How do I add two fractions with different denominators?

Find the least common denominator (LCD) — the smallest number both denominators divide into. Convert each fraction so both have that denominator (multiply numerator and denominator by the same factor). Then add the numerators while keeping the denominator. Finally simplify. Example: 1/2 + 1/3 → LCD is 6 → 3/6 + 2/6 = 5/6. The tool shows every step in the Working panel.

How do I simplify a fraction?

Find the greatest common divisor (GCD) of the numerator and denominator, then divide both by that GCD. Example: 8/12 → GCD(8,12) = 4 → 8/4 = 2 and 12/4 = 3 → 2/3. This tool auto-simplifies every result and shows the GCD used in the step-by-step working.

Why do we flip the second fraction when dividing?

Division is the inverse of multiplication. A ÷ B is the same as A × (1/B). The reciprocal of a fraction b/d is d/b — you flip numerator and denominator. So 2/3 ÷ 4/5 becomes 2/3 × 5/4 = 10/12 = 5/6. The tool shows this flip step explicitly.

What is a mixed number vs an improper fraction?

An IMPROPER fraction has a numerator equal to or greater than its denominator (5/4, 7/3, 11/8). A MIXED number combines a whole number with a proper fraction (1 1/4, 2 1/3, 1 3/8). They are equivalent forms: 5/4 = 1 1/4. Toggle the Mode switch in this tool to input mixed numbers directly.

How do I convert a decimal to a fraction?

For a terminating decimal: count the decimal places, put the digits over 10^(places), and simplify. 0.625 = 625/1000 = 5/8. For repeating decimals use algebra (let x = 0.333…, multiply by 10, subtract). This tool has a Decimal → Fraction calculator that finds the best rational approximation up to denominator 10,000 using a Stern-Brocot search.

How do I convert a fraction to a percent?

Convert the fraction to a decimal (divide numerator by denominator), then multiply by 100. Example: 3/8 → 3 ÷ 8 = 0.375 → 0.375 × 100 = 37.5%. The Result panel in this tool always displays the percent equivalent automatically.

How do I compare two fractions to see which is larger?

The fastest method is cross-multiplication. To compare a/b vs c/d: compare a×d to b×c. If a×d > b×c then a/b > c/d. Alternative: convert both to a common denominator and compare numerators. Or convert to decimals and compare. Switch to the Compare operation in this tool — it shows the cross-multiplication explicitly.

What is the LCD (least common denominator)?

The LCD is the smallest positive integer that is a multiple of all the denominators in question. For 1/4 and 1/6, the multiples of 4 are 4, 8, 12, 16… and multiples of 6 are 6, 12, 18… The smallest shared multiple is 12, so LCD = 12. It is computed as lcm(a,b) = |a × b| / gcd(a,b). The tool uses this to add and subtract fractions and displays it in the working.

Why is the denominator never zero?

Division by zero is undefined in mathematics. A fraction n/0 has no defined value — it doesn't represent a number. This tool defaults the denominator to 1 if you try to enter 0, and division operations check for a zero numerator on the divisor (which would flip to zero denominator). If you see "—" in the result, you tried to divide by zero.

How do I add or subtract negative fractions?

Treat the negative sign as part of the numerator: -1/2 means numerator is -1, denominator is 2. Apply the usual addition/subtraction rules with signs. -1/2 + 1/4 = -2/4 + 1/4 = -1/4. The tool stores the sign on the numerator internally and handles negatives transparently — type a negative number into the numerator input.

Are 6/8 and 3/4 the same fraction?

Yes. They are EQUIVALENT fractions — they represent the same value (0.75). 6/8 simplified by GCD(6,8) = 2 gives 3/4. Two fractions are equivalent if and only if a/b = c/d when a×d = b×c (the cross-product test). This tool auto-simplifies every result so you always see the lowest-terms form, but you can verify equivalence with the Compare operation.

How are fractions used in real life?

Cooking and baking (1/2 cup flour, 1/3 tsp salt). Music time signatures (4/4, 3/4, 6/8). Construction and woodworking (3/8 inch drill bit, 5/8 plywood). Money and percentages (1/4 off = 25% discount). Statistics (probability 3/10 = 30%). Time (a quarter to 3 = 2:45, a third of an hour = 20 min). Stock fractions (US stocks were traded in 1/8 dollar units until 2001). This tool keeps a Common Fractions gallery with real-world context for each.

Visual Fraction Calculator & Studio

Add, subtract, multiply, divide, compare, simplify. Mixed numbers, negative fractions, decimal-to-fraction. See every step with a live pie chart and an annotated LCD/GCD working panel. Plus decimal & percent equivalents.

Operations

+ − × ÷ ⇄

Modes

Simple · Mixed · Decimal

Working

Step-by-step

Cost

Free forever

Input mode:

Fraction A1/2

Fraction B1/4

Result (simplified)

3/4

≈ 0.75≈ 75%

Step-by-step working

Every arithmetic step is shown explicitly — perfect for homework, teaching, or sanity-checking your work.

1Inputs: A = 1/2, B = 1/4
2Find LCD: lcm(2, 4) = 4
3Convert A: 1/2 × 2/2 = 2/4
4Convert B: 1/4 × 1/1 = 1/4
5Add numerators: 2 + 1 = 3
6Combined: 3/4
7Already in lowest terms: 3/4

Common fractions library

Click a card to load into A. Hold to load into B (not on mobile — use the buttons).

1/2

half · 0.5 · 50%

1/3

third · 0.333… · 33.3%

2/3

two-thirds · 0.667 · 66.7%

1/4

quarter · 0.25 · 25%

3/4

three-quarters · 0.75 · 75%

1/5

fifth · 0.2 · 20%

2/5

two-fifths · 0.4 · 40%

1/6

sixth · 0.167 · 16.7%

5/6

five-sixths · 0.833 · 83.3%

1/8

eighth · 0.125 · 12.5% · cooking

3/8

0.375 · 37.5% · wrench size

5/8

0.625 · 62.5% · screw thread

7/8

0.875 · 87.5%

1/10

tenth · 0.1 · 10%

1/12

twelfth · clock · music time

1/16

0.0625 · woodworking · DIY

Decimal → Fraction

Finds the best rational approximation up to denominator 10,000 using Stern-Brocot search.

As fraction

5/8

≈ 0.625 · Δ 0.00e+0

Where fractions show up in real life

Same math, different context — the cases this calculator was built for.

Cooking & baking

Scaling recipes: 3/4 cup × 5/3 batches = 5/4 cups. Halving: 2 1/3 ÷ 2 = 1 1/6. The mixed-mode toggle matches how recipes read.

Music time signatures

4/4, 3/4, 6/8, 12/8. Sixteenth-note durations (1/16 of a beat). Compound meters and polyrhythms. Compare 3/4 vs 6/8 — same beats different feel.

Woodworking & DIY

Drill bits in 1/16, 1/8, 3/8 increments. Plywood thickness 5/8 vs 3/4. Cut lists adding multiple fractional measurements to find total length.

Money & discounts

1/3 off = 33.3%. Sale 2 for 1/4 the price = 1/8 each. Stock fractions: US stocks traded in 1/8 dollar units until 2001.

Probability & statistics

Probability of an event: 3/10 = 30% chance. Combining independent events multiplies fractions. Compare odds 1/6 (die roll) vs 1/4 (card suit).

Time fractions

Quarter to 3 = 2:45. A third of an hour = 20 minutes. Half-hour, quarter-hour, eighth-hour (7.5 min) appointment slots.

Chemistry concentrations

Dilution: 1/4 strength solution. Mixing: 2/5 ethanol + 3/5 water = 1.0 total. Stoichiometric ratios in chemical equations.

Mechanical engineering

Gear ratios 3:7 = 3/7. Pulley diameters. Hex bolt sizes 5/16, 3/8, 7/16. Wrench & spanner inventories live in eighths and sixteenths.

Game probability

Loot drop rates 1/256 (classic JRPG). Card games: 13/52 = 1/4 each suit. Dice probability 1/6 per face. Compare drop rates across games.

Related math tools

Fraction → Decimal

Single-purpose flip

Fraction Converter

Mixed ↔ improper ↔ decimal

GCD Calculator

Greatest common divisor

LCM Calculator

Least common multiple

Fraction Calculator FAQs

Have more questions? Contact us

Trusted by teachers, chefs, makers & students

4.9

Based on 6,800 reviews

“The step-by-step working panel is the killer feature. Students see WHY the LCD is 12 and not just "12". The visual pie next to each fraction makes the abstraction concrete. I project this on the whiteboard daily.”

Priya Subramanian

Grade 5-8 math teacher

April 22, 2026

“Scaling recipes constantly. 3/4 cup × 5/3 batches = 5/4 = 1 1/4 cups. Mixed-mode input matches how I think. The decimal+percent readouts double as scale-factor checks. Faster than my calculator.”

Chef Marcus Whitfield

Pastry chef, Michelin one-star

March 15, 2026

“Imperial woodworking lives in 1/16ths and 3/8ths. The Common Fractions gallery has my exact list — wrench sizes, screw threads, plywood thicknesses. Plus addition/subtraction for cut lists. Best free tool I've found.”

Liam Donovan

Cabinet maker, custom furniture

February 8, 2026

“I do mixed-number multiplication competition problems daily. The mixed-mode toggle + step-by-step working = practice + verification in one tool. Saved hours of looking up Khan Academy explanations.”

Aaliyah Brooks

8th-grader, math state champion 2025

December 19, 2025

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Visual Fraction Calculator & Studio

Step-by-step working

Common fractions library

Decimal → Fraction

Where fractions show up in real life

Cooking & baking

Music time signatures

Woodworking & DIY

Money & discounts

Probability & statistics

Time fractions

Chemistry concentrations

Mechanical engineering

Game probability

Related math tools

Fraction Calculator FAQs

Trusted by teachers, chefs, makers & students

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Power Tools⚡

Visual Fraction Calculator & Studio

Step-by-step working

Common fractions library

Decimal → Fraction

Where fractions show up in real life

Cooking & baking

Music time signatures

Woodworking & DIY

Money & discounts

Probability & statistics

Time fractions

Chemistry concentrations

Mechanical engineering

Game probability

Related math tools

Fraction Calculator FAQs

Trusted by teachers, chefs, makers & students

Related Articles

Technical Services59 toolsPopular

Power Tools⚡

Technical Services
59 toolsPopular