Fraction Comparison Calculator
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Step-by-step
How to Use This Fraction Comparison Calculator
"Which is bigger—3/8 or 5/12?" sounds simple until you are staring at two unlike denominators and no calculator allowed on the quiz. Cross-multiplying works, but writing it cleanly takes practice. This tool compares two fractions exactly, shows both cross products and a common-denominator rewrite, and adds a bar picture when a visual nudge helps.
- Pick simple or mixed mode. Simple mode uses numerator and denominator only; mixed mode adds whole-number fields for values like 2 1/4.
- Enter fraction A and fraction B. In mixed mode, keep the fractional part proper and put negatives on the whole field only.
- Press Compare. The headline states whether A is greater than, equal to, or less than B, with decimals to two places underneath.
- Read the step-by-step block. Mixed values convert to improper fractions first; then cross multiplication and LCD reasoning appear in order.
- Share or combine. Use Share Calculation for a link, or move to the Fraction Calculator if you need to add or subtract the two values next.
Fraction Comparison Formulas and Practical Applications
Comparing fractions is really comparing two division problems without finishing the division—like asking whether seven slices from a pizza cut eight ways beats five slices from one cut twelve ways.
Cross multiplication
a/b > c/d when ad > bc
Multiply each numerator by the opposite denominator. If ad beats bc, the left fraction is larger. Example: compare 3/4 and 2/3—3 × 3 = 9 versus 4 × 2 = 8, so 3/4 wins.
Common denominator method
Compare a/b and c/d via LCD: compare (a × LCD/b) and (c × LCD/d)
Rewrite both fractions with the same bottom number, then compare tops only. This mirrors how you would add fractions—useful when your teacher wants LCD work shown on the test.
Where comparisons show up
Recipe adjustments, probability comparisons, and grading rubrics often ask which ratio is larger without combining them. For operations after you decide which is bigger, switch to the Mixed Fraction Calculator or convert either value with the Fraction To Decimal Calculator.
Standard Units and Conversion Tables
Fractions compared here are dimensionless. When benchmarks help, these common pairs illustrate how close two ratios can look before cross multiplication settles the order:
| Fraction A | Fraction B | Larger |
|---|---|---|
| 1/2 | 3/8 | A (0.50 vs 0.375) |
| 2/3 | 3/5 | A (0.667… vs 0.60) |
| 5/6 | 7/8 | B (0.833… vs 0.875) |
| 3/4 | 3/4 | Equal |
See all math calculators for related fraction tools.
Frequently Asked Questions
Can I compare mixed numbers and simple fractions in the same tool?
Yes. Toggle Switch to Mixed Fractions to reveal whole-number fields. Mixed entries convert to improper fractions before any comparison logic runs.
How does the comparison work?
Exact rational arithmetic decides the order internally. The written steps explain that result using cross multiplication and a common denominator so you can reproduce the reasoning on paper.
What is cross multiplication for comparing fractions?
Multiply each top by the opposite bottom. Compare those products: larger product means larger fraction (for positive values). The step panel prints both products side by side.
Can I share a specific comparison?
Yes. Share Calculation copies a URL that restores inputs, mode, and steps when opened.
Why does the tool show a bar chart?
Bar lengths scale to the larger value so you can spot a small gap visually. Use decimals and written steps when you need the exact relationship for an assignment.
Disclaimer. RapidRatio is informational only—not academic or professional advice. Verify steps and results with your instructor when preparation counts.