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Chapter 5: Problem 6

Find fraction notation for each ratio. You need not simplify. $$ 2.3 \text { to } 22 $$

Short Answer

Expert verified
The fraction notation for the ratio is \( \frac{2.3}{22} \).

Step by step solution

01

Identify the two quantities

Identify the two quantities given in the ratio. Here the quantities provided are 2.3 and 22.
02

Write the ratio as a fraction

Write the ratio of the two quantities as a fraction. In this case, the ratio of 2.3 to 22 can be written as \[ \frac{2.3}{22} \]
03

Verify the fraction notation

Ensure that the fraction accurately represents the given ratio. \[ \frac{2.3}{22} \] is the fraction notation for the ratio 2.3 to 22.

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Key Concepts

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

Ratios
A ratio compares two quantities by showing how many times one value contains or is contained within the other. In our exercise, the ratio is given as 2.3 to 22. We can write this as 2.3:22. This shows a direct comparison between the two numbers. Ratios are useful for understanding relationships between different quantities. They are often seen in problems involving rates, such as speed (miles per hour) or density (people per square mile). When dealing with ratios, it is crucial to keep the order of the terms consistent, as it affects the relationship between the values.
Fractions
Fractions are a way of representing parts of a whole. When we talk about converting a ratio to fraction notation, we are essentially expressing the ratio as a division. For example, the ratio 2.3:22 can be written as the fraction \( \frac{2.3}{22} \). This fraction represents how many parts of 22 there are in 2.3. Fractions consist of a numerator (the top number) and a denominator (the bottom number). When converting ratios to fractions, the first term of the ratio becomes the numerator, and the second term becomes the denominator. In our case, 2.3 becomes the numerator, and 22 becomes the denominator.
Mathematical Notation
Mathematical notation provides a way to represent mathematical concepts clearly and unambiguously. It includes symbols and layouts used to write down mathematical ideas. In this exercise, we use fraction notation to express a ratio in a different form. The fraction notation for the ratio 2.3:22 is written as \( \frac{2.3}{22} \). This way, anyone can clearly interpret the relationship between the two values. Mathematical notation helps to communicate complex ideas more efficiently. It is essential to write the notation correctly to avoid misunderstandings. Always ensure the symbols and structures used align with standard mathematical practices.

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Most popular questions from this chapter

A scale model of an addition to a medical clinic is \(15 \mathrm{~cm}\) wide at the base and rises to a height of \(19 \mathrm{~cm} .\) If the actual base is to be \(120 \mathrm{ft},\) what will the actual height of the addition be?

Solve. $$ \frac{15}{y}=\frac{3}{4} $$

Solve. $$ \frac{\frac{1}{4}}{\frac{1}{2}}=\frac{\frac{1}{2}}{x} $$

Solve. $$ \frac{2}{5}=\frac{12}{x} $$

Find the unit price of each brand in Exercises 31-34. Then, in each exercise, determine which brand is the better buy based on unit price alone. $$ \begin{array}{|c|c|c|} \hline \text { Brand } & \text { Size } & \text { Price } \\ \hline \mathrm{B} & 32 \mathrm{oz} & \$ 5.99 \\ \mathrm{E} & 48 \mathrm{oz} & \$ 6.99 \\ \hline \end{array} $$
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