02 // Visual Math & Finance Solversa/b = (a × k) / (b × k) ⇔ a·d = b·c
Visual Equivalent Fractions & Common Denominator Comparator
Two fractions $\frac{a}{b}$ and $\frac{c}{d}$ are mathematically equivalent if and only if their cross-products are equal ($a \cdot d = b \cdot c$), meaning both span the exact same normalized length on the $[0,1]$ interval.
a/b = (a × k) / (b × k) ⇔ a·d = b·cInputs & Parameters (4)
1±116
1±116
1±116
1±116
Fraction A (Reduced)
2/3
0.6667 (66.67%)
Fraction B (Reduced)
2/3
0.6667 (66.67%)
Sum A + B (Simplified)
4/3
Mixed: 1 1/3 (1.3333)
Product A × B
4/9
Diff A − B = 0/1
20-Row Comparison Table
Compare across:
| # | First Numerator (a) | Combined Sum (A + B) | Reduced Sum | Sum % |
|---|---|---|---|---|
| 01 | 1 | 1 | 1/1 | 100% |
| 02 | 2 (Current) | 1.333 | 4/3 | 133.33% |
| 03 | 3 | 1.667 | 5/3 | 166.67% |
| 04 | 3 | 1.667 | 5/3 | 166.67% |
| 05 | 4 | 2 | 2/1 | 200% |
| 06 | 5 | 2.333 | 7/3 | 233.33% |
| 07 | 6 | 2.667 | 8/3 | 266.67% |
| 08 | 7 | 3 | 3/1 | 300% |
| 09 | 7 | 3 | 3/1 | 300% |
| 10 | 8 | 3.333 | 10/3 | 333.33% |
| 11 | 9 | 3.667 | 11/3 | 366.67% |
| 12 | 10 | 4 | 4/1 | 400% |
| 13 | 10 | 4 | 4/1 | 400% |
| 14 | 11 | 4.333 | 13/3 | 433.33% |
| 15 | 12 | 4.667 | 14/3 | 466.67% |
| 16 | 13 | 5 | 5/1 | 500% |
| 17 | 14 | 5.333 | 16/3 | 533.33% |
| 18 | 14 | 5.333 | 16/3 | 533.33% |
| 19 | 15 | 5.667 | 17/3 | 566.67% |
| 20 | 16 | 6 | 6/1 | 600% |
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Key Analytical Takeaways
- 01Multiplying both numerator and denominator by the same integer $k$ splits each bar segment into $k$ smaller pieces without changing the shaded total length.
- 02Cross-multiplication ($a \cdot d$ vs. $b \cdot c$) instantly reveals which fraction is larger without converting to decimals.
- 03The reduced form badge shows the fundamental irreducible ratio shared by all equivalent multiples.
Frequently Asked Questions
How can I quickly tell which of two fractions is larger?+
Compare the cross-products a×d and b×c. If a×d > b×c (for positive denominators), then a/b is strictly greater than c/d.
Why is 2/3 equal to 8/12?+
Because each of the 3 thirds is subdivided into 4 smaller parts (3×4 = 12 twelfths), turning the 2 shaded thirds into 2×4 = 8 shaded twelfths.
How does cross-multiplication prove two fractions are equivalent?+
Multiplying both sides of a/b = c/d by the product of denominators b·d eliminates fractions and yields a·d = b·c; if the cross-products match, the two ratios are identical.