How to Calculate a Ratio
A ratio compares two quantities and tells you how much of one there is for every unit of another. Learning how to calculate a ratio is a useful everyday skill, whether you are scaling a recipe, mixing a solution, comparing prices, or checking homework.
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Try the Ratio CalculatorHow Do I Calculate a Ratio Between Two Numbers?
To calculate the ratio between two numbers, write the two amounts with a colon between them and then simplify by dividing both sides by their greatest common divisor. If you have 30 red marbles and 20 blue marbles, you write 30:20. The largest number that divides both 30 and 20 evenly is 10, so you divide each side by 10 to get a simplified ratio of 3:2. That means there are three red marbles for every two blue marbles.
How Do I Simplify a Ratio?
Simplifying a ratio works the same way as simplifying a fraction. Find the greatest common divisor of the two numbers and divide both sides by it. The ratio 300:100 simplifies by 100 to 3:1. The ratio 45:60 divides by 15 to 3:4. Keep dividing by any common factor until the two sides share no common factor other than 1. A ratio in lowest terms is easier to read and compare.
How Do I Find a Ratio in Real Life?
Find the ratio by comparing two related amounts from your situation. If a cake recipe needs 250 grams of flour and 125 grams of sugar, the ratio of flour to sugar is 250:125, which simplifies to 2:1. If your commute is 12 miles one way and 18 miles the other way, the ratio is 12:18, which simplifies to 2:3. Write the two numbers in the order they are described, then reduce.
How Do I Find a Missing Value in a Ratio?
When you know one ratio and part of another, use cross multiplication to find the missing value. If 2:5 equals 8:x, then 2 times x equals 5 times 8, so 2x equals 40 and x equals 20. This is called solving a proportion, and it is how you scale a recipe or mix ingredients in the same proportion for a different batch size.
How Do I Check My Work?
Two ratios are equal when they simplify to the same pair of numbers. After you calculate a ratio, simplify it and compare it to the expected form. You can also convert both sides to a percentage of the total to double check that the relationship makes sense. The easiest check is to use a ratio calculator, which simplifies the pair and shows the steps instantly.
Worked Example
You have a class of 18 boys and 12 girls. Write the ratio of boys to girls as 18:12. Divide both sides by the greatest common divisor, 6, to get 3:2. The simplified ratio tells you there are three boys for every two girls in the class.
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