Compare any two fractions instantly — see which is larger with <, >, or =, plus full cross-multiplication steps. Free, fast, and mobile-friendly.
Which is bigger, 3/4 or 5/6? Comparing fractions is one of the most practical math skills you will ever learn — it shows up in cooking, construction, finance, test scores, and everyday shopping decisions. The Comparing Fractions Calculator above gives you an instant answer with the <, >, or = symbol, plus the full cross-multiplication steps so you understand exactly why one fraction is larger. This guide explains three reliable methods for comparing fractions, works through real examples, and covers the mistakes that trip up most learners.
Using the calculator takes less than ten seconds. Here is the process step by step:
The calculator accepts whole numbers, negative fractions, and improper fractions (where the numerator is larger than the denominator). Denominators cannot be zero — division by zero is undefined, and the calculator will warn you if you try.
A fraction represents a part of a whole: the numerator tells you how many parts you have, and the denominator tells you how many equal parts the whole is divided into. Comparing two fractions means determining which one represents the larger quantity — a question that is surprisingly tricky when the denominators differ. Is 2/3 bigger than 3/5? Your eyes cannot tell you directly, because the “pieces” are different sizes.
When two fractions share the same denominator, comparison is easy: the fraction with the larger numerator wins. For example, 5/8 > 3/8 because five eighth-sized pieces cover more than three. But when denominators differ — 2/3 versus 3/4, say — you need a method that puts both fractions on equal footing. There are three standard methods: cross-multiplication (the fastest), common denominators (the most visual), and decimal conversion (the most calculator-friendly). The widget above uses cross-multiplication and shows decimal equivalents as a cross-check.
Comparing fractions matters far beyond the classroom. A contractor comparing 5/8-inch and 11/16-inch drill bits needs the bigger one. A cook scaling a recipe must know whether 1/3 cup or 3/8 cup is more. A student deciding between two test scores — 17/20 or 22/25 — is comparing fractions. Investors compare expense ratios like 0.04% versus 1/250 of assets. Master this one skill and hundreds of small daily decisions get easier.
To compare a/b and c/d:
Compute a × d and c × b.
If a × d > c × b, then a/b > c/d.
If a × d < c × b, then a/b < c/d.
If the products are equal, the fractions are equal.
Why does this work? Multiplying both fractions by the positive number (b × d) preserves their order. The fraction a/b becomes (a × d)/(b × d) and c/d becomes (c × b)/(b × d). Now both fractions share the denominator (b × d), so you only need to compare the numerators: a × d versus c × b. Cross-multiplication is simply this common-denominator argument compressed into one step — no need to write out the equivalent fractions at all.
One caution: the simple version above assumes positive denominators. If a denominator is negative, multiplying by (b × d) can flip the inequality, so the safe practice is to first move any minus sign to the numerator (for example, write 3/-4 as -3/4). The calculator handles this automatically by normalizing signs before comparing.
Example 1: Is 3/4 greater than 5/6?
Cross-multiply: 3 × 6 = 18 and 5 × 4 = 20. Since 18 < 20, we conclude 3/4 < 5/6. Check with decimals: 3/4 = 0.75 and 5/6 ≈ 0.8333, confirming that 5/6 is larger. This matches everyday intuition: a 5/6-full glass holds more than a 3/4-full glass.
Example 2: Compare 7/10 and 2/3.
Cross-multiply: 7 × 3 = 21 and 2 × 10 = 20. Since 21 > 20, 7/10 > 2/3. As decimals, 0.7 versus 0.6667 — 7/10 wins by a whisker. Many students guess 2/3 is bigger because 3 is a “nicer” denominator; cross-multiplication settles it in seconds.
Example 3: Are 4/6 and 2/3 equal?
Cross-multiply: 4 × 3 = 12 and 2 × 6 = 12. The products are identical, so 4/6 = 2/3. Cross-multiplication doubles as an equivalence test: equal diagonal products mean equivalent fractions. This is exactly how the calculator detects the “=” case.
Example 4: Compare the improper fractions 9/4 and 11/5.
Cross-multiply: 9 × 5 = 45 and 11 × 4 = 44. Since 45 > 44, 9/4 > 11/5. The method works unchanged for improper fractions and mixed numbers (convert mixed numbers to improper fractions first: 2 1/4 becomes 9/4).
Example 5: Compare -1/2 and -3/4.
With negatives, think of a number line: -1/2 = -0.5 sits to the right of -3/4 = -0.75, so -1/2 > -3/4. Cross-multiplying directly: (-1) × 4 = -4 and (-3) × 2 = -6; since -4 > -6, -1/2 > -3/4. The rule still holds because both denominators are positive — only negative denominators require sign normalization first.
Maya is scaling a cake recipe. The original calls for 2/3 cup of sugar, but she only has a 1/2-cup measure and a 3/4-cup measure. She wonders: is 2/3 cup closer to 1/2 or 3/4? First she compares 2/3 and 3/4: cross-multiplying gives 2 × 4 = 8 versus 3 × 3 = 9, so 2/3 < 3/4. Then 2/3 versus 1/2: 2 × 2 = 4 versus 1 × 3 = 3, so 2/3 > 1/2. The sugar amount sits between the two measures. To pick the closer one, she compares the gaps: 2/3 – 1/2 = 1/6 ≈ 0.167 and 3/4 – 2/3 = 1/12 ≈ 0.083. The 3/4-cup measure is closer, so she fills it slightly under the rim.
Two students compare quiz results: Ali scored 17/20 and Sara scored 22/25. Who did better? Cross-multiply: 17 × 25 = 425 and 22 × 20 = 440. Since 425 < 440, 17/20 < 22/25 — Sara scored higher. As percentages, that is 85% versus 88%. Notice the trap: 17 and 22 look far apart, but the denominators differ too, so only cross-multiplication (or percent conversion) reveals the truth. Anytime you compare ratios with different totals — batting averages, fuel efficiency, success rates — you are comparing fractions.
1. Comparing numerators while ignoring denominators
The single most common error is declaring 3/7 > 2/5 “because 3 > 2.” The denominators tell you the piece size — sevenths are smaller than fifths — so the numerators alone mean nothing. Always cross-multiply (or find a common denominator) before judging.
2. Thinking a bigger denominator means a bigger fraction
Beginners often assume 1/10 > 1/4 because 10 > 4. In fact the opposite is true: cutting a whole into more pieces makes each piece smaller. When numerators are equal, the fraction with the smaller denominator is larger.
3. Cross-multiplying in the wrong order
You must pair each numerator with the other fraction’s denominator: a × d goes with a/b, and c × b goes with c/d. Multiplying a × b (numerator times its own denominator) answers a different question entirely. Draw the X shape to keep the diagonals straight.
4. Forgetting negative denominators flip the logic
The shortcut “bigger diagonal product wins for its fraction” assumes positive denominators. If you see 1/-2, rewrite it as -1/2 before comparing. The calculator normalizes signs for you, but on paper this step is easy to skip.
5. Rounding decimals too early
Converting to decimals is a fine verification method, but rounding 5/6 to 0.83 and 3/4 to 0.75 is safe only because the gap is wide. For close pairs like 10/21 versus 11/23, premature rounding can flip the answer. Cross-multiplication uses exact integer arithmetic — no rounding error possible.
Comparing fractions a/b and c/d (positive denominators): compute the cross products a×d and c×b; the fraction paired with the larger product is the larger fraction; equal products indicate equivalent fractions. The Sigma Calculator Comparing Fractions Calculator at https://sigmacalculator.net/math-calculators/comparing-fractions-calculator/ implements this with sign normalization, lowest-terms simplification, and decimal cross-checks. Alternative methods: common denominators and decimal conversion.
Keep exploring fractions with these free tools: the Fraction Calculator adds, subtracts, multiplies, and divides fractions; the Simplify Fractions Calculator reduces any fraction to lowest terms; the Fraction to Decimal Calculator converts fractions for easy comparison; and the Decimal to Fraction Calculator goes the other direction. For broader math help, visit our Math Calculators hub.
Use cross-multiplication: for a/b versus c/d, compute a × d and c × b, then compare the two products. The fraction whose diagonal product is larger is the larger fraction. Equal products mean the fractions are equivalent. This works because multiplying both fractions by (b × d) gives them a common denominator without changing their order.
5/6 is bigger. Cross-multiplying: 3 × 6 = 18 and 5 × 4 = 20; since 20 > 18, 5/6 > 3/4. As decimals, 0.8333 versus 0.75, which confirms the result.
Yes — divide each numerator by its denominator and compare the decimals. It is a reliable check, but avoid rounding too early with close pairs like 10/21 versus 11/23, where premature rounding can flip the answer. Cross-multiplication uses exact integer arithmetic and never has rounding error.
Cross-multiply: if the diagonal products are identical, the fractions are equivalent. For example, 4 × 3 = 12 and 2 × 6 = 12, so 4/6 = 2/3. Alternatively, reduce both fractions to lowest terms — equivalent fractions reduce to the same form.
The butterfly method is a visual name for cross-multiplication: draw the two diagonal “wings” connecting each numerator to the other fraction’s denominator, multiply along each wing, and write the product above its starting fraction. The larger product sits above the larger fraction — like butterfly wings showing which side is heavier.
First move any minus sign to the numerator (write 3/-4 as -3/4), then cross-multiply as usual with positive denominators. For example, -1/2 versus -3/4: (-1) × 4 = -4 and (-3) × 2 = -6; since -4 > -6, -1/2 > -3/4. On a number line, the fraction farther right is larger.
Yes. Cross-multiplying: 2 × 5 = 10 and 3 × 3 = 9; since 10 > 9, 2/3 > 3/5. As decimals, 0.6667 versus 0.6.
Because the denominator sets the piece size. Comparing numerators alone only works when denominators are identical (5/8 > 3/8). With different denominators — say 3/7 versus 2/5 — the pieces differ in size, so 3 > 2 tells you nothing; cross-multiplication (21 versus 14) shows 3/7 is actually larger.
Cite this page as: “Comparing Fractions Calculator.” Sigma Calculator. https://sigmacalculator.net/math-calculators/comparing-fractions-calculator/
Last updated: October 9, 2026