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Chapter 6: Problem 8

Write the ratio in two other ways. $$\frac{1}{8}$$

Short Answer

Expert verified
1:8 and '1 to 8'

Step by step solution

01

Understand the Ratio

The given ratio is written as a fraction \(\frac{1}{8}\). A ratio compares two quantities showing how many times the first number contains the second.
02

Write the Ratio with a Colon

Rewrite the fraction \(\frac{1}{8}\) using a colon. The fraction \(\frac{1}{8}\) can be written as 1:8.
03

Write the Ratio in Words

The ratio \(\frac{1}{8}\) can also be expressed in words as '1 to 8'.

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Key Concepts

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

Understanding Fractions to Ratios
To understand how to convert fractions to ratios, you need to grasp what a fraction represents. A fraction, like \( \frac{1}{8} \), shows a part of a whole. The number on the top is the numerator and represents how many parts we have. The number on the bottom is the denominator and represents how many equal parts the whole is divided into.

To convert this fraction into a ratio, we keep the numerator and denominator, but use a different notation to express their relationship. In this case, \( \frac{1}{8} \) becomes the ratio 1 to 8. It's important because it shows how much of one thing there is compared to another.
Using Colon Notation for Ratios
Colon notation is another common way to write ratios. It replaces the fraction bar with a colon.

If we start with the fraction \( \frac{1}{8} \), the colon notation becomes 1:8. This does not change the meaning; it simply illustrates the ratio in a different format.

Colon notation is straightforward and often used in various contexts. For example, in recipes or while describing odds in probability and statistics:
  • A recipe may say use a sugar to flour ratio of 1:3, meaning one part sugar to three parts flour.
  • Odds might be given as 4:1, meaning four chances of one event happening for every chance of another.
Colon notation is handy for concise communication and is widely recognizable.
Verbal Expression of Ratios
Expressing ratios verbally is another method that easily communicates the relationship between two numbers.

In our example, the ratio \( \frac{1}{8} \) can be written as 1:8 in colon notation, and can be expressed verbally as '1 to 8'.

This verbal expression helps when explaining ratios in conversation, making the relationship clear even without writing it down. It's also useful in oral instructions and storytelling.
  • In a classroom setting, a teacher might say there is a '1 to 5' ratio of teachers to students.
  • In sports, a coach might mention a '3 to 1' ratio of practice sessions to matches.
Verbal expressions make ratios accessible and understandable, adding clarity to spoken explanations.

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Most popular questions from this chapter

Determine whether the given value is a solution to the proportion. $$\frac{14}{x}=\frac{12}{-18}, \quad x=-21$$

The ratio of a person's height to the length of the person's lower arm (from elbow to wrist) is approximately 6.5 to \(1 .\) Measure your own height and lower arm length. Is the ratio you get close to the average of 6.5 to \(1 ?\)

Refer to the table showing Alex Rodriguez's salary (rounded to the nearest \(\$ 100,000\) ) for selected years during his career. Write each ratio in lowest terms. \begin{array}{l|l|l|l} \hline \text { Year } & \text { Team } & \text { Salary } & \text { Position } \\ \hline 2007 & \text { New York Yankees } & \$ 22,700,000 & \text { Third baseman } \\ \hline 2004 & \text { New York Yankees } & \$ 22,000,000 & \text { Third baseman } \\ \hline 2000 & \text { Seattle Mariners } & \$ 4,400,000 & \text { Shortstop } \\ \hline 1996 & \text { Seattle Mariners } & \$ 400,000 & \text { Shortstop } \\ \hline \end{array} Write the ratio of Alex's salary for the year 1996 to the year 2000 .

Write a proportion for each statement. Then solve for the variable. 9 is to 12 as \(w\) is to 30

Determine whether the ratios form a proportion. $$\frac{9}{10}=\frac{8}{9}$$
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