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Chapter 1: Problem 31

Evaluate each expression. $$6 / 2 \cdot 3$$

Short Answer

Expert verified
The value of the expression is 9.

Step by step solution

01

Identify the Order of Operations

According to the order of operations (PEMDAS/BODMAS), we need to perform division and multiplication from left to right. In the expression \(6 / 2 \cdot 3\), perform the division first.
02

Perform the Division

Divide 6 by 2. \[\frac{6}{2} = 3\]
03

Perform the Multiplication

Now, multiply the result by 3. \[3 \cdot 3 = 9\]

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Key Concepts

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

PEMDAS: Understanding the Order of Operations
In mathematics, the order of operations is a set of rules that dictates the correct sequence to evaluate a mathematical expression. The acronym PEMDAS helps you remember this sequence:

  • Parentheses first
  • Exponents (ie. powers and roots, etc.)
  • Multiplication and Division (left to right)
  • Addition and Subtraction (left to right)

This order ensures that everyone solves mathematical expressions uniformly. When you look at an expression like \(\frac{6}{2} \cdot 3\), always start with operations inside parentheses. If there are no parentheses, as in this case, move to any exponents, followed by Multiplication and Division from left to right, and finally Addition and Subtraction from left to right.
Division: Completing the First Step
When handling mathematical problems that involve division, you must follow the order of operations. In the expression \(\frac{6}{2} \cdot 3\), according to PEMDAS, perform the operations from left to right. Here, you start with division, as it appears first from the left following this sequence:

Divide 6 by 2:
\[ \frac{6}{2} = 3 \]
Now you have simplified the expression to 3. This step ensures that you establish an intermediate result to use in the next part of the problem.
Multiplication: Finalizing the Calculation
After performing the division step, you will continue to the multiplication step in the simplified expression, which now is 3 \cdot 3. Following PEMDAS means you process multiplication next:

\[ 3 \cdot 3 = 9 \]
You multiply 3 by 3, which gives you 9. Therefore, the value of the original expression \(\frac{6}{2} \cdot 3\) is 9. By following PEMDAS carefully, you ensure accurate results in every calculation you perform. Pay close attention to this order to avoid mistakes.

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Most popular questions from this chapter

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