Simplify complex ratios with Calcopolis
With Calcopolis Ratio Simplifier, you can simplify ratios with whole numbers, decimals, and even fractions or mixed numbers.
You can use our ratio simplifier to simplify ratio data for statistical purposes, presentations, and reports. To add, you can use it simply to recheck your calculations or simplify results from other applications.
What Is a Ratio?
We define a ratio as the quantitative relationship between two values. It’s used to compare two or more numbers in relation to one another.
How Do You Simplify a Ratio?
Simplifying ratios is pretty straightforward. To simplify, you need to find the greatest common factor of both values in the ratio.
Once you have your GCF, divide both sides of the ratio by the GCF, and you’ll have your reduced, simplified form.
Take a look at a few examples and givens.
Method 1: For Whole Number Ratios
If both numbers in the ratio are whole numbers, we follow the basic steps above.
Consider the ratio of 8:16.
- Find the GCF of 8 and 16 by listing all their factors.
- 1, 2, 4, and 8 are the factors of 8
- 1, 2, 4, 8, and 16 are the factors of 16
- Your GCF is 8
- Divide both sides of the ratio by 8 to get 8 ÷ 8:16 ÷ 8 = 1:2
- The simplified ratio of 8:16 is 1:2
Method 2: For Ratios With Mixed Numbers, Decimals, and Fractions
Mixed numbers need to be converted into an improper fraction. If your ratios have decimal values, you need to get rid of the decimal by multiplying both sides of the ratio by 10.
If you have a ratio with a whole number and a fraction, you need to change the fraction into a whole number or convert the whole number into an improper fraction.
If both sides of the ratio are fractions with unlike denominators, their LCD must be calculated. Afterward, rewrite both fractions with the LCD as their denominator.
For fractions with the same denominator, change the fractions into whole numbers. To do this, cancel out the denominator by multiplying both fractions by their common denominator.
Consider the ratio of 5:2 1/2.
- Convert the mixed fraction into an improper fraction: 2 1/2 = 5/2
- Change the whole number into a fraction with 1 as its denominator to get 5/1:5/2
- Eliminate the unlike denominators by replacing them with their LCD
- The LCD of 5/1 and 5/2 is 2
- Rewrite both fractions with the LCD as the new denominator and you’ll get 10/2:5/2
- Because they now have similar denominators, you can now multiply them by 2 to cancel out the denominator and get whole numbers: (10/2:5/2) 2 = 10:5
- Finally, divide both sides of the fraction by their GCF to get the ratio’s simplified form.
- The GCF of 10 and 5 is 5, so you’ll get 10 ÷ 5:5 ÷ 5 = 2:1
- The answer is 2:1
Math problems that involve large ratios will be easier if you reduce the ratios to their simplest form. That being said, our ratio simplifier will help you simplify ratios with a few simple steps.
Visit our ratio to fraction converter if you need help with turning complex ratios into simple fractions.