Generate multiple equivalent fractions, verify whether two fractions represent the exact same ratio using cross-multiplication, and solve for missing numerators or denominators.
Equivalent fractions represent the identical proportional value of a whole, despite using different numbers. Whether scaling culinary recipes, calculating gear ratios, or simplifying algebra problems, follow these methods:
Select Generate List to expand a fraction, or Check Equivalence to compare two ratios.
Multiply numerator and denominator by the exact same non-zero integer (2, 3, 4...).
To check two fractions a/b and c/d, verify that cross-products match: a × d = b × c.
Review decimal values, irreducible simplest form, and visual equivalence bars.
Multiplying both numerator and denominator by k is identical to multiplying by 1 (k/k = 1):
Example: (3 × 4) / (5 × 4) = 12 / 20 = 3 / 5.
Two fractions a/b and c/d are equivalent if and only if their cross-products are equal:
Example: 4/6 and 6/9 → 4 × 9 = 36 and 6 × 6 = 36 → Equal!
Multiply numerator 3 and denominator 4 by consecutive integers:
Use cross-multiplication: 7 × x = 5 × 28 = 140 → x = 140 / 7 = 20.
You cannot add unlike fractions (e.g. 1/3 + 1/4) directly. Generating equivalent fractions with shared denominators (4/12 and 3/12) is the fundamental prerequisite for fractional addition.
Quickly finds unknown numerators or denominators in ratios (like 5/7 = x/28) using cross-multiplication or integer scale factors.
Tradespeople frequently convert complex measured fractions like 12/16 in into their simpler equivalents (3/4 in) to communicate clearly on job sites.
Tests whether two different fractional representations (such as 15/25 and 27/45) describe identical underlying values without rounding error.
Generates equivalent fractions across multipliers ×2 through ×12 plus any custom scaling multiplier.
Tests two fractions with cross-multiplication butterfly proofs and solves for any single blank term.
Interactive SVG comparison bars illustrate how identical areas are partitioned into different numbers of slices.
Multiply both the numerator and denominator by the exact same scaling constant 6:
Cross-multiply numerator of each fraction by the opposite denominator:
| Base Fraction | × 2 Multiplier | × 3 Multiplier | × 4 Multiplier | Decimal Equivalent |
|---|---|---|---|---|
| 1/2 | 2/4 | 3/6 | 4/8 | 0.5 |
| 1/3 | 2/6 | 3/9 | 4/12 | 0.3333 |
| 2/3 | 4/6 | 6/9 | 8/12 | 0.6667 |
| 3/4 | 6/8 | 9/12 | 12/16 | 0.75 |
| 3/5 | 6/10 | 9/15 | 12/20 | 0.6 |
The fundamental rule of equivalent fractions is balance: whatever you multiply or divide the numerator by, you must do identically to the denominator. Multiplying both by 4/4 is mathematically multiplying by 1, leaving the total value unchanged.
Kitchen measuring sets and tape measures are graduated in specific increments. Recognizing that 6/8 inch on a ruler is identical to 3/4 inch, or that 4/8 cup is identical to 1/2 cup, prevents errors when reading tool markings.
Reduce fractions to simplest form using Euclidean GCD.
Solve proportions, simplify ratios, and scale part-to-whole totals.
Solve direct and inverse proportions for unknown variables.
Convert fractions to exact terminating or repeating decimals.
Find the least common denominator across multiple fractions.
Compare fractions with butterfly cross-multiplication.
