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Chapter 7: Problem 12

Translate each to a proportion. Do not solve.9.6 is what percent of \(96 ?\)

Short Answer

Expert verified
\( \frac{9.6}{96} = \frac{x}{100} \)

Step by step solution

01

Identify the Unknown

We need to determine what percentage 9.6 is of 96. Let the unknown percentage be represented by the variable \( x \).
02

Proportion Setup

Translate the phrase '9.6 is what percent of 96' into the equation \( \frac{9.6}{96} = \frac{x}{100} \). Here, 9.6 is a part of the whole, 96, and \( x \) represents the percentage which is generated when the fraction is proportionally related to 100.

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Key Concepts

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

Percentages Insights
A percentage is a way to express a number as a part of a whole, specifically out of 100. It tells us how large or small a quantity is, relative to another quantity. Here, the problem asks us what percentage 9.6 is of 96.
  • The term 'percent' means 'out of 100'. Thus, calculating a percentage involves converting a fraction into a form where the denominator is 100.
  • The percentage represents the given part (in this case, 9.6) relative to the whole (which is 96).
  • Percentages are often used in everyday life for discounts, statistics, and comparisons. Understanding how to find a percentage is crucial for dealing with many real-world scenarios.
Knowing how to express one number as a percentage of another allows us to quantify comparisons in a straightforward manner.
Equations in Proportion Problems
Equations are mathematical statements that assert equality between two expressions. In the context of our problem, we set up a proportion equation to relate numbers in different ratios to each other. The equation format used here is crucial in solving percentage-related questions.
  • The equation \( \frac{9.6}{96} = \frac{x}{100} \) sets two ratios equal: the ratio of part to whole, \( \frac{9.6}{96} \), and the ratio for finding percentages, \( \frac{x}{100} \).
  • This sort of equation is called a proportion. A proportion shows that two ratios or fractions are equivalent.
  • The purpose of setting the equation's second part \( \frac{x}{100} \) is because we are interested in expressing the first part in terms of percentages, where percentages are fractions of 100.
  • Using equations in this way provides a clear method to convert between direct numbers and their percentage equivalents.
Equations allow us to logically determine unknown values through known relationships.
Understanding Fractions
Fractions represent a part of a whole. They consist of a numerator (the top number, which tells how many parts we have) and a denominator (the bottom number, which tells how many parts make up a whole). In our exercise, we're dealing with fractions like \( \frac{9.6}{96} \), which represents the relationship between the part and whole.
  • Fractions can be converted to other forms like decimals and percentages. For instance, \( \frac{9.6}{96} \) can be viewed as a step toward finding the percentage by comparing with 100.
  • The meaning of the fraction changes when expressed as a percentage, but the value remains proportionally the same.
  • Fractions are foundational in mathematics for expressing ratios and proportions, which are pivotal in percentage problems.
Mastering fractions is critical because they are everywhere in math and provide a basis for more complex operations like proportions and percentages.

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Most popular questions from this chapter

Complete each table. $$\begin{array}{|c|c|c|} \hline \text { Percent } & \text { Decimal } & \text { Fraction } \\ \hline & 0.525 & \\ \hline & & \frac{3}{4} \\ \hline 66\frac{1}{2} \% & & \\ \hline & & \frac{5}{6} \\ \hline 100 \%& & \\ \hline & & \frac{7}{50} \\ \hline\end{array}$$

Perform each indicated operation. See Sections 4.3 through \(4.5,4.7,\) and 5.2 through \(5.4 .\) $$9.2+1.98$$

Solve. \(78 \%\) of 24 is what number?

In 1999, Napster, a free online file-sharing service, debuted. iTunes, which debuted in 2003 , is given credit for getting people to start paying for digital music. In \(2015,\) for the first time, streaming music was the largest revenue producer in the music industry. By comparing prices, a particular music album downloads from a low of \(\$ 2.99\) to a high of \(\$ 7.99 .\) Find the percent of increase from \(\$ 2.99\) to \(\$ 7.99 .\)

In a particular year, 0.781 of all electricity produced in France was nuclear generated. Write this decimal as a percent.
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