Simplify Calculator
Use this simplify calculator to reduce a fraction or a ratio to its lowest terms, with the greatest common divisor, decimal, and step-by-step working shown.
Simplify Calculator
Enter values above to see results
About This Simplify Calculator
This simplify calculator reduces fractions and ratios to their simplest form by dividing out the greatest common divisor. Choose fraction or ratio mode, enter your values, and review the reduced result along with the decimal, percentage, or mixed-number forms and the steps used.
It is useful for homework, cooking measurements, scale drawings, and any time a fraction or ratio should be written in its cleanest form.
What Does It Mean to Simplify?
To simplify a fraction or a ratio means to write it with the smallest whole numbers that keep the same value. A fraction is in lowest terms when the numerator and denominator share no common factor greater than 1.
How to Simplify a Fraction
The method is:
- Find the greatest common divisor (GCD) of the numerator and denominator.
- Divide both by the GCD.
For example, to simplify 18/24, the GCD of 18 and 24 is 6. Dividing both by 6 gives 3/4.
The formula is:
a/b = (a ÷ gcd) / (b ÷ gcd)
What Is the Greatest Common Divisor?
The greatest common divisor, or GCD, is the largest whole number that divides two or more numbers exactly. Dividing by it removes every shared factor in a single step, which is why the result is guaranteed to be in lowest terms.
How to Simplify a Ratio
A ratio is simplified the same way, but every part is divided by the GCD of all the parts. For example, in 10:15:25 the parts share a divisor of 5, so the ratio simplifies to 2:3:5.
The proportion stays the same — 2:3:5 describes exactly the same relationship as 10:15:25, just with smaller numbers.
How to Use the Calculator
- Choose fraction or ratio mode.
- For a fraction, enter the numerator and denominator.
- For a ratio, enter the parts separated by a colon, such as 10:15:25.
- Click calculate.
- Review the simplified result and the steps.
Fractions, Decimals, and Mixed Numbers
In fraction mode the calculator also shows the decimal and percentage forms. When the fraction is improper — larger than 1 — it shows the mixed-number form too. For example, 7/3 simplifies to 7/3 and can be written as the mixed number 2 1/3.
Simplifying Fractions with Negatives
The calculator keeps a single negative sign on the numerator. So 3/-4 is written as -3/4 once reduced, which is the standard way to show a negative fraction.
What About Decimals?
Simplifying works on whole numbers, so convert a decimal to a fraction first. For example, 0.5 is 1/2 and 0.75 is 3/4. Enter the whole-number fraction and the calculator does the rest.
When Should You Use This Tool?
- Reducing fractions for math homework
- Simplifying ratios and proportions
- Converting improper fractions to mixed numbers
- Checking a manual answer
- Working with recipes, scales, or measurements
Related Calculators
You may also find these tools useful:
- Percentage Calculator
- Long Division Calculator
- Fraction Calculatorcoming soon
- Mixed Number Calculatorcoming soon
- Ratio Calculatorcoming soon
- GCF Calculatorcoming soon
Start Calculating
Enter your fraction or ratio above and use the simplify calculator to reduce it to lowest terms and see how the answer is found.
Frequently Asked Questions
What does this tool simplify?
It reduces a fraction or a ratio to its lowest terms. Fraction mode also shows the decimal, percentage, and mixed-number forms.
How do you simplify a fraction?
Find the greatest common divisor of the numerator and denominator, then divide both by it. For example, 18 and 24 share a divisor of 6, so 18/24 reduces to 3/4.
What is the greatest common divisor?
The greatest common divisor, or GCD, is the largest whole number that divides two or more numbers exactly. Dividing by it removes every shared factor at once.
How do you simplify a ratio?
Divide every part of the ratio by the greatest common divisor of all the parts. For example, 10:15:25 all share a divisor of 5, so the ratio simplifies to 2:3:5.
Can I simplify a fraction with a negative sign?
Yes. The calculator keeps a single negative sign on the numerator, so 3/-4 is shown as -3/4 in lowest terms.
What if the fraction is already simplified?
If the numerator and denominator share no common factor greater than 1, the calculator reports that the fraction is already in lowest terms.
Can I enter decimals?
Simplifying works on whole numbers, so convert a decimal to a fraction first. For example, 0.5 is 1/2, and 0.25 is 1/4.