CalculationTime

Fraction Calculator

Add, subtract, multiply or divide two fractions, reduce the answer to simplest form, show the mixed number and decimal check, and print a classroom or measurement worksheet record.

Live math canvas

Your numbers, formula and explanation together

Fraction Calculator: 23/20. common denominator add: raw result 23/20; divide by GCD 1 to simplify. Mixed number 1 3/20; decimal 1.15.

Formula applied

The exact method behind this answer

CalculationTime keeps the method visible so the number can be checked instead of blindly trusted.

For addition/subtraction: a/b ± c/d = (ad ± bc) ÷ bd. For multiplication: a/b × c/d = ac ÷ bd. For division: a/b ÷ c/d = ad ÷ bc. Simplify by dividing numerator and denominator by their greatest common divisor.
  1. Apply the formulaFor addition/subtraction: a/b ± c/d = (ad ± bc) ÷ bd. For multiplication: a/b × c/d = ac ÷ bd. For division: a/b ÷ c/d = ad ÷ bc. Simplify by dividing numerator and denominator by their greatest common divisor.23/20common denominator add: raw result 23/20; divide by GCD 1 to simplify. Mixed number 1 3/20; decimal 1.15.

Your live breakdown

Current inputs in the calculation

These values come from the controls above and update when the calculator changes.

First numerator
3
Top number of the first fraction.
First denominator
4
Bottom number. Use a non-zero whole number.
Operation
0 add, subtract, multiply or divide
Choose the arithmetic operation with the buttons shown in the calculator.
Second numerator
2
Top number of the second fraction.
Second denominator
5
Bottom number of the second fraction. It must not be zero.

Resulting answer

23/20

common denominator add: raw result 23/20; divide by GCD 1 to simplify. Mixed number 1 3/20; decimal 1.15.

Answer
23/20
Live support
common denominator add: raw result 23/20; divide by GCD 1 to simplify. Mixed number 1 3/20; decimal 1.15.

Assumptions used

What this answer assumes

Exact simplified fraction first; decimal shown for checking and measurement notes.

  • Denominators are rounded to whole numbers and must not be zero.
  • The operation selector uses add, subtract, multiply and divide buttons; internally these map to deterministic arithmetic modes.
  • The calculator reduces the final fraction after the operation, not each intermediate display only.
  • Division by a zero second fraction is undefined.
  • Decimal output is a checking aid; the exact simplified fraction is the primary result.

Master’s Tip

How to use the result well

Master’s Tip: keep the exact fraction beside the decimal when teaching, quoting recipe changes or checking construction marks. A rounded decimal can hide whether the result is exact or only an approximation.

Printable record

What belongs in the saved calculation

Save the inputs, result, formula, assumptions, page URL and date together so the calculation can be reviewed later.

First numerator
3
Top number of the first fraction.
First denominator
4
Bottom number. Use a non-zero whole number.
Operation
0 add, subtract, multiply or divide
Choose the arithmetic operation with the buttons shown in the calculator.
Second numerator
2
Top number of the second fraction.

Embeddable calculator

Embed this calculator

Copy a clean iframe version with the required CalculationTime attribution link built in.

Formula

For addition/subtraction: a/b ± c/d = (ad ± bc) ÷ bd. For multiplication: a/b × c/d = ac ÷ bd. For division: a/b ÷ c/d = ad ÷ bc. Simplify by dividing numerator and denominator by their greatest common divisor.

Worked example

For 3/4 + 2/5, use a common denominator: (3 × 5 + 2 × 4) ÷ (4 × 5) = (15 + 8) ÷ 20 = 23/20. As a mixed number, 23/20 is 1 and 3/20. As a decimal, it is 1.15.

Professional note

Master’s Tip: keep the exact fraction beside the decimal when teaching, quoting recipe changes or checking construction marks. A rounded decimal can hide whether the result is exact or only an approximation.

Regional and unit assumptions

Standard or basis: integer fraction arithmetic using common denominators and greatest-common-divisor simplification. No measurement, tax, legal or curriculum standard is claimed.

Operation proof

Same fractions, different operations

The page keeps the exact fraction result visible first, then shows the decimal check. Addition and subtraction use a common denominator, multiplication uses numerator times numerator and denominator times denominator, and division uses the reciprocal of the second fraction.

Visible checks

What the page now proves

  • Common denominator trail
  • Greatest-common-divisor simplification
  • Mixed-number and decimal cross-check

Assumptions and limitations

Methodology & Accuracy

How this calculator is checked

CalculationTime pages are built around visible arithmetic: the formula, assumptions, worked example and practical limitations are shown so the result can be checked rather than simply trusted.

Formula used

For addition/subtraction: a/b ± c/d = (ad ± bc) ÷ bd. For multiplication: a/b × c/d = ac ÷ bd. For division: a/b ÷ c/d = ad ÷ bc. Simplify by dividing numerator and denominator by their greatest common divisor.

Standard or basis

Standard or basis: integer fraction arithmetic using common denominators and greatest-common-divisor simplification. No measurement, tax, legal or curriculum standard is claimed.

Where a calculator follows a named legal, trade or industry standard, that standard is cited visibly. Otherwise the page uses transparent general arithmetic and states its limits.

Master's Tip

Master’s Tip: keep the exact fraction beside the decimal when teaching, quoting recipe changes or checking construction marks. A rounded decimal can hide whether the result is exact or only an approximation.

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Questions

How do you add fractions?

Use a common denominator, add the adjusted numerators, then reduce the result by the greatest common divisor.

How do you subtract fractions?

Use the same common-denominator method as addition, but subtract the adjusted second numerator from the adjusted first numerator.

How do you multiply fractions?

Multiply the numerators together, multiply the denominators together, then simplify the final fraction.

How do you divide fractions?

Multiply the first fraction by the reciprocal of the second fraction, then simplify the final fraction.

Why does the calculator show a decimal too?

The decimal helps with checking, measuring and comparison, but the simplified fraction remains the exact result when the inputs are exact whole-number fractions.

Calculation note

Fraction arithmetic is one of the oldest practical forms of calculation because people needed to divide food, land, materials, money and time before decimal notation was common. A useful fraction calculator should show the exact fraction, the simplification step and the decimal check instead of hiding the working.

Fractions record parts of a whole

A fraction writes a relationship between a numerator and a denominator: how many parts are counted and how many equal parts make the whole. That makes fractions useful anywhere a whole object, length, quantity or batch is split into equal parts.

Common denominators make addition and subtraction visible

Adding unlike fractions requires both fractions to describe the same size parts. Multiplying each numerator by the other denominator creates equivalent fractions over a common denominator, which is why the calculator shows the cross-multiplication method.

Simplifying protects readability

Fractions such as 46/40 and 23/20 have the same value, but the reduced version is easier to read and compare. The greatest common divisor gives a deterministic way to reduce the answer without changing its value.

Decimal checks are useful but not always exact

Some fractions have terminating decimals, while others repeat forever in base ten. Keeping the simplified fraction beside the decimal helps students, cooks, makers and tradespeople avoid treating a rounded decimal as exact.

Sources and further readingEncyclopaedia Britannica: FractionNIST: Guide for the Use of the International System of Units