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Chapter 2: Problem 317

In the following exercises, translate from algebra to English. $$ 3 \cdot 8 $$

Short Answer

Expert verified
Three times eight.

Step by step solution

01

Identify the Mathematical Expression

The given mathematical expression is $$ 3 \times 8 $$.
02

Translate the Operation Symbol

In algebra, the symbol $$ \times $$ represents the operation of multiplication. This means we need to multiply the numbers on either side of the symbol.
03

Translate Each Number

Identify each number and their positions. Here, we have the number 3 and the number 8.
04

Combine the Translated Elements

Now, combine everything into a phrase: 'Three times eight.'

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Key Concepts

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

Multiplication Operation
The multiplication operation is an essential part of mathematics. It is represented by symbols such as \( \times \) or \( \cdot \). When you multiply two numbers, you are essentially adding one number to itself a certain number of times.

In our example, $$ 3 \times 8 $$, the number 3 is being added to itself 8 times.

To break it down:
  • 3 added once is 3
  • 3 added twice is 6
  • 3 added three times is 9
  • ... continue this process until you've added 3 a total of 8 times
Eventually, you will have $$ 3 \times 8 = 24 $$.

So, multiplication is a quick way to perform repeated addition.
Mathematical Expressions
Mathematical expressions are combinations of numbers, symbols, and operators that represent a value. Expressions can include operations like addition, subtraction, multiplication, and division.

For instance, in the expression $$ 3 \times 8 $$, you have:
  • Two numbers (3 and 8)
  • A multiplication symbol (\( \times \))
To translate this mathematical expression into English, follow these steps:
  • Identify the numbers (3 and 8)
  • Recognize that the symbol \( \times \) means multiplication
  • Put it all together: 'Three times eight'
Mathematical expressions help simplify and shorten the process of performing calculations.
Basic Arithmetic
Basic arithmetic involves the fundamental operations of addition, subtraction, multiplication, and division. These are the building blocks of more advanced math topics.

Let's look at each operation:
  • Addition (\( + \)): Combining two or more numbers to get a sum
  • Subtraction (\( - \)): Finding the difference between two numbers
  • Multiplication (\( \times \)): Adding a number to itself a certain number of times
  • Division (\( \div \)): Splitting a number into equal parts
In our focus example, $$ 3 \times 8 $$, we see multiplication in action. Knowing these basic operations is crucial for solving more complex math problems. They are the groundwork for algebra, geometry, and beyond.

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