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Chapter 8: Problem 25

Write each fraction as a percent. $$\frac{1}{4}$$

Short Answer

Expert verified
Question: Convert the fraction $$\frac{1}{4}$$ into a percentage. Answer: $$25\%$$

Step by step solution

01

Divide the Numerator by the Denominator

To begin, we will divide the numerator (1) by the denominator (4). This will give us a decimal value. $$\frac{1}{4} = 0.25$$
02

Multiply the Decimal Value by 100

Now that we have the decimal value, we will multiply it by 100 to convert it into a percentage. $$0.25 \times 100 = 25$$
03

Write the Result as a Percent

Finally, we write the result from the previous step as a percentage. $$25\%$$ So, $$\frac{1}{4}$$ as a percent is $$25\%$$.

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Key Concepts

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

Understanding Fractions
Fractions are a way to represent parts of a whole. They consist of a numerator and a denominator.
The numerator is the number on top and shows how many parts you have. The denominator is the number on the bottom and tells how many equal parts the whole is divided into.

Consider the fraction \(\frac{1}{4}\).
  • Here, 1 is the numerator, meaning one part out of the four total parts.
  • 4 is the denominator, indicating the total number of equal parts.
Understanding fractions is crucial as they are the building blocks for converting values to percentages. They help in understanding proportions and can be applied in everyday situations like measuring ingredients in cooking or dividing a bill among friends.
Converting Fractions to Percentages
Converting fractions to percentages involves transforming a fraction into a familiar and easily comparable form: a percentage.
This conversion is helpful as percentages provide a straightforward way of understanding fractions in terms of 100 鈥� the whole.

To convert \(\frac{1}{4}\) into a percentage:
  • First, divide the numerator by the denominator. This gives you a decimal. So, \(\frac{1}{4} = 0.25\).
  • Next, multiply the decimal by 100. This step adjusts the fraction to a percentage form. Hence, \(0.25 \times 100 = 25\).
The percentage representation of \(\frac{1}{4}\) is 25%.
Using percentages simplifies comparison between different values, as they normalize fractions to a scale of 100.
The Role of Division in Fraction Conversion
Division plays an essential role when converting fractions to percentages. It is the first step where you take the value of the fraction and express it as a decimal.

For the fraction \(\frac{1}{4}\):
  • The numerator, 1, is divided by the denominator, 4.
  • This calculation is represented as \(1 \div 4 = 0.25\).
Division helps to simplify the fraction into a decimal.
Once in decimal form, it becomes easier to multiply by 100 to transform it into a percentage, making the fraction easier to interpret and use in comparisons.
The Importance of Multiplication in Finding Percentages
Multiplication is the next step after division when converting a fraction to a percentage. Once you have the decimal, you multiply it by 100.
This step is crucial as it scales the decimal to a percentage, which is a part of a whole expressed out of 100.

Using our example \(0.25 \), the calculation is:
  • Multiply \(0.25\) by 100 to find its percentage form.
  • This gives \(0.25 \times 100 = 25\).
  • Thus, \(\frac{1}{4}\) is equal to 25%.
Multiplication in this context serves as a scaling device, converting the more abstract decimal into a commonly understood percentage, making comparisons across different fractions easier.

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Most popular questions from this chapter

Suppose in a 24 -hour period a person spends 8 hours sleeping, 7 hours working, 1 hour commuting, and 1 hour eating. What percent of the day is left?

Write each decimal number as a percent. $$0.96$$

Draw a circle graph showing each percent. After listening to a speaker at a conference, participants are asked to rate the presentation as excellent, good, fair, or poor. The following table shows the response. $$\begin{array}{l|c} \text { Excellent } & 32 \% \\ \hline \text { Good } & 48 \% \\ \hline \text { Fair } & 12 \% \\ \hline \text { Poor } & 8 \% \end{array}$$ (GRAPH CANT COPY)

What number is \(2 \%\) of \(70 ?\) $$ \begin{array}{l} n=0.2 \cdot 70 \\ n=14 \end{array} $$

Write each fraction as a percent. $$\frac{1}{9}$$
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