## Definition

The ratio is used for comparing two quantities of the same kind. The ratio formula for two numbers says *a* and *b* is given by *a : b* or *a/b*. When two or more such ratios are equal, they are said to be in proportion. The concept of ratio and proportion is majorly based on ratios and fractions. The ratio and proportion are the key foundations for various other concepts in mathematics. Ratio and proportion have their applications in solving many daily life problems, while we are comparing heights, weights, distance or time or dealing with business transactions or while adding ingredients in cooking, and so on.^{1}

### Definition of Ratio

The ratio refers to the relationship between the quantities of two or more objects and it indicates the amount of one object contained in the other. It is used in certain situations when it comes to the comparison of two quantities and follows the method of division which is considered efficient enough. In other words, the ratio is defined as the comparison of two quantities of the same kind. This relation depicts how many times one quantity is equal to the other quantity. It is the number that can be used to express one quantity as a fraction of the other ones. Ratios are denoted by the symbol of the colon (:).^{1}

### Definition of Proportion

Proportion refers to a part, share, or number considered in relation to a whole, majorly a comparative relation. Two equivalent ratios are always in proportion. It is an equation or statement that is used to depict that the two ratios or fractions are equal. It is a mathematical comparison between two numbers. Accordingly, the ratios are said to be directly proportional to each other, if two sets of given numbers are increasing or decreasing in the same ratio. Proportions are denoted by the symbol (: 🙂 or equal to (=).^{1}

There are two types of proportions.

- Direct Proportion
- Inverse Proportion

## Who

No matter what you do, you will use ratios and proportions everyday.

## What

### Gears

For example, you are dealing with something that has a gear ratio that you need to understand.

- cars: engine, transmission, differential
- bicycles
- motorcycles
- clocks
- washing machines

### Everyday Uses

Or you are trying a new recipe and need to change the number of servings. When you are buying your groceries, you probably need to compare the prices at different stores so that you can decide where to buy at a cheaper price.

**What is principle of proportion in art?**^{ 6}

Proportion is one of the principles of art and design that organizes and arranges their structural elements, together with balance, unity, rhythm, and emphasis. The relationship between parts is the main issue in proportion, which is often discussed in terms of context and used standards.

**What is proportion as a principle of design?** ^{6}

Proportion refers to the relationship between one part of a design and another part or to the whole design. It is a comparison of sizes, shapes, and quantities.

## Why

Have you ever tried pedaling a bicycle up a really steep hill? It’s pretty much impossible unless you use the right gear to increase your climbing force. Once you’re back on the straight, it’s a different story. Flick to a different gear and you can go incredibly fast: you can magically make your wheels turn round much faster than you’re pedaling. Gears are helpful in machines of all kinds, not just cars and cycles. They’re a simple way to generate more speed or force or send the force of a machine off in another direction. In science, we say gears are simple machines.^{2}

While every professional kitchen uses recipes for certain preparations, the bulk of food production falls into routine techniques and procedures that cooks learn through practice and repetition. ** Culinary ratios** are one tool that helps cooks be more efficient and productive in the kitchen without the need for recipes. Ratios aid in recipe analysis and formulation, and open up a chef’s creativity to modify and create new recipes while helping achieve a better understanding of the science of cooking.

^{3}

You use ratios and proportions in daily activities, often without realizing you are making mathematical calculations. For example, you divide a pie among four people, proportioning it equally. You talk of a car giving you 30 miles per gallon, which is a ratio.^{4}

We are always interacting with ratios often without realizing it. From comparing the heights of different people to comparing crowd sizes, ratios are an everyday experience. Ratios are a useful way of comparing two or more quantities of different things in order to better understand how they relate to each other. They can be expressed mathematically to give a precise picture of proportions.^{5}

See Theoretical Knowledge Vs Practical Application.

## How

Many of the **References** and **Additional Reading** websites and **Videos** will assist you with your understanding of ratios.

As some professors say: “It is intuitively obvious to even the most casual observer.“

## References

^{1} “Ratio And Proportion – Basics, Definitions, Examples – Cuemath”. 2022. *Cuemath*. https://www.cuemath.com/commercial-math/ratio-and-proportion/.

^{2} Woodford, Chris. “Gears”. 2021. https://www.explainthatstuff.com/gears.html.

^{3} “Culinary Ratios — The Culinary Pro”. 2022. *The Culinary Pro*. https://www.theculinarypro.com/culinary-ratios.

^{4} Wilcox, Manon. 2022. “How Do We Use Ratios And Proportions In Everyday Life?”. *colors-newyork.com*. https://colors-newyork.com/how-do-we-use-ratios-and-proportions-in-everyday-life/.

^{5} “10 Examples Of Ratios In Daily Life – The Boffins Portal”. 2021. *The Boffins Portal*. https://boffinsportal.com/10-examples-of-ratios-in-daily-life/.

^{6} “How Are Proportions Used In Real Life? – Chetumenu.Com”. 2022. *Chetumenu.Com*. https://chetumenu.com/how-are-proportions-used-in-real-life/.

## Additional Reading

Drive, Learning, and How Car. 2022. “Why Are Gears Used In Cars » Learn Driving Tips”. *Learn Driving Tips*. https://learndriving.tips/learning-to-drive/how-to-change-gear-in-manual-car/why-are-gears-used-in-cars/.

“Dummies Guide To Bicycle Gears And Cycling Faster”. 2018. *European Cycling Tours » Road Cycling Holidays Europe » Supported Cycling Holidays For Groups And Individuals » Established Cycling Event Organiser » Charity UK Cycling Events » Corporate Cycling Events*. https://europeancyclingtours.com/dummies-guide-to-bicycle-gears/.

HowStuffWorks, Auto, Hood, and Drivetrain. 2000. “How Gear Ratios Work”. *Howstuffworks*. https://auto.howstuffworks.com/gears.htm.

“Intro To Ratios (Video) | Khan Academy”. 2022. *Khan Academy*. https://www.khanacademy.org/math/cc-sixth-grade-math/cc-6th-ratios-prop-topic/intro-to-ratios/v/ratios-intro.

“Ratio And Proportion – Definition, Formulas And Examples”. 2022. *BYJUS*. https://byjus.com/maths/ratios-and-proportion/.

“Ratios And Proportions | Lesson (Article) | Khan Academy”. 2022. *Khan Academy*. https://www.khanacademy.org/test-prep/praxis-math/praxis-math-lessons/praxis-math-number-and-quantity/a/gtp–praxis-math–article–ratios-and-proportions–lesson.

Santopietro, Ian. “What are gears in automobile?” 2018. https://qr.ae/pvy0NQ.

“Types Of Gears And Their Applications – Smlease Design”. 2018. *Smlease Design*. https://www.smlease.com/entries/mechanism/types-of-gear-and-applications/.

## Videos

### Ratios

### Gears

Gear ratios are foundational to mechanical machine design. This video will take you through the basics and get you well on your way to understanding all things about gears!

An introduction to gears from the simple machines perspective. Which are force multipliers? Which are speed multipliers? How do we calculate mechanical advantage?

What is a Compound Gear Train? How are compound gears different from Idler gears? How do you calculate the gear ratio in a compound gear train? By creating compound gear trains it is possible to produce enormous gear ratios that would be impossible to produce with just a simple gear set made up of two gears. In this video we take a look at compound gear trains. Calculating the gear ratio for a compound gear train is not hard but it is important to recognize that the two gears which share an intermediate shaft share angular quantities not tangential quantities. Even though there are four gears in a compound gear train, there are only two lines of action between the input and output shafts and really only two gear sets.

Gear ratios are a basic concept that will help you understand your bike better and will allow you to make informed decisions for future upgrades.

### Golden Ratio

This mathematics video tutorial provides a basic introduction into the Fibonacci sequence and the golden ratio. It explains how to derive the golden ratio and provides a general formula for finding the nth term in the Fibonacci sequence. This sequence approaches a geometric sequence when n becomes very large.