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Chapter 5: Problem 1

Find fraction notation for each ratio. You need not simplify. $$ 4 \text { to } 5 $$

Short Answer

Expert verified
\( \frac{4}{5} \)

Step by step solution

01

Understand the Ratio Definition

A ratio is a relationship between two numbers showing how many times the first number contains the second. Ratios can be represented in fraction form.
02

Identify the Numbers in the Ratio

In the given ratio '4 to 5', the first number is 4 and the second number is 5.
03

Write the Fraction Notation

To write the ratio as a fraction, place the first number (4) as the numerator and the second number (5) as the denominator. This gives the fraction \(\frac{4}{5}\).

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Key Concepts

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

Understanding Ratios
A ratio is a way to compare two quantities by showing the relative size of one quantity to the other. It tells us how many times one number is contained within another number. Ratios help us understand relationships between quantities in a simple and intuitive way.
For example, a ratio of 4 to 5 tells us that for every 4 of a certain item, there are 5 of another.
  • If you have 4 apples and 5 oranges, the ratio of apples to oranges is 4 to 5.
Ratios are often written in three different ways: as a fraction (4/5), with a colon (4:5), or using the word 'to' (4 to 5). However you write it, the important thing is understanding the relationship between the two numbers.
Fraction Form of a Ratio
Converting a ratio to fraction form is simple and straightforward. A ratio like '4 to 5' can be expressed as the fraction \(\frac{4}{5}\).
Here鈥檚 the step-by-step process to convert a ratio into its fraction form:
  • First, identify the two numbers in the ratio. For '4 to 5', the first number is 4, and the second number is 5.
  • Next, place the first number (4) as the numerator.
  • Then, place the second number (5) as the denominator.
So the ratio '4 to 5' becomes \(\frac{4}{5}\) in fraction form. When you see or write fractions from ratios, remember they describe the same relationship as the original ratio.
Numerator and Denominator: Key Components of Fractions
Understanding the parts of a fraction is essential when working with ratios in fraction form. A fraction consists of two parts:
  • Numerator: The top number of the fraction, representing the number of parts we have.
  • Denominator: The bottom number of the fraction, indicating the total number of equal parts that make up a whole.
In our example, the ratio '4 to 5' is written as \(\frac{4}{5}\). Here, the numerator is 4 and the denominator is 5.
The numerator (4) shows how many parts are being considered, and the denominator (5) shows into how many parts the whole is divided. This structure helps to clearly indicate the relationship between the two quantities. Mastering this concept allows you to easily convert and interpret ratios.

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Most popular questions from this chapter

To measure the height of a hill, a string is stretched from level ground to the top of the hill. A 3 -ft stick is placed under the string, touching it at point \(P, \underline{a}\) distance of \(5 \mathrm{ft}\) from point \(G,\) where the string touches the ground. The string is then detached and found to be \(120 \mathrm{ft}\) long. How high is the hill?

Solve. $$ \frac{328.56}{627.48}=\frac{y}{127.66} $$

A student eats 3 hamburgers in \(15 \mathrm{~min}\). What is the rate in hamburgers per minute? in minutes per hamburger?

Solve. $$ \frac{8}{2.4}=\frac{6}{y} $$

Solve. $$ \frac{0.12}{0.04}=\frac{t}{0.32} $$
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