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Chapter 2: Problem 34

Simplify each given expression. \(6 \cdot 3\)

Short Answer

Expert verified
The expression simplifies to 18.

Step by step solution

01

Identify the Operation

In the expression \(6 \cdot 3\), the operation to be performed is multiplication. The symbol \(\cdot\) indicates that we need to multiply the two numbers, 6 and 3.
02

Perform the Multiplication

Multiply the two numbers: 6 and 3. To do this, you calculate 6 times 3. This can be done manually or using a calculator. Performing the multiplication gives us \(6 \times 3 = 18\).
03

Write the Simplified Expression

After solving the multiplication, the simplified expression is simply the result of the operation, which is 18. Therefore, \(6 \cdot 3 = 18\).

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Key Concepts

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

Understanding Multiplication
Multiplication is a fundamental mathematical operation that helps us find the total number of items in groups of the same size. Consider it as repeated addition. For instance, multiplying 6 by 3 means adding the number 6 three times. Here's how it looks:
  • First 6: 6
  • Second 6: 6 + 6 = 12
  • Third 6: 12 + 6 = 18
Using multiplication instead of addition simplifies the process and reduces computation time. So, when we see an expression like \(6 \cdot 3\), it's telling us to multiply these two numbers.
Multiplication is represented by symbols such as "x", "路", or simply by placing numbers adjacent to each other. Becoming comfortable with multiplication is essential as it's widely used in various areas of mathematics.
Simplifying Expressions
Simplifying expressions means making them easier to understand or solve. In multiplication, this involves carrying out the operation between numbers and writing the result in its most straightforward form.
Let's take the expression \(6 \cdot 3\) as an example. To simplify, we follow a straightforward process:
  • Identify the operation, which is multiplication here.
  • Execute the operation: multiply 6 by 3.
  • Write down the result: 18.
The simplified expression is just the result of multiplying the numbers, without any extra symbols or operations left to perform. Simplifying makes expressions clear and ready for further use in calculations or real-world applications.
Mathematical Operations and Their Role
Mathematical operations are the actions we perform on numbers to solve expressions or equations. The basic operations include addition, subtraction, multiplication, and division.
  • Addition: Combines numbers to find a total.
  • Subtraction: Finds the difference between numbers.
  • Multiplication: Finds the total amount in groups, as we've seen in our example \(6 \cdot 3\).
  • Division: Splits a total into equal parts.
Understanding these operations is crucial because they form the foundation for all other mathematical concepts. Mastery of operations, especially multiplication, aids in solving complex problems by breaking them into smaller, manageable parts. Each operation has its own rules and properties, which help in simplifying and calculating various expressions and equations.

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Most popular questions from this chapter

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