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Operations, simplify, mixed numbers, decimals

Fraction Calculator

Add, subtract, multiply, and divide fractions.

By Jeff Beem

Updated

Fraction operations

Add, subtract, multiply, or divide two fractions. Result is simplified. Common denominator logic is shown for + and −.

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Result
Fraction3/4

= 0.75

Steps

  • Common denominator (LCM of 2 and 4) = 4
  • Scale: 1/2 = 2/4, 1/4 = 1/4
  • Result before simplify: 3/4
  • Simplified: 3/4

Part-to-whole

First

Second

Result

Addition & subtraction rules

Addition: a/b + c/d = (ad + bc)/bd, common denominator to combine units.

Subtraction: a/b − c/d = (ad − bc)/bd, difference between two parts of a whole.

Simplification: Divide by GCD(Numerator, Denominator) to reduce to lowest terms.

When to Use Each Fraction Tool

Use the tabs above for operations, mixed numbers, simplification, decimal conversion, or big-number fractions. Trusted by students and educators for homework and exams. Formulas and definitions are in the article below. All calculations run locally.

Workflow Tips

Operations

Use when you have two fractions to add, subtract, multiply, or divide. Steps show LCM and common denominator for + and −.

Mixed Numbers

Use when either input is a whole number plus a fraction. Enter whole, numerator, and denominator for each; result is shown as mixed or improper.

Simplifier

Use when you have one fraction (or mixed number with optional whole) to reduce to lowest terms. GCD is shown; pie chart visualizes part-to-whole.

Decimal ↔ Fraction

Use to convert a terminating decimal you type (finite digits) to a reduced fraction, or a fraction to its decimal value. Non-terminating decimals are only as exact as the digits you enter.

Big Number

Use when numerators or denominators exceed normal precision (e.g. 16+ digits). BigInt keeps full precision for all four operations.

Fraction Calculator: Add, Subtract, Simplify & Convert

Free fraction calculator: add, subtract, multiply, divide fractions and mixed numbers; fraction times whole number; mixed number calculator with steps. How to add fractions with different denominators; simplify fractions online, reduce to lowest terms, convert decimal to fraction. LCM and GCD shown. Trusted by students and educators. No sign-up, all calculations run locally.

What This Fraction Calculator Does & Who It's For

Calculator Purpose & Ideal Users

This fraction calculator gives you five tools in one: add, subtract, multiply, and divide fractions; work with mixed numbers; simplify fractions online (including mixed); convert decimal to fraction or fraction to decimal; and handle big-number fractions with full precision.
  • What You'll Get:
    Operations: Result for two fractions; Steps list LCM scaling for + and −; part-to-whole pie previews for both inputs and the result. Mixed numbers: Whole + numerator/denominator for both inputs; result as mixed or improper. Simplifier: Reduce any fraction or mixed number to lowest terms; GCD shown; optional whole number; before/after pie charts. Decimal ↔ Fraction: Terminating decimal to reduced fraction (e.g. 0.375 → 3/8) or fraction to decimal. Big Number: Integer numerators and denominators with BigInt arithmetic. Pie charts: SVG part-to-whole (slice count capped for readability).
  • Ideal Users:
    Students & teachers: How to add fractions with different denominators, mixed numbers calculator with steps, reduce fraction to lowest terms, convert decimal to fraction, fraction to decimal converter. Homework & exams: Step-by-step LCM and GCD; pie charts for part-to-whole. Anyone: Quick fraction arithmetic and conversions, no sign-up.
  • Scope & Limits:
    Operations, Mixed, and Simplifier use integer numerators and denominators; zero denominator is invalid. Decimal→Fraction builds the fraction from the decimal string you type (terminating decimals); very long digit strings follow floating-point parsing limits. Big Number mode accepts integer strings only. All calculations run in your browser; no data is sent to servers.

How the Math Works

This calculator implements standard rational arithmetic: add, subtract, multiply, divide, simplify, convert, and large-integer fractions. Addition and subtraction use a common denominator; one equivalent form is:
ab±cd=ad±bcbd\frac{a}{b} \pm \frac{c}{d} = \frac{ad \pm bc}{bd}
In practice, the Operations tab scales numerators to the LCM of the denominators so intermediate numbers stay smaller. Multiplication multiplies numerators and denominators; division multiplies by the reciprocal:
ab÷cd=a⋅db⋅c\frac{a}{b} \div \frac{c}{d} = \frac{a \cdot d}{b \cdot c}
A whole number n can be written as n/1, so multiplying a fraction by a whole number uses the same product rule. Results are reduced by the GCD. Worked example for addition: 2/3 + 3/4 → LCM(3, 4) = 12 → 8/12 + 9/12 = 17/12 = 1 5/12. Simplifier example: 18/24 → GCD = 6 → 3/4. Decimal conversion uses the decimal digits you typed to form a power-of-ten denominator (0.625 → 625/1000) then reduces (5/8). The Big Number tab uses JavaScript BigInt on integer inputs. Zero denominators are rejected. The sections below use other numeric examples so this article does not repeat that addition walkthrough.

How to Use This Calculator

Choose the tab that matches your task: Operations for two-fraction arithmetic, Mixed Numbers when either value includes a whole part, Simplifier to reduce a single fraction to lowest terms, Decimal ↔ Fraction for conversions, or Big Number for integer-string arithmetic. On the Operations tab, enter numerators and denominators for both fractions, then select add, subtract, multiply, or divide. The result is simplified automatically. For addition and subtraction, a Steps panel lists the LCM, scaled numerators, and the simplified result; for multiply and divide it shows the unsimplified product or quotient line. Part-to-whole pie previews appear for both inputs and the result. On the Simplifier tab, enter one fraction (with optional whole part) to see the GCD and reduced form with before-and-after pie charts. In Decimal ↔ Fraction, type a terminating decimal to get a reduced fraction, or enter a fraction to see its decimal value (floating-point for fraction → decimal).

How do you multiply a fraction by a whole number?

Any whole number n can be written as n/1, so fraction times whole number is still fraction multiplication: multiply the numerators, multiply the denominators, then simplify. This matches how teachers phrase problems such as “two thirds times four” or “three fourths of eight” once you translate the wording into symbols. On the Operations tab, keep your fraction on one side and enter the whole number as n over 1 on the other side with the multiply operation selected.

Worked examples (paper check)

Example A walks through three fourths times two. The steps are shown in the display below.
34×2=34×21=64=32=112\frac{3}{4} \times 2 = \frac{3}{4} \times \frac{2}{1} = \frac{6}{4} = \frac{3}{2} = 1\frac{1}{2}
Example B is two fifths times five. The numerator and the whole number share a factor, so you can cancel before you multiply if you prefer mental math.
25×5=105=2\frac{2}{5} \times 5 = \frac{10}{5} = 2
Use the Operations tab to confirm either layout.

Adding mixed numbers: step-by-step examples

The key idea is to add the whole parts and the fraction parts separately, then combine and simplify. When denominators differ, build a common denominator for the fractional pieces only, then add the wholes from any improper fraction you create. The patterns below are for pencil-and-paper practice; use the Mixed Numbers tab to verify.

Example 1 (like denominators)

You want the sum below.
218+3582\frac{1}{8} + 3\frac{5}{8}
Add the whole parts, then the fraction parts.
2+3=5and18+58=68=342 + 3 = 5 \quad\text{and}\quad \frac{1}{8} + \frac{5}{8} = \frac{6}{8} = \frac{3}{4}
The combined result is 5345\frac{3}{4}.

Example 2 (unlike denominators)

You want this sum.
423+1124\frac{2}{3} + 1\frac{1}{2}
The whole parts add to 5. The fraction parts need LCD(3, 2) = 6.
23=46,12=36\frac{2}{3} = \frac{4}{6},\quad \frac{1}{2} = \frac{3}{6}
Add the converted fractions.
46+36=76=116\frac{4}{6} + \frac{3}{6} = \frac{7}{6} = 1\frac{1}{6}
Add that extra whole to the 5 you already had.
5+116=6165 + 1\frac{1}{6} = 6\frac{1}{6}

Subtracting mixed numbers when you need to borrow

Subtract the whole parts and the fraction parts. If the first fraction is smaller than the second, borrow 1 whole from the whole part of the first mixed number, rewrite it as a fraction with the same denominator, add it to the existing fraction, then subtract. This is the same restructuring you would show on paper; the calculator handles the bookkeeping once you enter the mixed numbers correctly.

Example 1 (common denominator already)

Compute the subtraction below.
534−2185\frac{3}{4} - 2\frac{1}{8}
The LCD of 4 and 8 is 8, so rewrite the first mixed number with eighths.
534=5685\frac{3}{4} = 5\frac{6}{8}
Subtract whole parts and fraction parts.
5−2=3and68−18=585 - 2 = 3 \quad\text{and}\quad \frac{6}{8} - \frac{1}{8} = \frac{5}{8}
The result is 3583\frac{5}{8}.

Example 2 (borrowing)

Subtract the expression below.
614−2346\frac{1}{4} - 2\frac{3}{4}
Because one fourth is less than three fourths, borrow one whole from 6 and rewrite.
14<34and614=554\frac{1}{4} < \frac{3}{4} \quad\text{and}\quad 6\frac{1}{4} = 5\frac{5}{4}
Subtract whole parts and fraction parts after the borrow.
5−2=3and54−34=24=125 - 2 = 3 \quad\text{and}\quad \frac{5}{4} - \frac{3}{4} = \frac{2}{4} = \frac{1}{2}
The final value is 3123\frac{1}{2}.

Multiplying mixed numbers (convert, multiply, convert back)

Always convert each mixed number to an improper fraction first. The multiplication rule is the usual product of numerators over the product of denominators.
ab×cd=acbd\frac{a}{b} \times \frac{c}{d} = \frac{ac}{bd}
Simplify the result, then change back to a mixed number if the assignment asks for one. You may cancel common factors between numerators and denominators before multiplying to keep the arithmetic small.

Example 1

Multiply the two mixed numbers below.
112×2131\frac{1}{2} \times 2\frac{1}{3}
Rewrite each factor as an improper fraction in one line.
112=32and213=731\frac{1}{2} = \frac{3}{2} \quad\text{and}\quad 2\frac{1}{3} = \frac{7}{3}
32×73=216=72\frac{3}{2} \times \frac{7}{3} = \frac{21}{6} = \frac{7}{2}
In mixed form the answer is 3123\frac{1}{2}.

Example 2 (cancel before multiplying)

Multiply the factors below.
335×4163\frac{3}{5} \times 4\frac{1}{6}
Convert to improper fractions.
335=185and416=2563\frac{3}{5} = \frac{18}{5} \quad\text{and}\quad 4\frac{1}{6} = \frac{25}{6}
After you cancel 6 with 18 and 5 with 25, the product simplifies to a whole number.
185×256=31×51=15\frac{18}{5} \times \frac{25}{6} = \frac{3}{1} \times \frac{5}{1} = 15
The final answer is 15.

Dividing mixed numbers (invert and multiply)

Convert both mixed numbers to improper fractions. Replace division by the reciprocal of the divisor, multiply, simplify, and optionally rewrite as a mixed number. This is the same rule as dividing two fractions; mixed form is only notation on top.

Example 1

Find the quotient for this division.
312÷1143\frac{1}{2} \div 1\frac{1}{4}
Use improper fractions, then invert and multiply.
72÷54=72×45=2810=145\frac{7}{2} \div \frac{5}{4} = \frac{7}{2} \times \frac{4}{5} = \frac{28}{10} = \frac{14}{5}
As a mixed number that is 2452\frac{4}{5}.

Example 2

Divide the following.
513÷2235\frac{1}{3} \div 2\frac{2}{3}
Improper form and invert-multiply give this chain.
163÷83=163×38\frac{16}{3} \div \frac{8}{3} = \frac{16}{3} \times \frac{3}{8}
Cancel the 3s and divide 16 by 8 to finish.
21=2\frac{2}{1} = 2

How do I use an online fraction calculator with steps for homework?

Match the tab to the worksheet layout. Two fractions with add, subtract, multiply, or divide belong in Operations; open the Steps panel there for LCM detail on addition and subtraction. “Simplest form” or “reduce” tasks fit Simplifier so the GCD is explicit. Notation like 2 3/4 belongs in Mixed Numbers. Example you can check by hand: 2/3 + 1/4 → LCM(3, 4) = 12 → 8/12 + 3/12 = 11/12. When a word problem gives a percent and you need a fractional share, convert with a percentage calculator first, then use this tool for fraction arithmetic. For long division that shows up next to fraction work, a long division calculator can check intermediate steps.

How do simplifying fractions calculators put answers in simplest form, and how do I turn a mixed number into a decimal?

A simplifying fractions calculator divides numerator and denominator by their GCD so no common factor remains. Example: 18/24 → GCD(18, 24) = 6 → 3/4. The Simplifier tab here does that and shows the GCD. If you want to see the same divisor from prime steps, use the greatest common factor calculator. For mixed number to decimal style questions, convert the fractional part to a decimal (or use Decimal ↔ Fraction with the improper form) and add the whole: 3 1/8 = 3 + 0.125 = 3.125. When teachers ask for a rounded decimal, round only after you understand the exact value; a rounding calculator compares standard rounding modes side by side.

What Is a Fraction? Part-to-Whole and This Fraction Calculator

A fraction is a part of a whole, written as a/b (numerator over denominator). The denominator is how many equal parts the whole is split into; the numerator is how many of those parts you have (e.g. 3/4 = three out of four parts). Definitions of numerator, denominator, and why the denominator cannot be zero are in the FAQ above. This fraction calculator supports proper and improper fractions, mixed numbers, and very large integers (BigInt) so you can add, subtract, multiply, divide, simplify, and convert without losing precision.

How to Add Fractions with Different Denominators: Common Denominator and LCM

To add or subtract fractions you need a common denominator. One standard form for the sum is:
ab+cd=ad+bcbd\frac{a}{b} + \frac{c}{d} = \frac{ad + bc}{bd}
Subtraction replaces the plus with a minus in the combined numerator:
ab−cd=ad−bcbd\frac{a}{b} - \frac{c}{d} = \frac{ad - bc}{bd}
In practice we use the Least Common Multiple (LCM) of the denominators so intermediate numerators stay smaller, then scale. The Operations tab lists that LCM and the scaled fractions in its Steps panel.
Multiplication and division do not need a common denominator. The rules are:
ab×cd=acbd\frac{a}{b} \times \frac{c}{d} = \frac{ac}{bd}
ab÷cd=adbc\frac{a}{b} \div \frac{c}{d} = \frac{ad}{bc}

Simplify Fraction to Lowest Terms: GCD and Reduce Fractions

A fraction is in lowest terms when numerator and denominator have no common factor except 1. To reduce a fraction, divide both by their GCD (Greatest Common Divisor):
agcd⁡(a,b),bgcd⁡(a,b)\frac{a}{\gcd(a,b)}, \frac{b}{\gcd(a,b)}
The Simplifier tab accepts a fraction or mixed number (optional whole), shows the GCD used, and displays the result in lowest terms. For step-by-step examples (e.g. 8/12 → 2/3), see the FAQ above.

Fraction Calculator FAQ

What is a numerator?

The numerator is the top number in a fraction. It tells you how many parts of the whole you have. In the fraction 3/4, 3 is the numerator, you have 3 out of 4 equal parts. The numerator can be zero (meaning no parts) or any integer; it is always written above the fraction bar.

Why can the denominator not be zero?

The denominator (the bottom number) cannot be zero because division by zero is undefined. A fraction represents numerator ÷ denominator; dividing by zero has no meaningful value in standard arithmetic. So fractions like 5/0 or 1/0 are invalid. This calculator will treat zero denominators as an error and prompt you to enter a non-zero denominator.

How do you simplify a fraction?

To simplify a fraction, divide both the numerator and the denominator by their Greatest Common Divisor (GCD). For example, 8/12 has GCD(8,12) = 4, so (8÷4)/(12÷4) = 2/3. The result is in lowest terms. Use the Simplifier tab in this calculator to reduce any fraction to its simplest form and see the GCD used.

How do I add fractions with different denominators?

To add fractions with different denominators, first find a common denominator, usually the Least Common Multiple (LCM) of the denominators. Convert each fraction to that denominator by scaling numerator and denominator, then add the numerators. Example: 1/2 + 1/3 → LCM(2,3)=6 → 3/6 + 2/6 = 5/6. The Operations tab shows this step-by-step with LCM and scaled numerators.

How do I convert a decimal to a fraction?

To convert a decimal to a fraction, write the decimal as a fraction with a power of 10 in the denominator (e.g. 0.375 = 375/1000), then simplify. This calculator does it automatically: enter the decimal in the Decimal → Fraction converter and get the reduced fraction (e.g. 0.375 → 3/8).

How do I use a fraction calculator with steps?

Open the Operations tab for two-fraction arithmetic. The Steps panel below the result lists the common denominator (LCM) and scaled numerators for addition and subtraction, and shows the multiply or divide setup before simplification. Use the Simplifier tab for one fraction or mixed number to see the GCD. Use Mixed Numbers when you need whole + fraction inputs. Each tab matches a different homework pattern.

What does simplest form mean for a fraction?

Simplest form (or lowest terms) means the numerator and denominator share no common factor other than 1. Example: 10/15 simplifies to 2/3 because GCD(10, 15) = 5. The Simplifier tab reduces any fraction or mixed number and shows the GCD used. For manual practice, a GCF calculator confirms the divisor you should use.

How do I convert a mixed number to a decimal?

Use Mixed Numbers mode to enter the whole part and the fraction, then read the result as a fraction and (where shown) its decimal equivalent, or use Decimal ↔ Fraction after you know the improper fraction. Example: 2 1/2 = 5/2 = 2.5. If you only need to round a long decimal before comparing, a rounding calculator can help.

How do you multiply two fractions?

Multiply numerators together and denominators together, then simplify. Formula: (a/b) × (c/d) = (ac)/(bd). Example: (2/3) × (3/4) = 6/12 = 1/2 after dividing by GCD 6. On the Operations tab, choose multiply and read the Steps panel for the intermediate fraction before it is reduced.

How do you multiply a fraction by a whole number?

Write the whole number as a fraction with denominator 1, then multiply as usual: (a/b) × n = (a × n)/b, then simplify. Example: (3/4) × 2 = 6/4 = 3/2 or 1 1/2. On the Operations tab, enter n as n/1 next to your fraction. Full worked examples are in the article below.

How do you divide mixed numbers?

Convert each mixed number to an improper fraction, change division to multiplication by the reciprocal of the second fraction, multiply, simplify, and convert back to a mixed number if needed. Example: (3 1/2) divided by (1 1/4) is (7/2) divided by (5/4) = 7/2 × 4/5 = 28/10 = 2 4/5. The article below shows add, subtract, multiply, and divide patterns step by step; use the Mixed Numbers tab to verify answers.

Mathematical Reference Note

Calculation Logic: This tool uses standard mathematical algorithms. While we strive for accuracy, errors in logic or user input can result in incorrect data.

Verification: Results should be cross-checked if used for important academic, professional, or personal calculations.

Standard Terms: This tool is provided free of charge and as-is. CalcRegistry provides no warranty regarding the accuracy or fitness of these results for your specific needs.

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