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Chapter 1: Problem 58

Write the following expressions in words, using the word product. \(5 \cdot x\)

Short Answer

Expert verified
The given expression \(5 \cdot x\) in words is 'the product of 5 and x'.

Step by step solution

01

Identify the Components

The expression given is \(5 \cdot x\). This expression consists of two parts: the number \(5\) and the variable \(x\), with a multiplication symbol \(\cdot\) between them.
02

Define the Word 'Product'

The term 'product' is used in mathematics to denote the result of multiplying two or more numbers or expressions. In this context, 'product' will be used to describe the result of the multiplication between \(5\) and \(x\).
03

Write the Expression in Words

To write \(5 \cdot x\) in words using the word 'product', we state the expression as 'the product of 5 and x'. This uses 'product' to express the multiplication relationship between the number and the variable.

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Key Concepts

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

Multiplication
Multiplication is one of the fundamental arithmetic operations in mathematics. It's essentially a quicker way of adding the same number multiple times. For instance, instead of writing \(5 + 5 + 5\), you can write \(5 \times 3\) or \(3 \times 5\). Both represent the same idea: adding the number five, three times.

In the expression \(5 \cdot x\), multiplication is shown with the dot (\(\cdot\)) symbol. This tells us to multiply the numeric value, which is 5, by another value, which could vary, represented by \(x\).
  • Multiplication helps simplify long addition.
  • The \(\cdot\) symbol or "times" symbol \(\times\) indicates the operation.
  • Understanding multiplication is crucial for advanced math concepts.
Variables
Variables are symbols or letters used in mathematics to represent numbers or values that can change. In the expression \(5 \cdot x\), the letter \(x\) is a variable. This means \(x\) can assume any value, depending on the context or given situation.

Variables are important because they allow us to work with unknowns in equations or expressions. Instead of solving a problem with specific numbers every time, using variables makes it possible to express broader mathematical relationships and to find solutions that work for a variety of situations.
  • Variables are typically represented by letters such as \(x\), \(y\), or \(z\).
  • They help generalize mathematical concepts.
  • Using variables allows the development of formulas and functions.
Mathematics Vocabulary
Understanding vocabulary in mathematics is just as important as the numbers and letters themselves. Words like "product" relate directly to mathematical operations. In our expression, \(5 \cdot x\), the word "product" tells us about the operation involved, which is multiplication.

Mathematics has its own language, and understanding this vocabulary helps in processing and solving mathematical problems effectively. By knowing terms like "sum," "difference," "product," and "quotient," students can better comprehend and solve expressions and equations they encounter.
  • The word "product" refers to the result of multiplying numbers or expressions.
  • Using correct vocabulary is crucial in expressing mathematical ideas.
  • Familiarity with terms enhances problem-solving skills.

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Most popular questions from this chapter

Find a solution for each equation. $$17=n+9$$

Add each of the following. (All problems involve carrying in at least one column. $$\begin{array}{l} 6,205 \\ 9,999 \\ \hline \end{array}$$

Write each of the following in symbols. a. The sum of 4 and 8 is 12 b. The sum of \(a\) and \(b\) is 6

Add each of the following. (All problems involve carrying in at least one column. $$\begin{array}{l} 8,888 \\ 9,999 \\ \hline \end{array}$$

Rewrite each of the following using the commutative property of addition. $$5+9$$
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