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Chapter 1: Problem 67

Evaluate the given expression. Remember to follow the order of operations. $$12-4 \cdot 3+6$$

Short Answer

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6

Step by step solution

01

- Identify the Expression

Start with the given expression: \(12 - 4 \cdot 3 + 6\)
02

- Apply Multiplication

According to the order of operations (PEMDAS/BODMAS), handle the multiplication first. \[-4 \cdot 3 = -12\]So the expression becomes: \(12 - 12 + 6\)
03

- Perform Subtraction

Next, perform the subtraction: \[12 - 12 = 0\]So the expression now is: \(0 + 6\)
04

- Perform Addition

Finally, carry out the addition: \[0 + 6 = 6\]

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Key Concepts

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

PEMDAS
PEMDAS is a handy acronym that helps you remember the order of operations in mathematics. It represents:
  • P: Parentheses (or brackets)
  • E: Exponents
  • M: Multiplication
  • D: Division
  • A: Addition
  • S: Subtraction
Following this sequence is crucial when evaluating expressions. It ensures that everyone solves complex equations the same way. For example, consider the expression given:
\(12 - 4 \cdot 3 + 6\).
According to PEMDAS, we start by dealing with the multiplication first. Here, \(-4 \cdot 3 = -12\), giving us a new expression:
\(12 - 12 + 6\). By following PEMDAS, we make sure calculations are performed correctly.
Evaluating Expressions
Evaluating expressions involves finding the value of an algebraic expression by following the order of operations. Let's break it down:
  • Identify the terms in the expression.
  • Apply the operations according to PEMDAS.
In the exercise, we start with \(12 - 4 \cdot 3 + 6\).
First, we handle the multiplication to get: \(-4 \cdot 3 = -12\). Next, our expression becomes \(12 - 12 + 6\).
Then, we perform the subtraction: \(12 - 12 = 0\), and lastly, addition: \(0 + 6 = 6\).
Thus, the evaluated expression turns out to be 6. By understanding the order and individual steps, you can tackle any similar problems confidently.
Elementary Algebra
Elementary algebra introduces the concepts of variables, constants, and operations. In this example, no variables were present, but basic operations like addition, subtraction, and multiplication were used. The fundamentals of algebra involve:
  • Understanding and using the order of operations (PEMDAS).
  • Applying basic arithmetic operations.
  • Combining like terms and simplifying expressions.
For instance, given the equation \(12 - 4 \cdot 3 + 6\), evaluating each part sequentially helps in arriving at the correct solution systematically.
Mastering these key skills makes algebra less intimidating and helps build a solid foundation for more advanced topics in mathematics.

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Most popular questions from this chapter

Evaluate the given expression. Remember to follow the order of operations. $$\frac{7 \cdot 2+4 \cdot 5-2 \cdot 2}{9 \cdot 3-2 \cdot 6-3 \cdot 3}$$

Compute the given expression. Round off your answer to two decimal places where necessary. $$5.2-1.4(2.8-0.7)$$

Compute the given expression. Round off your answer to two decimal places where necessary. $$12.8-9.2(3.4-1.6)$$

Graph the given set on a number line. \(\\{x | x \text { is an even natural number less than } 10\\}\)

Factor the given number into its prime factors. If the number is prime, say so. $$1,904$$
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