Learn about proportions, how they are used, attempt quiz on proportions

Last updated : 1 January 2024, Monday

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Table of Topics |
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What is a proportion? |

How are Proportions Used ? |

How to Solve Proportions Problems? |

Proportions practice |

## What is a proportion ?

A proportion is a mathematical statement that two ratios are equal.

Proportions can be written in various ways, including:

- Using a double colon (::) : For example, 3:5 :: 6:10.
- As fractions: For example, 3/5 = 6/10
- Using the equals sign (=): 3:5 = 6:10
- In words: “Three to five is equal to six to ten.”

## How are Proportions Used ?

Proportions are used in many different areas of mathematics, including geometry, algebra, and trigonometry. They are also used in many real-world applications, such as cooking, construction, and finance.

Here are some examples of how proportions are used:

- Cooking: A recipe may call for a certain proportion of ingredients, such as 1 part flour to 2 parts milk. This means that for every 1 cup of flour, you need to use 2 cups of milk.
- Construction: Architects and engineers use proportions to design buildings and other structures.For example, the Golden Ratio is a specific proportion that is often used in architecture to create visually pleasing designs.
- Finance: Investors use proportions to compare the performance of different investments. For example, a mutual fund may have a return of 10% per year, while a stock market index may have a return of 5% per year. This means that the mutual fund is outperforming the stock market index by a proportion of 2:1.

## How to Solve Proportions Problems?

There are two main ways to solve proportion problems:

- Using cross-multiplication: This method involves multiplying the numerator of one ratio by the denominator of the other ratio, and vice versa. For example, to solve the proportion “3:5 = 6:10,” you would multiply 3 by 10 and 5 by 6. This gives you the equation 30 = 30, which is true.
- Using the unit rate: This method involves dividing both sides of the proportion by the same number. For example, to solve the proportion “3:5 = 6:10” you would divide both sides by 5. This gives you the equation 3=3, which is also true.