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Chapter 3: Problem 86

Evaluate each expression. $$ 3 \cdot 3 \cdot 3 $$

Short Answer

Expert verified
27

Step by step solution

01

- Identify the expression

The expression given is \(3 \cdot 3 \cdot 3\). This indicates that we need to multiply three 3s together.
02

- Multiply the first two numbers

First, multiply the first two 3s together: \(3 \cdot 3 = 9\).
03

- Multiply the result by the third number

Now, take the result from the previous step (which is 9) and multiply it by the third 3: \(9 \cdot 3 = 27\).

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Key Concepts

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

Step-by-Step Solution
Following a step-by-step approach helps to break down problems into manageable parts.

It involves identifying the expression and then solving it piece by piece.

For the given problem, we follow three steps:

  • Identify the expression: Notice what needs to be solved. Here, it is \(3 \cdot 3 \cdot 3\).
  • Multiply the first two numbers: Start with the first pair of numbers. \(3 \cdot 3 = 9\).
  • Multiply the result by the third number: Take the product from the previous step and multiply it by the remaining number. \(9 \cdot 3 = 27\).

This method can be applied to a wide range of multiplication problems, helping to ensure accuracy and build confidence in solving similar tasks.
Multiplying Integers
To multiply integers, follow the basic arithmetic rules, which are the same for all whole numbers.

Here's how you can approach it:

  • Start by pairing the numbers for easier calculation. For example, in our problem, we paired the first two 3s together first.
  • Remember the order of operations. When there are multiple multiplications, you can solve them from left to right.
  • Understand that multiplying positive integers always results in a positive product.

For our specific example, we multiplied \(3\) by \(3\) to get \(9\) and then multiplied \(9\) by another \(3\) to get \(27\). Each multiplication follows straightforward integer rules, making it easy once you know the process.
Mathematical Expressions
Mathematical expressions are ways to represent numbers and operations in a compact form.

They include symbols, numbers, and operators like addition, subtraction, multiplication, and division.

For example:

  • \(3 \cdot 3 \cdot 3\)
is a mathematical expression indicating a sequence of multiplications.

Understanding how to read and interpret these expressions is crucial for solving them accurately.

  • Identify the numbers and operations: Notice all the numbers and the operators (like \(\cdot\) indicating multiplication) in the expression.
  • Follow the order of operations: In this case, all operations are of the same type (multiplication), so you perform them sequentially from left to right.
  • Solve step-by-step: Break down the problem into smaller steps, as shown in our earlier sections.

In our example, interpreting \(3 \cdot 3 \cdot 3\) correctly and solving step-by-step ensures we reach the right answer, \(27\). By mastering the basics of expressions and their operations, you can handle more complex mathematical challenges with ease.

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