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Chapter 4: Problem 6

In Exercises \(1-10,\) write each of the phrases as a ratio. 5 with to 11 without

Short Answer

Expert verified
5:11 or \(\frac{5}{11}\)

Step by step solution

01

Identify the elements

Locate the numbers mentioned in the phrase. Here, the numbers are 5 (with) and 11 (without).
02

Write the ratio

Write the ratio of 5 to 11. Ratios can be expressed using a colon or as a fraction.
03

Format the ratio

The ratio of 5 with to 11 without is expressed as 5:11 or \(\frac{5}{11}\).

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Key Concepts

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

writing ratios
Writing ratios is a fundamental skill in algebra. Ratios are used to compare two or more quantities. Here is how to write a ratio step-by-step:

First, identify the numbers you need to compare. In the example, we look at '5 with to 11 without'. The numbers we need are 5 and 11.

Next, write the ratio by placing the numbers in the order mentioned. You can express this as 5:11 or as a fraction, \(\frac{5}{11}\).

Using both formats can be helpful, especially when solving different types of problems. Practice makes it easier to write ratios correctly and quickly.
elementary algebra
Elementary algebra helps us understand how to work with numbers and variables. It's the building block for more complex mathematics.

One key concept in elementary algebra is the use of ratios, which compare quantities and show the relationship between them.

For example, the ratio 5:11 tells us that for every 5 units of one quantity, there are 11 units of another.

Algebra also teaches us to manipulate these expressions through addition, subtraction, multiplication, and division to solve problems. Once you grasp these foundational concepts, you'll find it easier to tackle more advanced topics in algebra.
mathematical expressions
Mathematical expressions consist of numbers, variables, and operators. They represent real-world phenomena in a simplified, precise way.

For instance, in the exercise, the ratio \(\frac{5}{11}\) is a simple mathematical expression showing the relationship between 'with' and 'without'.

Understanding how to read and write these expressions is crucial for solving algebra problems efficiently. It involves recognizing different symbols and knowing how to apply mathematical operations. This skill not only aids in mathematics but is also useful in fields like science and engineering.

Practice regularly by converting word problems into mathematical expressions to enhance your understanding.

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Most popular questions from this chapter

Set up an equation or inequality and solve the problem. Be sure to indicate clearly what quantity your variable represents. Round to the nearest tenth where necessary. Sal has \(\$ 3200\) invested in an account paying \(7.2 \%\) interest per year. At what rate must he invest an additional \(\$ 2800\) so that the annual interest from the two investments will be \(\$ 390 ?\)

Use a calculator to do the computation. Round off to three decimal places where necessary. $$\frac{2}{5} \div \frac{8}{9}$$

Solve the equations and inequalities. $$0.155 x+0.075(80-x)=8.4$$

In each of the following exercises, perform the indicated operations. Express your answer as a single fraction reduced to lowest terms. $$\frac{2}{5 x y}+\frac{1}{10 x^{2}}$$

Set up an equation or inequality and solve the problem. Be sure to indicate clearly what quantity your variable represents. Round to the nearest tenth where necessary. A car that is insured by the Reliable Auto Insurance Company is damaged in an accident. The company will pay for damages to the car up to \(75 \%\) of its Kelley Blue Book value. If the company pays \(\$ 8700\) on a certain claim, what can you say about the Kelley Blue Book value of the car?
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