Fraction Calculator
Simplify fractions and calculate addition, subtraction, multiplication, division, decimals, and percent forms. Use the formula section to check each operation.
Operations
+, -, x, ÷
Outputs
Simplified + Decimal
Denominators
Positive Integers
Live calculator
Fraction inputs
Simplified first fraction
3/4
Second fraction
2/5
First decimal
0.75
First percent
75%
Operations
Sum
23/20
Decimal: 1.15
Difference
7/20
Decimal: 0.35
Product
3/10
Decimal: 0.3
Quotient
15/8
Decimal: 1.875
Simplify and operate on two fractions
Simplified forms
Reduce each fraction to lowest terms with the same value and cleaner notation.
Four operations
Calculate sum, difference, product, and quotient in simplified form.
Decimal connection
Compare fraction notation with decimal and percent forms for easier interpretation.
Fraction formulas used on this page
Fraction operations use numerator and denominator relationships. Addition and subtraction need common denominators, while multiplication and division use direct products and reciprocals.
Working formulas
Simplify
a/b = (a ÷ gcd(a,b)) / (b ÷ gcd(a,b))
Divide numerator and denominator by their greatest common divisor.
Add or subtract
a/b ± c/d = (ad ± cb) / bd
Create a common denominator before combining numerators.
Multiply and divide
(a/b)(c/d) = ac/bd; (a/b) ÷ (c/d) = ad/bc
Division by a fraction multiplies by the reciprocal of the second fraction.
Symbols
- a,c - numerators
- The top values of the first and second fractions.
- b,d - denominators
- The bottom values of the fractions; denominators cannot be zero.
- gcd - greatest common divisor
- The largest whole number that divides both numerator and denominator.
Fraction answers that keep the method visible
Operation coverage
- The calculator simplifies both input fractions before showing operation results.
- Addition and subtraction use a common denominator and simplify the final result.
- Multiplication and division are shown as simplified fraction outputs.
- Undefined quotient cases are handled when the second fraction is zero.
Classroom clarity
- The reusable formula section explains the arithmetic behind each operation.
- Denominators are kept positive to avoid confusing notation in beginner examples.
- Related links connect fractions to percentages and ratios for broader number sense.
- Copy and print controls keep the result attached to the entered fractions.
Fraction support for learning and practical arithmetic
Students
Check fraction homework while keeping simplification and operation formulas visible.
Recipe and measure work
Add, subtract, or scale fractional quantities before converting to decimals.
Teaching examples
Create quick examples that connect fractions, decimals, and percent notation.
How it works in three quick steps.
Enter two fractions
Add numerator and denominator values for the first fraction and the second fraction.
Review simplified values
Check each fraction in simplified form with decimal and percent equivalents.
Compare operations
Read the sum, difference, product, and quotient in simplified fraction form.
Save or print fraction work
Copy the operations
Copy simplified input fractions and the operation results into notes.
Print the result
Print inputs, simplified forms, and formulas for classroom review.
Compare forms
Use simplified, decimal, and percent forms to explain the same value.
Why fraction calculators should show operations and simplification
Fractions are compact, but the notation can hide several different tasks. Sometimes the goal is to reduce a single fraction. Other times the problem asks for addition, subtraction, multiplication, division, decimal conversion, or a percent interpretation. Toolarithm's Fraction Calculator keeps those outputs together while showing the formulas that make each result possible.
The calculator simplifies fractions using the greatest common divisor, then uses standard arithmetic rules for operations. Addition and subtraction create a common denominator, multiplication multiplies across, and division uses the reciprocal of the second fraction. The page keeps denominators positive and identifies undefined quotient cases, which is important for reliable learning. The related percentage and ratio tools help connect fractions to other representations of proportional thinking, making the page useful for students, teachers, recipe adjustments, measurement problems, and quick arithmetic checks.
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