Fraction Division Calculator: Simplify & Convert Mixed Numbers

How to use the tool

1. Enter Fraction 1
   • Numerator example: 7
   • Denominator example: 9
2. Enter Fraction 2
   • Numerator example: 11
   • Denominator example: 12
3. Pick options
   • Show Steps: “Yes” for a line-by-line solution.
   • Result Format: choose Simplified Fraction or Mixed Number.
4. Press “Calculate.” Your answer and, if requested, the working appear instantly.

Core formulas

• Division rule: $$rac{a}{b}\;÷\;rac{c}{d}=rac{a}{b}×rac{d}{c}$$
• GCD (Euclidean): repeat a mod b until remainder 0.
• Mixed conversion: $$rac{p}{q}=k+rac{r}{q},\;k=\lfloor|p|/|q|\rfloor ,\;r=|p|\bmod|q|$$

Example A

Divide $$rac{7}{9}÷rac{11}{12}$$

$$ rac{7}{9}×rac{12}{11}=rac{84}{99} $$GCD(84, 99)=3 → $$rac{84}{99}=rac{28}{33}$$ (simplified). Mixed form not needed because 28 < 33.

Example B

Divide $$rac{-15}{4}÷rac{2}{3}$$

$$ -rac{15}{4}×rac{3}{2}=-rac{45}{8} $$GCD(45, 8)=1 → already simplest. Mixed: $$-rac{45}{8}=-5rac{5}{8}$$

Quick-Facts

• Input range: ±9 007 199 254 740 991 (JavaScript Number.MAX_SAFE_INTEGER) (MDN, docs).
• Algorithm: Euclidean GCD guarantees lowest terms (Cormen et al., 2009).
• Outputs: simplified or mixed meet CCSS NF.B.3 display norms (CCSSI, 2010).
• Zero denominators blocked; division by zero is undefined (ISO/IEC 9899, 1999).
• Step-by-step mode supports conceptual learning—“visual models improve fraction sense” (NCTM, 2020).

FAQ

Why multiply by the reciprocal?

You convert division into multiplication, a single operation that preserves value and simplifies computation (Brown & Larsen, 2014).

How do I turn a mixed number into an improper fraction?

Multiply the whole part by the denominator, add the numerator, then place over the original denominator—standard Grade 5 method (CCSSI, 2010).

Does the tool handle negatives correctly?

Yes. It keeps the negative sign with the final simplified result, consistent with integer rules (NCTM, 2020).

What happens if I enter 0 as a denominator?

The form blocks submission and shows “Denominator cannot be zero,” preventing undefined math (ISO/IEC 9899, 1999).

Can I input decimals?

No. Convert decimals to fractions first; e.g., 0.2 becomes $$rac{1}{5}$$ (MathWorld, 2022).

How large can the numbers be?

Stay within ±9 × 10¹⁵; beyond that JavaScript loses integer precision (MDN Number, 2023).

Which algorithm finds the GCD?

The calculator uses the classical Euclidean algorithm, “the oldest non-trivial algorithm still in common use” (Knuth, 1997).

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