How do you subtract fractions?

Same with minus: a/b − c/d = (ad−bc)/bd. Example: 3/4−1/6 = (18−4)/24 = 14/24 = 7/12.

How do you multiply fractions?

Straight across: a/b × c/d = ac/bd, then reduce. Example: 2/3×3/4 = 6/12 = 1/2. Cancel first for ease.

How do you divide fractions?

Flip the second: a/b ÷ c/d = ad/bc. Example: 1/2÷1/4 = 1/2×4 = 2.

How do you simplify a fraction?

Divide top and bottom by their GCD. 12/16 → GCD 4 → 3/4. Use Simplify mode above for instant reduction.

What is a mixed number?

A whole plus a fraction: 7/6 = 1 1/6. Divide (7÷6=1 rem 1), keep remainder over original denominator.

Math · Free tool

Fraction Calculator

Add, subtract, multiply, divide and simplify fractions exactly.

Half a pizza plus two-thirds of another — is that 1⅙? Recipes (¾ cup + ⅔ cup), timber cuts (5⅞″ − 2¼″), exam questions and sewing patterns all demand exact fraction arithmetic that decimal rounding corrupts (⅓ as 0.33 + 0.33 ≠ ⅔). This fraction calculator adds, subtracts, multiplies, divides and simplifies fractions exactly, returning the reduced form, mixed number, and decimal side-by-side with the GCD working teachers require.

The rules are few but strict: add/subtract via common denominator (a/b ± c/d = (ad ± bc)/bd), multiply straight across, divide by flipping the second fraction, then reduce by the greatest common divisor. Negative handling, zero-denominator rejection, and whole-number display (6/3 → 2) are automatic. All computation uses integer arithmetic — no floating-point drift — so 1/3 + 1/3 + 1/3 is exactly 1, not 0.999999.

Enter two numerators and denominators, pick the operation (or Simplify for single fractions like 12/16 → 3/4), and press Calculate. Mixed numbers (1 1/6) and decimals appear for practical measuring.

Updated 2026-09-01 · 6-min read · Formula + steps included

● Fraction workstation

Math →

Fraction formulas

a/b ± c/d = (ad ± bc)/bd • a/b × c/d = ac/bd • a/b ÷ c/d = ad/bc • reduce by GCD

Addition needs shared units, hence cross-multiplication to bd. Multiplication scales areas directly. Division asks 'how many c/d fit in a/b', answered by the reciprocal. Reduction divides top and bottom by their greatest common divisor (Euclid's algorithm), with sign normalised to the numerator.

a/b, c/d: Input fractions in lowest or unreduced form; denominators cannot be zero.
GCD: Greatest common divisor. 12/16 → GCD 4 → 3/4. Mixed: 7/6 → 1 1/6.
Mixed/decimal: Practical views: 7/6 = 1 1/6 ≈ 1.166667 for cups, inches, exams.

Worked example: 1/2 + 2/3

The pizza problem, step by step:

Common denominator: 2×3 = 6.
Convert: 1/2 = 3/6; 2/3 = 4/6.
Add: (1×3 + 2×2)/6 = (3+4)/6 = 7/6.
GCD(7,6) = 1 — already reduced.
Mixed: 7 ÷ 6 = 1 remainder 1 → 1 1/6; decimal ≈ 1.166667.

Result: 1/2 + 2/3 = 7/6 = 1 1/6 ≈ 1.166667.

How to use this fraction calculator

Exact in, exact out.

Step 1: Enter first fraction

Numerator over denominator (e.g. 3 over 4). Whole numbers? Use denominator 1 (5 = 5/1).

Step 2: Pick operation

+ − × ÷, or Simplify to reduce one fraction (second inputs ignored).

Step 3: Enter second fraction

For mixed inputs like 1½, convert first: 1½ = 3/2, then enter 3/2.

Step 4: Calculate and read three forms

Reduced fraction, mixed number, and decimal — copy whichever the recipe, ruler or mark scheme wants.

Use cases

Where fractions beat decimals:

Cooking

¾ + ⅔ cup = 17/12 = 1 5/12 cups (~1.42). Scale recipes by multiplying: ⅔ × 1.5 = 1 cup exactly.

Carpentry

5⅞ − 2¼ = 47/8 − 9/4 = 29/8 = 3⅝″. Exact eighths beat 3.625″ misreads on tape.

Exams

GCSE/IGCSE demand simplified exact forms: 4/6 must be 2/3 for full marks. Show GCD working from the tool.

Sewing & crafts

⅝″ seam + ¼″ hem = ⅞″. Halving patterns: ⅞ ÷ 2 = 7/16″ — decimal 0.4375″ invites error.

Music

Half + dotted-quarter note values and time signatures are fraction sums musicians do intuitively.

Pro tips

Fraction fluency:

Memorise benchmarks: ½=0.5, ⅓≈0.333, ¼=0.25, ⅕=0.2, ⅛=0.125 — estimate before calculating.
Cross-cancel before multiplying: 4/9 × 3/8 = (4÷4)(3÷3)/(9÷3)(8÷4) = 1/6 — smaller numbers, fewer errors.
Keep denominators positive; carry sign on top (−3/4, not 3/−4).
For three+ fractions, chain pairwise: ((a/b + c/d) + e/f) — order does not matter for +/×.
Photograph the steps for homework; method marks often exceed answer marks.