Toolarithm

Math Calculator

Fraction Calculator

Simplify fractions and calculate addition, subtraction, multiplication, division, decimals, and percent forms. Use the formula section to check each operation.

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

Operations

+, -, x, ÷

Outputs

Simplified + Decimal

Denominators

Positive Integers

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What Can You Create?

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.

Formula

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.
Read the Result

Interpret this calculation before using it

Fraction operations should be read in exact form before using a decimal approximation. Addition and subtraction require a common denominator; multiplication combines numerators and denominators directly; division multiplies by the reciprocal of the nonzero divisor. The simplified fraction preserves the exact rational value even when its decimal expansion repeats.

Worked example

For 3/4 + 2/3, the common denominator is 12. Rewrite 3/4 as 9/12 and 2/3 as 8/12, giving 17/12, or 1 5/12. Its decimal is approximately 1.4167 when rounded to four places. The exact 17/12 result should be retained for later algebra so decimal rounding does not accumulate.

Assumptions to keep

  • Numerators and denominators are interpreted as integers, and every entered denominator must be nonzero.
  • A negative sign may be carried by the numerator; normalization can move it without changing the value.
  • Decimal output is a display approximation when the reduced denominator produces a repeating expansion.

Limits of this result

The calculator checks arithmetic but does not explain why a fraction is the right model for a word problem. Very large integer inputs can also approach JavaScript's safe-integer boundary. Keep the exact reduced result, inspect the operation selected, and use the decimal only at a precision appropriate to the downstream task.

Useful next step: Ratio Calculator — Use a ratio when comparing two quantities or scaling equivalent parts rather than combining rational numbers arithmetically.

Factual reference:OpenStax Prealgebra 2e
Why Users Love This Tool

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.
Perfect For

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

How it works in three quick steps.

1

Enter two fractions

Add numerator and denominator values for the first fraction and the second fraction.

2

Review simplified values

Check each fraction in simplified form with decimal and percent equivalents.

3

Compare operations

Read the sum, difference, product, and quotient in simplified fraction form.

Download & Print

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.

FAQ

Frequently Asked Questions

What does this fraction calculator do?
This calculator simplifies two fractions and calculates their sum, difference, product, and quotient. It also shows decimal and percent forms for the first fraction, which helps connect fraction notation with other number representations. The tool is designed for classroom checks, homework practice, recipe scaling, and quick arithmetic review.
How does the calculator simplify a fraction?
A fraction is simplified by dividing the numerator and denominator by their greatest common divisor. For example, 12/18 has a greatest common divisor of 6, so it simplifies to 2/3. The value of the fraction does not change; only the notation becomes smaller and easier to compare or use in later calculations.
How are fractions added or subtracted?
To add or subtract fractions, the calculator uses a common denominator. For a/b and c/d, the common denominator is b times d. The numerators become a times d and c times b, then they are added or subtracted. The final result is simplified so the answer is easier to read.
How are fractions multiplied?
To multiply fractions, multiply numerator by numerator and denominator by denominator. For a/b times c/d, the product is ac/bd before simplification. This is usually more direct than addition because no common denominator is needed first. The calculator still simplifies the final result so the answer is in lowest terms.
Why can the quotient be undefined?
Dividing by a fraction means multiplying by its reciprocal. If the second fraction has a numerator of zero, its reciprocal would require a zero denominator, which is undefined. In that case the quotient is not a valid number. The calculator keeps that case visible instead of returning a misleading value.
Can this handle negative fractions?
Yes, numerators can be negative, so the calculator can handle negative fraction values. Denominators are kept positive in the input because that creates cleaner notation and avoids sign ambiguity. A negative result is shown by placing the sign on the numerator of the simplified fraction.
About This Tool

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.

Editorial Transparency

Who maintains this page

Ownership and review

Written and maintained by the Toolarithm editorial team. No review date is shown without a maintained editorial record. No independent professional review is claimed.

Methodology

Equations are checked by substituting worked examples into the stated relationship and comparing the result with the interactive implementation.

Read the editorial methodology

Dates and sources

Review dates change only after a substantive method or content check.

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