctly.
Remember: Multiplication takes precedence over subtraction, which directly impacts the final value. Once the steps are done in the correct order, you end up with the solution: -9. This systematic approach ensures no steps are overlooked.

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