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Chapter 6: Problem 14

Translate to a proportion. Do not solve. $$ 63.1 \% \text { of } 80 \text { is what? } $$

Short Answer

Expert verified
63.1% of 80 is \( \frac{63.1}{100} = \frac{x}{80} \).

Step by step solution

01

- Understand the Problem

We are given a percentage (63.1%) and a number (80). We need to find what 63.1% of 80 is.
02

- Convert percentage to fraction

Convert 63.1% to a fraction by dividing by 100: 63.1% = \( \frac{63.1}{100} \).
03

- Set up the proportion

We can write the statement '63.1% of 80 is what?' as a proportion: \( \frac{63.1}{100} = \frac{x}{80} \).

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Key Concepts

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

Percentage
A percentage is a way of expressing a number as a fraction of 100. It is denoted by the symbol %.
For example, 63.1% means 63.1 out of 100.
To find out what 63.1% of a certain number is, you need to convert the percentage into a fraction. This makes it easier to work with and calculate.
Whenever you see a percentage, remember to think of it in terms of 'per 100'.
This makes it simpler to understand and use in various problems.
Fraction Conversion
Converting a percentage to a fraction is simple. Just divide the percentage by 100.
For example, 63.1% becomes \(\frac{63.1}{100}\).
Why do we do this? Because percentages are essentially fractions themselves.
When converting, always place the percentage number above 100.
This converts the percentage into a fraction that is easier to handle.
In our exercise, 63.1% is converted to \(\frac{63.1}{100}\), which can be used in further calculations.
Mathematics Education
Understanding these concepts is crucial in math education.
Percentage and fraction conversion are fundamental skills used in many areas of mathematics including proportions and algebra.
Proportions are used to compare two ratios or fractions, and they often appear in real-life scenarios.
Breaking down problems step by step, like in the given exercise, helps to understand the process better.
In math education, it's important to convert abstract concepts into familiar terms.
This helps students grasp difficult ideas more easily by relating them to everyday experiences.

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Most popular questions from this chapter

The average American family spends approximately \(16 \%\) of its income on transportation. If a family's yearly income is \(\$ 69,700,\) how much is its transportation expenditure?

Solve. The sales tax is \(\$ 35.80\) on the purchase of a refrigeratorfreezer that sells for \(\$ 895 .\) What is the sales tax rate?

Solve. The sales tax on the purchase of a used car is \(\$ 434\) and the sales tax rate is \(7 \%\). What is the purchase price?

Solve. Animal Instinct Pet Supply borrows \(\$ 6500\) at \(5 \frac{1}{4} \%\) for 90 days. Find (a) the amount of interest due and (b) the total amount that must be paid after 90 days.

The Mississippi River, which extends from its source at Lake Itasca in Minnesota to the Gulf of Mexico, is 2348 mi long. Approximately \(77 \%\) of the river is navigable. How many miles of the river are navigable?
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