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Chapter 1: Problem 14

Use mathematical symbols to translate each phrase. Eight times a number

Short Answer

Expert verified
The expression is \( 8x \).

Step by step solution

01

Identify the Variable

Choose a variable to represent the unknown number. Let's use the variable \( x \) to represent the number.
02

Translate the Words to Symbols

The phrase 'Eight times a number' implies multiplication of the number, which we've represented as \( x \), by 8.
03

Write the Expression

Combine the variable and the number using the multiplication operation. This gives us the expression \( 8x \).

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Key Concepts

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

Variables
Variables are symbols used to represent unknown values or quantities in mathematical expressions. In the given exercise, we use the letter x as our variable. Think of variables as placeholders. They hold the place for values we either do not know yet or values that can change.

For example, in the phrase 'Eight times a number,' the exact number is not given. By choosing a variable like x, we can easily refer to this unknown number in a mathematical expression.
Multiplication
Multiplication is one of the basic arithmetic operations. It involves combining equal groups. In algebra, multiplication is used to scale a variable.

In the exercise, the phrase 'Eight times a number' implies that the number, represented by x, is multiplied by 8. Here, we multiply 8 and x to get the product, which is written as 8x.

Remember, when multiplying a number by a variable in algebra, we write them next to each other without any symbols in between. For instance, 8x means '8 times x.'
Translation of Words to Symbols
Translating words into mathematical symbols is a critical skill in algebra. It involves converting phrases and sentences into algebraic expressions.

For the phrase 'Eight times a number,' the process is straightforward:
  • First, identify the variable (the unknown number). We use x.
  • Second, recognize the operation described. 'Times' indicates multiplication.
  • Third, write the expression by combining the number 8 and the variable x using multiplication, which results in 8x.

By translating words into symbols, we make it much easier to manipulate and solve mathematical problems.

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Most popular questions from this chapter

Solve and check. The symbol \(\sqsubseteq\) indicates an exercise designed to be solved with a calculator. $$ 8 x-\\{3 x-[2 x-(5 x-(7 x-1))]\\}=8 x+7 $$

Classify each statement as either true or false. The following sets are used: \(\mathrm{N}=\) the set of natural numbers; \(W=\) the set of whole numbers; \(\mathbb{Z}=\) the set of integers; \(\mathbb{C}=\) the set of rational numbers; \(\mathrm{H}=\) the set of irrational numbers; \(\mathrm{R}=\) the set of real numbers. $$ \mathrm{N} \subseteq W $$

Write an equivalent expression using the distributive law. $$ 3(a+5) $$

Classify each statement as either true or false. The following sets are used: \(\mathrm{N}=\) the set of natural numbers; \(W=\) the set of whole numbers; \(\mathbb{Z}=\) the set of integers; \(\mathbb{C}=\) the set of rational numbers; \(\mathrm{H}=\) the set of irrational numbers; \(\mathrm{R}=\) the set of real numbers. $$ \mathrm{H} \subseteq R $$

To the student and the instructor: Synthesis exercises are designed to challenge students to extend the concepts or skills studied in each section. Many synthesis exercises require the assimilation of skills and concepts from several sections. On a quiz, Mia answers \(6 \in \mathbb{Z}\) while Giovanni writes \(\\{6\\} \in \mathbb{Z} .\) Giovanni's answer does not receive full credit while Mia's does. Why?
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