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Chapter 6: Problem 33

Translate to a proportion. Do not solve. $$ \text { What is } 9.4 \% \text { of } \$ 8300 ? $$

Short Answer

Expert verified
Setup the proportion as \( \frac{9.4}{100} = \frac{x}{8300} \).

Step by step solution

01

Identify the percentage and the whole

First, determine the given percentage and the whole value. In this case, the percentage is 9.4% and the whole value is $8300.
02

Express percentage as a fraction

Convert the percentage to a fraction or a decimal. Here, 9.4% can be written as \( \frac{9.4}{100} \) or 0.094.
03

Set up the proportion

Translate the problem into a proportion. Let \( x \) be the unknown value. The proportion will be \( \frac{9.4}{100} = \frac{x}{8300} \).

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Key Concepts

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

percentage conversion
Percentage conversion is an essential skill in mathematics. A percentage represents a number out of 100. To convert a percentage into a fraction, place the percentage number over 100. For example, 9.4% can be written as \(\frac{9.4}{100}\). This fraction represents the portion of the whole (in this case, 8300) that the percentage is trying to quantify.

You can also convert a percentage to a decimal. This is done by dividing the percentage by 100. For instance, 9.4% becomes 0.094 when converted to a decimal. Decimals and fractions provide alternative numeric forms that can be easier to work with in various calculations.
mathematical proportion
A mathematical proportion is an equation that equates two ratios. For example, if you are given 9.4% of 8300, you can set up a proportion to solve for the unknown quantity (let's call it x). The proportion can be set up as \(\frac{9.4}{100} = \frac{x}{8300}\).

This shows that the ratio of the percentage to 100 is equal to the ratio of the unknown quantity to the whole value (8300). Proportions are useful for solving problems involving part-whole relationships, such as finding an unknown part when given the whole and a percentage.
fraction to decimal conversion
Converting fractions to decimals is another critical mathematical skill. To convert a fraction like \(\frac{9.4}{100}\) to a decimal, you simply perform the division of the numerator by the denominator. Therefore, \(\frac{9.4}{100}\) becomes 0.094.

Understanding both fractions and decimals helps you move seamlessly between different forms of numbers. This flexibility can be particularly beneficial when solving complex problems that involve diverse mathematical operations.

Remember, you often need to convert between percentages, fractions, and decimals, so getting comfortable with these conversions will help immensely in comprehending and solving various math problems.

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Most popular questions from this chapter

Multiply and simplify. $$ \frac{4}{15} \times \frac{3}{20} $$

Convert to decimal notation. \(\frac{25}{11}\)

Solve. The sales tax on the purchase of a new fishing boat is \(\$ 904,\) and the sales tax rate is \(8 \%\). What is the purchase price (the price before tax is added)?

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On a test of 40 items, Christina got \(91 \%\) correct. (There was partial credit on some items.) How many items did she get correct? incorrect?
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