math calculator

Fraction Calculator

Add, subtract, multiply, divide, and simplify fractions.

Formula Verified by Dr. Elena Rostova, PhD

Quick actions: Save inputs, view saved runs, print, share, or export results

Saved Runs

Inputs

Operation

First numerator

First denominator

Second numerator

Second denominator

Results

Simplified fraction

5/6

Unsimplified fraction5/6

Decimal0.8333

Bookmark this Fraction Calculator

Save this page for classroom work, woodworking measurements, recipe adjustments, and ratio conversions.

Formula

Fraction operation

Add/subtract: ad +/- bc over bd; multiply: ac over bd

Fractions are combined using a common denominator, then simplified by the greatest common divisor.

Step by step

How the calculation works

1Read each fraction as numerator over denominator.
2Apply the selected operation.
3Simplify using the greatest common divisor.
4Show both the fraction and decimal form.

Example

Example fraction calculation

1/2 + 1/3 becomes 3/6 + 2/6, which simplifies to 5/6.

Related guides

Learn more about this calculation

Guide

Fraction Operations Guide: Add, Subtract, Multiply, Divide

Learn the rules for adding, subtracting, multiplying, and dividing fractions, with simplification steps and live DTC calculator workflows.

Guide

Ratio and Proportion Guide: Simplify, Solve, Split Totals

Learn how to simplify ratios, solve proportions, and split totals with worked examples tied to the live DTC ratio calculator.

Prime Factorization

Prime Factorization Calculator

Factor any integer into its prime components to simplify fractions and calculate GCD.

Partial Fractions

Partial Fractions Calculator

Decompose rational expressions into partial fractions for integration.

How to understand and use this calculator

How to Simplify Fractions in 3 Easy Steps

Simplifying a fraction means reducing it to its lowest terms — where the numerator and denominator have no common factors other than 1. Here's how you do it:

Step 1: Find the Greatest Common Factor (GCF) of the numerator and denominator. The GCF is the largest number that divides evenly into both numbers.
Step 2: Divide both the numerator and denominator by the GCF.
Step 3: Write the simplified fraction.

Example: Simplify 6/8

GCF of 6 and 8 is 2
$6 \div 2 = 3$, $8 \div 2 = 4$
Answer: 3/4

See how easy that is? Our simplify fractions calculator follows these exact steps — but it does all the work in milliseconds! If you need to convert fractions to decimals, you can also try our Fraction to Decimal Calculator.

Simplify Improper Fractions to Mixed Numbers

An improper fraction is any fraction where the numerator (top number) is greater than the denominator (bottom number), such as 16/3, 81/9, or 525/71.

When you simplify an improper fraction, you convert it to a mixed number — a whole number plus a proper fraction.

Our simplify improper fractions tool handles this conversion automatically. Here's how it works:

Example 1: Simplify 16/3

Step 1: Divide 16 by 3 → $16 \div 3 = 5$ with remainder 1.
Step 2: The whole number is 5.
Step 3: The remainder (1) becomes the new numerator.
Step 4: The denominator stays 3.
Answer: 5 1/3

Example 2: Simplify 45/10

Step 1: Find the GCF of 45 and 10 → GCF is 5.
Step 2: Divide both by 5 → $45 \div 5 = 9$, $10 \div 5 = 2$ → 9/2.
Step 3: Divide 9 by 2 → $9 \div 2 = 4$ with remainder 1.
Answer: 4 1/2

Using a simplify improper fractions calculator makes this process instant and error-free. To convert mixed numbers or improper fractions, you can also use our specialized Mixed Number Fraction Calculator.

Simplify Mixed Fractions — Quick Method

A mixed fraction combines a whole number and a proper fraction, like 4 1/2 or 2 3/4. When you need to simplify mixed fractions, you follow this process:

Step 1: Convert the mixed number to an improper fraction: Multiply the whole number by the denominator, add the numerator, and keep the same denominator.
Step 2: Simplify the improper fraction using the GCF method.
Step 3: Convert back to a mixed number (if needed).

Example: Simplify 2 4/8

Step 1: $2 \times 8 = 16$, $16 + 4 = 20$ → 20/8
Step 2: GCF of 20 and 8 is 4 → $20 \div 4 = 5$, $8 \div 4 = 2$ → 5/2
Step 3: $5 \div 2 = 2$ with remainder 1
Answer: 2 1/2

Our simplify mixed fractions calculator does all this work for you — instantly!

Practice with a Simplifying Fractions Worksheet

Want to test your skills? Here's a simplifying fractions worksheet with 5 practice problems. Try them yourself, then check your answers below.

Practice Problems (Simplifying Fractions Worksheet):

1. Simplify 8/12 → _____

2. Simplify 15/25 → _____

3. Simplify 18/24 → _____

4. Simplify 7/14 → _____

5. Simplify 20/30 → _____

Answer Key (Fractions Simplify Worksheet):

1. 8/12 → 2/3 (GCF is 4 → $8 \div 4 = 2$, $12 \div 4 = 3$)

2. 15/25 → 3/5 (GCF is 5 → $15 \div 5 = 3$, $25 \div 5 = 5$)

3. 18/24 → 3/4 (GCF is 6 → $18 \div 6 = 3$, $24 \div 6 = 4$)

4. 7/14 → 1/2 (GCF is 7 → $7 \div 7 = 1$, $14 \div 7 = 2$)

5. 20/30 → 2/3 (GCF is 10 → $20 \div 10 = 2$, $30 \div 10 = 3$)

Pro tip: This fractions simplify worksheet is perfect for students, teachers, and parents helping with homework. You can print it out for extra practice!

Advanced: Simplifying Exponents Fractions

When you're working with algebra, you might encounter fractions with exponents, like $(x^2/y^2)$ or $(2/3)^2$. Simplifying exponents fractions follows a simple rule:

Basic Rule: $(a/b)^n = a^n / b^n$

This means you apply the exponent to both the numerator and the denominator.

Example 1: $(2/3)^2$ → Numerator: $2^2 = 4$, Denominator: $3^2 = 9$ → Answer: 4/9
Example 2: $(x/y)^3$ → Numerator: $x^3$, Denominator: $y^3$ → Answer: $x^3/y^3$
Example 3: $(3x/4y)^2$ → Numerator: $(3x)^2 = 9x^2$, Denominator: $(4y)^2 = 16y^2$ → Answer: $9x^2/16y^2$

Our simplifying exponents fractions tool handles these automatically — but understanding the rule helps you check your work.

Real-Life Applications — When Will You Use This?

You might be wondering: "When will I ever need to simplify fractions in real life?" The answer — more often than you think!

1. Cooking and Baking: You're following a recipe that calls for 3/4 cup of flour, but you only have a 1/2 cup measuring cup. Simplifying fractions helps you figure out equivalent proportions.

2. Splitting Bills: You and your friends are splitting a $30 bill 5 ways. That's $30/5 = 6/1$ → each person pays $6.

3. Measurements: You're working on a DIY project and your measurement is 12/16 inch. Simplified, that's 3/4 inch — much easier to read on your tape measure!

4. Shopping Discounts: A store offers a "buy 2 get 1 free" deal. That means $2/3$ of the items are paid for.

Our simplify fractions calculator helps you with all these scenarios and more!

Step-by-Step Visual Example

Let's work through a complete simplifying fraction problem together. This visual guide shows you exactly what happens.

Problem: Simplify 24/36

Step 1: Find the GCF of 24 and 36.

* Factors of 24: 1, 2, 3, 4, 6, 8, 12, 24

* Factors of 36: 1, 2, 3, 4, 6, 9, 12, 18, 36

* Common factors: 1, 2, 3, 4, 6, 12 → GCF = 12

Step 2: Divide numerator by GCF: $24 \div 12 = 2$.
Step 3: Divide denominator by GCF: $36 \div 12 = 3$.
Step 4: Write simplified fraction → Answer: 2/3

*(Check your work: $2/3 \times 12/12 = 24/36$)*

Related Calculators You Might Need

Once you've mastered simplifying fractions, you might find these calculators helpful too:

Long Division Calculator — Need help with the division step? Try our long division calculator for step-by-step solutions.
Slope Calculator — Just like simplifying fractions, our slope calculator shows step-by-step work for finding slope between two points.
Midpoint Calculator — If you're studying algebra, you might also need our midpoint calculator for geometry problems.

Related concepts

Fraction Calculator

Reduce, add, subtract, multiply, and divide fractions easily.

Decimal to Fraction

Convert repeating and terminating decimal numbers back to fractions.

Fraction Operations

Read our [Fraction Operations Guide](/blog/math/fraction-operations-guide) to master fraction arithmetic.

Frequently Asked Questions

How do you simplify fractions step by step?+

Step 1: Find the GCF of the numerator and denominator. Step 2: Divide both by the GCF. Step 3: Write the simplified fraction. Our simplify fractions calculator does this instantly.

What is the easiest way to simplify fractions?+

The easiest way is to divide by the smallest common factor repeatedly until you can't divide anymore — or find the GCF and divide once. Using a simplify fractions calculator is the quickest method!

How do you simplify improper fractions?+

Divide the numerator by the denominator. Write the whole number result, then put the remainder over the original denominator. Example: 16/3 → 5 remainder 1 → 5 1/3.

Can you simplify fractions with exponents?+

Yes! Apply the exponent to both the numerator and denominator. Example: (2/3)² = 4/9.

Is this simplify fractions calculator free?+

Yes — completely free! No registration, no hidden fees, use it as much as you need.

What's the difference between simplifying and reducing fractions?+

Nothing! They mean the same thing — writing a fraction in its lowest terms where the numerator and denominator share no common factors other than 1.

How do you simplify mixed fractions?+

Convert the mixed number to an improper fraction, simplify, then convert back to a mixed number if needed. You can also use our Mixed Number Fraction Calculator for direct calculations.

How to understand and use this calculator

How to Simplify Fractions in 3 Easy Steps

Simplifying a fraction means reducing it to its lowest terms — where the numerator and denominator have no common factors other than 1. Here's how you do it:

Step 1: Find the Greatest Common Factor (GCF) of the numerator and denominator. The GCF is the largest number that divides evenly into both numbers.
Step 2: Divide both the numerator and denominator by the GCF.
Step 3: Write the simplified fraction.

Example: Simplify 6/8

GCF of 6 and 8 is 2
$6 \div 2 = 3$, $8 \div 2 = 4$
Answer: 3/4

Simplify Improper Fractions to Mixed Numbers

An improper fraction is any fraction where the numerator (top number) is greater than the denominator (bottom number), such as 16/3, 81/9, or 525/71.

When you simplify an improper fraction, you convert it to a mixed number — a whole number plus a proper fraction.

Our simplify improper fractions tool handles this conversion automatically. Here's how it works:

Example 1: Simplify 16/3

Step 1: Divide 16 by 3 → $16 \div 3 = 5$ with remainder 1.
Step 2: The whole number is 5.
Step 3: The remainder (1) becomes the new numerator.
Step 4: The denominator stays 3.
Answer: 5 1/3

Example 2: Simplify 45/10

Step 1: Find the GCF of 45 and 10 → GCF is 5.
Step 2: Divide both by 5 → $45 \div 5 = 9$, $10 \div 5 = 2$ → 9/2.
Step 3: Divide 9 by 2 → $9 \div 2 = 4$ with remainder 1.
Answer: 4 1/2

Simplify Mixed Fractions — Quick Method

A mixed fraction combines a whole number and a proper fraction, like 4 1/2 or 2 3/4. When you need to simplify mixed fractions, you follow this process:

Step 1: Convert the mixed number to an improper fraction: Multiply the whole number by the denominator, add the numerator, and keep the same denominator.
Step 2: Simplify the improper fraction using the GCF method.
Step 3: Convert back to a mixed number (if needed).

Example: Simplify 2 4/8

Step 1: $2 \times 8 = 16$, $16 + 4 = 20$ → 20/8
Step 2: GCF of 20 and 8 is 4 → $20 \div 4 = 5$, $8 \div 4 = 2$ → 5/2
Step 3: $5 \div 2 = 2$ with remainder 1
Answer: 2 1/2

Our simplify mixed fractions calculator does all this work for you — instantly!

Practice with a Simplifying Fractions Worksheet

Want to test your skills? Here's a simplifying fractions worksheet with 5 practice problems. Try them yourself, then check your answers below.

Practice Problems (Simplifying Fractions Worksheet):

1. Simplify 8/12 → _____

2. Simplify 15/25 → _____

3. Simplify 18/24 → _____

4. Simplify 7/14 → _____

5. Simplify 20/30 → _____

Answer Key (Fractions Simplify Worksheet):

1. 8/12 → 2/3 (GCF is 4 → $8 \div 4 = 2$, $12 \div 4 = 3$)

2. 15/25 → 3/5 (GCF is 5 → $15 \div 5 = 3$, $25 \div 5 = 5$)

3. 18/24 → 3/4 (GCF is 6 → $18 \div 6 = 3$, $24 \div 6 = 4$)

4. 7/14 → 1/2 (GCF is 7 → $7 \div 7 = 1$, $14 \div 7 = 2$)

5. 20/30 → 2/3 (GCF is 10 → $20 \div 10 = 2$, $30 \div 10 = 3$)

Pro tip: This fractions simplify worksheet is perfect for students, teachers, and parents helping with homework. You can print it out for extra practice!

Advanced: Simplifying Exponents Fractions

When you're working with algebra, you might encounter fractions with exponents, like $(x^2/y^2)$ or $(2/3)^2$. Simplifying exponents fractions follows a simple rule:

Basic Rule: $(a/b)^n = a^n / b^n$

This means you apply the exponent to both the numerator and the denominator.

Example 1: $(2/3)^2$ → Numerator: $2^2 = 4$, Denominator: $3^2 = 9$ → Answer: 4/9
Example 2: $(x/y)^3$ → Numerator: $x^3$, Denominator: $y^3$ → Answer: $x^3/y^3$
Example 3: $(3x/4y)^2$ → Numerator: $(3x)^2 = 9x^2$, Denominator: $(4y)^2 = 16y^2$ → Answer: $9x^2/16y^2$

Our simplifying exponents fractions tool handles these automatically — but understanding the rule helps you check your work.

Real-Life Applications — When Will You Use This?

You might be wondering: "When will I ever need to simplify fractions in real life?" The answer — more often than you think!

1. Cooking and Baking: You're following a recipe that calls for 3/4 cup of flour, but you only have a 1/2 cup measuring cup. Simplifying fractions helps you figure out equivalent proportions.

2. Splitting Bills: You and your friends are splitting a $30 bill 5 ways. That's $30/5 = 6/1$ → each person pays $6.

3. Measurements: You're working on a DIY project and your measurement is 12/16 inch. Simplified, that's 3/4 inch — much easier to read on your tape measure!

4. Shopping Discounts: A store offers a "buy 2 get 1 free" deal. That means $2/3$ of the items are paid for.

Our simplify fractions calculator helps you with all these scenarios and more!

Step-by-Step Visual Example

Let's work through a complete simplifying fraction problem together. This visual guide shows you exactly what happens.

Problem: Simplify 24/36

Step 1: Find the GCF of 24 and 36.

* Factors of 24: 1, 2, 3, 4, 6, 8, 12, 24

* Factors of 36: 1, 2, 3, 4, 6, 9, 12, 18, 36

* Common factors: 1, 2, 3, 4, 6, 12 → GCF = 12

Step 2: Divide numerator by GCF: $24 \div 12 = 2$.
Step 3: Divide denominator by GCF: $36 \div 12 = 3$.
Step 4: Write simplified fraction → Answer: 2/3

*(Check your work: $2/3 \times 12/12 = 24/36$)*

Related Calculators You Might Need

Once you've mastered simplifying fractions, you might find these calculators helpful too:

Long Division Calculator — Need help with the division step? Try our long division calculator for step-by-step solutions.
Slope Calculator — Just like simplifying fractions, our slope calculator shows step-by-step work for finding slope between two points.
Midpoint Calculator — If you're studying algebra, you might also need our midpoint calculator for geometry problems.

Related concepts

Fraction Calculator

Reduce, add, subtract, multiply, and divide fractions easily.

Decimal to Fraction

Convert repeating and terminating decimal numbers back to fractions.

Fraction Operations

Read our [Fraction Operations Guide](/blog/math/fraction-operations-guide) to master fraction arithmetic.

Frequently Asked Questions

How do you simplify fractions step by step?+

Step 1: Find the GCF of the numerator and denominator. Step 2: Divide both by the GCF. Step 3: Write the simplified fraction. Our simplify fractions calculator does this instantly.

What is the easiest way to simplify fractions?+

The easiest way is to divide by the smallest common factor repeatedly until you can't divide anymore — or find the GCF and divide once. Using a simplify fractions calculator is the quickest method!

How do you simplify improper fractions?+

Divide the numerator by the denominator. Write the whole number result, then put the remainder over the original denominator. Example: 16/3 → 5 remainder 1 → 5 1/3.

Can you simplify fractions with exponents?+

Yes! Apply the exponent to both the numerator and denominator. Example: (2/3)² = 4/9.

Is this simplify fractions calculator free?+

Yes — completely free! No registration, no hidden fees, use it as much as you need.

What's the difference between simplifying and reducing fractions?+

Nothing! They mean the same thing — writing a fraction in its lowest terms where the numerator and denominator share no common factors other than 1.

How do you simplify mixed fractions?+

Convert the mixed number to an improper fraction, simplify, then convert back to a mixed number if needed. You can also use our Mixed Number Fraction Calculator for direct calculations.

Fraction Calculator

Inputs

Results

Bookmark this Fraction Calculator

Fraction operation

How the calculation works

Example fraction calculation

Learn more about this calculation

Fraction Operations Guide: Add, Subtract, Multiply, Divide

Ratio and Proportion Guide: Simplify, Solve, Split Totals

Prime Factorization Calculator

Partial Fractions Calculator

Fraction Calculator

Inputs

Results

Bookmark this Fraction Calculator

Key output metrics

Decimal Comparison

Result Fraction Terms

How to understand and use this calculator

How to Simplify Fractions in 3 Easy Steps

Simplify Improper Fractions to Mixed Numbers

Simplify Mixed Fractions — Quick Method

Practice with a Simplifying Fractions Worksheet

Advanced: Simplifying Exponents Fractions

Real-Life Applications — When Will You Use This?

Step-by-Step Visual Example

Related Calculators You Might Need

Related concepts

Frequently Asked Questions

Fraction operation

How the calculation works

Example fraction calculation

Learn more about this calculation

Fraction Operations Guide: Add, Subtract, Multiply, Divide

Ratio and Proportion Guide: Simplify, Solve, Split Totals

Prime Factorization Calculator

Partial Fractions Calculator

Key output metrics

Decimal Comparison

Result Fraction Terms

How to understand and use this calculator

How to Simplify Fractions in 3 Easy Steps

Simplify Improper Fractions to Mixed Numbers

Simplify Mixed Fractions — Quick Method

Practice with a Simplifying Fractions Worksheet

Advanced: Simplifying Exponents Fractions

Real-Life Applications — When Will You Use This?

Step-by-Step Visual Example

Related Calculators You Might Need

Related concepts

Frequently Asked Questions