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Chapter 11: Problem 3

Translate to an algebraic expression. The product of \(97 \%\) and some number

Short Answer

Expert verified
0.97x

Step by step solution

01

Identify the elements

The phrase 'the product of' suggests a multiplication operation; '97%' is a percentage and 'some number' represents an unknown variable.
02

Convert percentage to decimal

Convert 97% into its decimal form by dividing it by 100: 97% = 97/100 = 0.97
03

Assign a variable

Let the 'some number' be represented by the variable x.
04

Translate to algebraic expression

Now, translate the phrase into an algebraic expression: The product of 0.97 and x is written as 0.97x

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Key Concepts

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

Multiplication
Multiplication is a fundamental arithmetic operation that signifies combining groups of equal sizes. It鈥檚 often represented through symbols like \(*\).

For instance, the phrase 'the product of' in the problem indicates we need to multiply.

In algebra, multiplying a number by another means finding the total when you have some number of groups of a certain size. Here, we are multiplying 0.97 by a variable, which means we are taking 97% of an unknown value. We'll discuss converting this percentage soon.
Percentages to Decimals Conversion
Converting percentages to decimals is straightforward. To convert a percentage to a decimal, divide the percentage value by 100. This is because 'percent' means per hundred.

For instance, in the problem, we need to convert 97%. Here鈥檚 the step-by-step conversion:
  • Start with 97%.
  • Divide by 100: \(97 \div 100 = 0.97\)

So, 97% becomes 0.97 when converted to a decimal. This conversion is essential as it simplifies the operation into a standard numerical form.
Variable Representation
In algebra, variables are used to represent unknown values. We commonly use alphabet letters like x, y, or z for variables.

For this problem, 'some number' is unknown, so we assign it the variable x. This step converts verbal expressions into a mathematical one for further operations.

This step-by-step approach helps in creating an algebraic expression from a word problem and makes complex problems more manageable.

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Most popular questions from this chapter

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Solve using the multiplication principle. Don't forget to check! $$ \frac{3}{4} x=27 $$

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