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Chapter 6: Problem 6

Write the ratio in two other ways. $$8: 13$$

Short Answer

Expert verified
The ratio 8:13 can also be written as \(\frac{8}{13}\) and 8 to 13.

Step by step solution

01

Title - Convert to Fraction

Write the ratio as a fraction. For the ratio 8:13, it can be written as \(\frac{8}{13}\).
02

Title - Use 'to' Notation

Express the ratio using the word 'to'. For the given ratio 8:13, it can be written as 8 to 13.

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Key Concepts

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

fractions
In mathematics, a fraction represents a part of a whole. A fraction consists of a numerator (the top number) and a denominator (the bottom number). The fraction \(\frac{8}{13}\) means that 8 parts are being considered out of a total of 13 parts. Fractions are a way to express ratios, as we see in the ratio 8:13, which is expressed as a fraction in Step 1 of our exercise. Fractions can be useful in comparing different quantities and understanding proportions in a more intuitive way.
proportions
A proportion is an equation that states that two ratios or fractions are equal. For example, if \(\frac{8}{13} = \frac{x}{y}\), where x and y are different quantities, this is a proportion. In our exercise, the ratio 8:13 can be used to make different proportions. This helps in solving problems where relationships between quantities are constant. Knowing how to work with proportions is crucial in many areas of mathematics and science, where finding equivalent ratios can simplify problem-solving.
mathematical notation
Mathematical notation is a system of symbols and signs used to represent numbers, operations, and relations. It helps communicate mathematical ideas clearly and efficiently. In our exercise, the ratio 8:13 is a type of notation that shows the relationship between two quantities. Writing it as \(\frac{8}{13}\) or '8 to 13' are other forms of mathematical notation. Using proper notation makes it easier to perform operations and solve equations systematically.

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Most popular questions from this chapter

In a recent year, the rate of breast cancer in women was 110 cases per \(100,000\) women. At that time, the state of California had approximately \(14,000,000\) women. How many women in California would be expected to have breast cancer?

Write a proportion for each statement. Then solve for the variable. 25 is to 100 as 9 is to \(y\)

Solve the proportion. Be sure to check your answers. $$\frac{6}{5}=\frac{-\frac{1}{2}}{t}$$

Determine whether the given value is a solution to the proportion. $$\frac{x}{40}=\frac{1}{-8} ; \quad x=-5$$

Solve the proportions. $$\frac{x-2}{4 x}=\frac{3}{8}$$
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