Fractions: adding, subtracting, multiplying and dividing
Fractions appear everywhere precision matters: recipes, measurements, and construction tolerances all use exact ratios. A fraction calculator performs addition, subtraction, multiplication, and division on fractions, automatically simplifying the result to its lowest terms and showing the decimal equivalent, eliminating the common-denominator drudgery by hand.
TL;DR
- Addition and subtraction require a common denominator, obtained by cross-multiplying
- Fraction Addition Formula: a/b + c/d = (a×d + b×c) / (b×d) | a/b ÷ c/d = (a×d) / (b×c)
- Example 1: Adding 1/2 and 1/3
How it works
Addition and subtraction require a common denominator, obtained by cross-multiplying. Multiplication multiplies numerators and denominators directly. Division inverts the second fraction and multiplies. The result is simplified by dividing numerator and denominator by their greatest common divisor (GCD).
The math
For a/b + c/d, compute (a×d + b×c) / (b×d) and simplify. For a/b × c/d, compute (a×c) / (b×d). For a/b ÷ c/d, compute (a×d) / (b×c). In every case, divide the final numerator and denominator by the GCD to obtain the simplest form.
Cross-multiplication produces a common denominator for sums, and the invert-and-multiply rule converts division into multiplication.
Examples
Example 1: Adding 1/2 and 1/3
- Cross-multiply: (1×3 + 2×1) / (2×3)
- Numerator: 3 + 2 = 5
- Denominator: 6
- Result: 5/6 ≈ 0.833
Example 2: Dividing 3/4 by 1/2
- Invert the second fraction: 1/2 → 2/1
- Multiply: (3×2) / (4×1) = 6/4
- Simplify by GCD 2: 3/2
- Result: 3/2 = 1.5
When to use it
✦ Cooking and Baking
Recipes require halving or doubling fractional measurements, which is exact and fast with a fraction calculator.
✦ Carpentry and Construction
Woodworkers and builders combine fractional inch measurements during layout and cutting planning.
⚠ Common mistakes
- Forgetting to Simplify: Reporting 6/4 instead of 3/2 is technically correct but hides the simplest form.
- Sign Errors with Negatives: Negative fractions demand careful sign tracking during cross-multiplication.
- Inverting the Wrong Fraction: Division requires inverting the divisor (the second fraction), not the dividend.
FAQ (6)
Can I convert a decimal to a fraction?
Yes, decimals convert to fractions, for example 0.75 = 3/4, and the tool shows decimal equivalents of every fraction result.
What is the greatest common divisor?
It is the largest number that divides both numerator and denominator exactly; dividing by it produces the simplest form.
Do you save the numbers I type for area, volume or conversions?
Not at all. Every conversion — kg to lbs, area, fraction math — runs locally. No form data is posted anywhere. You can convert 1,500 kg to lbs on a shared computer and walk away knowing nothing was logged.
Will it work without internet in class?
Yes — that's why students like it. Load once on Wi-Fi, then fraction, base-converter or standard deviation work offline in class or in an exam hall without signal. It's just math in JavaScript, no server round-trip.
How accurate are the math results?
We use standard definitions (e.g. 1 kg = 2.20462 lbs, BIPM SI) and double-check edge cases via automated tests. For homework or site measurements it's more than enough, but for certified engineering or lab work, cross-check with the primary standard.
Can I share a calculation with a classmate?
Tap 'Share Link' — it puts the inputs in the URL. Your classmate opens it and sees the same 3/4 → 0.75 → 75% breakdown instantly, without retyping.