A proportion is a mathematical expression that represents the ratio of two numbers, showing how many times one value contains another or is contained within it. An example of a proportion is "the ratio of apples to oranges" in a fruit basket. Knowing how to work out a proportion helps you understand many different concepts, such as how much to increase the different amounts in a recipe if you are doubling the portion, or how much you will need to anticipate for a certain amount of guests. If you want to know how to set it up, just follow these steps.
Steps
Method 1 of 2: Report
Step 1. Use a symbol to denote the relationship
To indicate that you are using a ratio, you can use a division sign (/), a colon (:), or the word “a”. For example, if you wanted to say "For every five men at the party, there are three women," you could use any of the three symbols shown. Here's how you would do it:
- 5 men / 3 women.
- 5 men: 3 women.
- 5 men to 3 women.
Step 2. Write the first quantity to the left of the symbol
Note the quantity of the first item preceding the symbol you have chosen. You should also remember to indicate the unit you are working with, in addition to the number, be it men or women, chickens or goats, kilometers or meters.
Example: 20 g of flour
Step 3. Write the second number to the right of the symbol
After writing the first data followed by the symbol, you should add the second, with its unit.
Example: 20 g of flour / 8 g of sugar
Step 4. Simplify your report (optional)
You can simplify your report to do something akin to repurposing a recipe. If you're using 20g of flour for a recipe, you know you need 8g of sugar, and you're done. But if you want to scale the report as much as possible, then it will be necessary to simplify it, writing it in the form of its minimum terms. It's a good idea to use the same process you would use to simplify a fraction. To do this, you need to find the greatest common denominator (GCD) and then see how many times that number is in any given quantity.
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To find the GCD between 20 and 8, write down all the factors of the two numbers and find the largest number that is divisor of both. Here's how to do it:
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20: 1, 2,
Step 4., 5, 10, 20
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8: 1, 2,
Step 4., 8
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- 4 is the GCD between 20 and 8: it is the largest number that divides both numbers. To get your simplified ratio, just divide both numbers by 4:
- 20 ÷ 4 = 5.
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8 ÷ 4 = 2.
The new ratio is 5 g of flour / 2 g of sugar
Step 5. Put the ratio as a percentage (optional)
If you want to turn the ratio into a percentage, you just need to complete the following steps:
- Divide the first number by the second. Example: 5 ÷ 2 = 2, 5.
- Multiply the result by 100. Example: 2.5 x 100 = 250.
- Add a percent sign: 250%.
- This means that, for each unit of sugar, there are 2.5 units of flour, i.e. there is 250% flour compared to sugar.
Method 2 of 2: Learn More About Reports
Step 1. The order in which the quantities are considered does not matter
The ratio simply represents the ratio of two quantities: the proportion "5 apples to 3 pears" equals "3 pears to 5 apples". Therefore, 5 apples / 3 pears makes as much sense as 3 pears / 5 apples.
Step 2. A ratio can also be used to describe probability
For example, the probability of rolling a 2 is 1/6 or a six.
Step 3. You can re-proportion a ratio between numerator and denominator
While you may be used to simplifying numbers whenever you can, you can also apply the reverse procedure. For example, if you know you need 2 cups of water for every single cup of pasta, but you want to boil 2 cups of pasta, then you will need to re-proportion the ratio to know how much water to use: you simply multiply the numerator and denominator by the same number.
