Calculate, simplify, scale, or compare ratios using the ratio calculator below.
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How to Calculate Ratios
A ratio is a comparison of the size of one number to another number. Ratios can compare the size of an object, a quantity, an angle, or another unit of measure.
A ratio is expressed as one number to another number and is denoted in the form A:B, where the first term is separated from the second term with a colon (:). For example, the ratio of 3 to 2 can be written as 3:2.
Ratios are widely used in our everyday world. In addition to mathematics, ratios are used in financial calculations, for instance when comparing someone’s debt-to-income (how much you owe to how much income you have). Ratios are also used in in photography or video applications for comparing aspect ratios or even architecture and engineering to scale dimensions. Furthermore, ratios can be used for things like the lottery to express the odds of winning.
How to Solve a Ratio in a Proportion
A proportion is an equation showing two equivalent ratios. Given a proportion with one ratio and one part of an equivalent ratio, it is possible to solve the proportion’s missing value.
Start by finding the decimal value for the complete ratio. Divide the left side of the ratio by the right side, or use our ratio to decimal calculator.
Transform the incomplete ratio into a fraction by placing the left side on top of the right side. Thus, the left side becomes the numerator and the right becomes the denominator.
Next, form an equation for the proportion with the decimal on one side and the fraction on the other side. The decimal comes from dividing the numerator by the denominator.
decimal value = known value / unknown value
Finally, solve the equation to find the missing value in the second ratio of the proportion.
For example, let’s solve for x in the proportion 6:4 = 12:x
Start by converting 6:4 to decimal form
6:4 = 6 / 4 = 1.5
Next, put 12:x into fraction form
12:x = 12 / x
Then, position the converted values into an equation representing the proportion and solve
1.5 = 12 / x
12 / 1.5 = x
8 = x
The resulting proportion is thus 6:4 = 12:8
How to Compare Ratios
How do you know if two ratios are equivalent or if one is larger than the other? The answer is to compare them using a two simple steps.
The first step is to convert both ratios to decimal by dividing the left of each ratio by the right of each ratio.
Then, compare the decimal values to determine if the ratios are equal or if one is larger than the other.
For example, let’s compare 3:2 and 5:3
Start by converting to decimal form
3:2 = 3 / 2 = 1.5
5:3 = 5 / 3 = 1.67
Then compare the decimal values
1.5 < 1.67
Thus, 3:2 is less than 5:3
How to Reduce a Ratio
Ratios can be reduced just like a fraction can be reduced. In fact, the process of simplifying a ratio is the exact same as simplifying a fraction.
To reduce a ratio, find the greatest common factor of the left and right sides. The greatest common factor is the largest number that can be evenly divided into both the numbers on the left and right sides.
Then, divide the left and right sides by the greatest common factor. The result is a reduced ratio in the simplest form. This reduced ratio is equivalent to the original ratio.
For example, let’s reduce 6:4
Start by finding the greatest common factor of both 6 and 4
- Factors of 6: 1, 2, 3, 6
- Factors of 4: 1, 2, 4
The greatest common factor of both 6 and 4 is 2
Divide the left and right side by the common factor
6 / 2 = 3
4 / 2 = 2
6:4 = 3:2
Thus, the reduced ratio is 3:2 shown by the proportion 6:4 = 3:2
How to Scale a Ratio
Ratios can be scaled larger or smaller in the same proportion to the original. To scale it, simply multiply the left and right sides by the scaling factor.
For example, let’s scale 7:4 by a factor of 2
Multiply the numbers on the left and right side by 2
7 × 2 = 14
4 × 2 = 8
Thus the scaled ratio is 14:8
How to Convert a Ratio to a Percentage
We’ve shown how to convert a ratio to a decimal and to a fraction, but did you know that you can also convert a ratio to a percentage? You can convert a ratio to a percentage in a few easy steps.
First, convert the ratio to a decimal by dividing the left side by the right side.
Then, convert the decimal to percentage by multiplying it by 100. Don’t forget to add the percent symbol (%).
For example, let’s convert 3:2 to a percentage
Convert 3:2 to a decimal
3:2 = 3 ÷ 2 = 1.5
Multiply the decimal value to 100
1.5 × 100 = 150%
Thus, 3:2 converted to a percentage is 150%. You can also use our ratio to percentage conversion calculator to convert more easily.
Frequently Asked Questions
What is a ratio in math?
A ratio is an ordered pair of numbers that does not equal 0. For example: if there are 3 dogs and 4 cats you would write 3:4 as the ratio.
How do you identify a ratio question on a test?
Ratio questions usually compare two units. For example: A pet shop has 20 animals. There are 12 dogs and 8 cats. What is the ratio for dogs to cats?
12:8 or 12 to 8 or 12/8
Is the order of numbers important in a ratio?
Yes! The ratio 5:4 represents a different relationship than 4:5.
When would you use a ratio?
You would use ratios to compare one value to another.
What are three ways to write a ratio?
1 to 2, 1:2, 1/2