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Chapter 8: Problem 1

If one sector of a circle graph represents \(25 \%\) of the total graph, what fraction of the circle is represented by that sector?

Short Answer

Expert verified
The sector represents 1/4 or one fourth of the circle graph.

Step by step solution

01

Understanding Percentages and Fractions

Percent just means 'per hundred'. So, '25%' means 25 per hundred, or more simply 25/100.
02

Simplify the Fraction

Reduce the fraction 25/100 into its simplest form by dividing both the numerator and denominator by their biggest common factor, which in this case is 25. This results in 1/4.
03

Final Answer

After simplifying the fraction, it is concluded that the sector represents 1/4 or one fourth of the circle graph.

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Key Concepts

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

Understanding Percentages
Percentages are a way to express numbers as parts of a whole. A percentage represents how many parts out of 100 you have. For instance, if we say 25%, we mean 25 out of every 100 parts. This is the basis of understanding percentages:
  • Per hundred: The word "percent" literally means "per hundred."
  • Expressing fractions: Any percentage can be turned into a fraction by placing the number over 100.
These features make percentages a valuable tool for comparing different quantities and understanding their proportions to a whole. In a circle graph, percentages help show how large each sector is relative to the entire circle.
Exploring Fractions
Fractions are a way of dividing a whole into parts. They consist of a numerator and a denominator.
  • Numerator: The top part of a fraction, showing how many parts we are looking at.
  • Denominator: The bottom part, indicating into how many parts the whole is divided.
For example, the fraction \( \frac{1}{4} \) indicates that we have 1 out of 4 equal parts. Fractions are crucial in math since they allow us to break down quantities into smaller, more manageable pieces. In a circle graph, fractions translate percentages into a practical understanding of the graph's sectors.
Simplifying Fractions
To simplify fractions, we aim to reduce the fraction to its lowest terms.
  • Identify the greatest common factor (GCF): This is the biggest number that divides both the numerator and denominator without leaving a remainder.
  • Divide both parts of the fraction by the GCF: By doing this, the fraction is reduced to its simplest form.
In our example, simplifying \( \frac{25}{100} \) involves identifying 25 as the GCF. Dividing both 25 and 100 by 25 gives us \( \frac{1}{4} \). This smaller fraction, \( \frac{1}{4} \), is easier to work with and understand, clearly showing that one-quarter of the circle graph is being represented.

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Most popular questions from this chapter

Environment Carbon dioxide is among the gases that contribute to global warming. Carbon dioxide emissions of ten countries for a recent year are listed below. The figures are emissions in millions of metric tons per year. $$\begin{array}{|ll|l|} \hline \text { Canada } & 0.64 & \text { Japan } & 1.26 \\ \hline \text { China } & 5.01 & \text { Russian Federation } & 1.52 \\ \hline \text { Germany } & 0.81 & \text { South Korea } & 0.47 \\ \hline \text { India } & 1.34 & \text { United Kingdom } & 0.59 \\ \hline \text { Italy } & 0.45 & \text { United States } & 6.05 \\ \hline \end{array}$$ a. Find the range, the first quartile, the third quartile, and the interquartile range. b. Draw a box-and-whiskers plot of the data. c. Is the data value 21 in the interquartile range?

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