Is 3/5 bigger than 5/8? When the numerators and denominators both differ, it is hard to tell at a glance. This calculator answers with the symbol <, > or =, and shows three ways to see why: cross-multiplication, rewriting over a common denominator, and decimals, plus a pair of fraction bars drawn to scale.
How to use the calculator
- Enter the first fraction or mixed number.
- Enter the second fraction or mixed number.
- The tape shows the comparison, which value is larger, the exact difference, both decimals and the common denominator.
- The steps show each method, and for simple fractions the bar model shows both amounts shaded on equal-length bars.
Three ways to compare
1. Cross-multiplication
Whichever product is larger belongs to the larger fraction.
2. Common denominator
Rewrite both fractions over their least common denominator; then the larger numerator wins. This is slower but makes the reason visible, and it extends to comparing many fractions at once.
3. Decimals
Divide each numerator by its denominator and compare the decimals. Fast with a calculator, but repeating decimals need enough digits to separate close values.
Worked example: 3/5 vs 5/8
- Cross-multiply: 3 × 8 = 24 and 5 × 5 = 25. Since 24 < 25, 3/5 < 5/8.
- Common denominator: the LCD of 5 and 8 is 40. 3/5 = 24/40 and 5/8 = 25/40, so 24/40 < 25/40.
- Decimals: 3/5 = 0.6 and 5/8 = 0.625.
- The difference is 5/8 − 3/5 = 1/40 = 0.025 — close, which is why the shortcut is helpful.
Mental shortcuts
| Situation | Rule | Example |
|---|---|---|
| Same denominator | Larger numerator is larger | 5/9 > 4/9 |
| Same numerator | Smaller denominator is larger | 3/4 > 3/5 |
| Compare with 1/2 | Is the numerator more or less than half the denominator? | 4/9 < 1/2 < 5/8 |
| Compare with 1 | How many pieces short of a whole? | 7/8 (1/8 short) > 6/7 (1/7 short) |
The benchmark tricks are the same ones used to estimate fractions.
Comparing mixed numbers
Compare the whole parts first — 3 1/8 is larger than 2 7/8 no matter what the fractions are, because 3 > 2. Only when the whole parts match do you need to compare the fraction parts: 2 3/5 versus 2 5/8 comes down to 3/5 versus 5/8, so 2 3/5 < 2 5/8. The calculator converts mixed numbers to improper fractions (13/5 and 21/8) and cross-multiplies, which gives the same answer: 13 × 8 = 104 is less than 21 × 5 = 105. Negative mixed numbers reverse the logic: −2 3/5 is greater than −2 5/8 because it is closer to zero.
Equal fractions
If the cross products are equal, the fractions are equivalent: 2/4 and 1/2 give 2 × 2 = 4 and 1 × 4 = 4. The equivalent fractions calculator lists more fractions with the same value.
Comparing more than two
To put a whole list in order, use the ordering fractions calculator, which rewrites every fraction over one common denominator. To see fractions as positions on a line, try the fractions on a number line tool.
Frequently asked questions
How do you compare two fractions?
Cross-multiply: multiply the first numerator by the second denominator and the second numerator by the first denominator, then compare the products. For 3/5 and 5/8: 3 × 8 = 24 and 5 × 5 = 25, and 24 < 25, so 3/5 < 5/8.
Why does cross-multiplication work?
It is a shortcut for using the common denominator b × d. Rewriting a/b and c/d over b × d gives numerators a × d and c × b, and fractions with the same denominator compare by their numerators.
How do I compare fractions with the same numerator?
The one with the smaller denominator is larger, because the whole is cut into fewer, bigger pieces. 3/4 is greater than 3/5.
How do I compare negative fractions?
The calculator handles signs for you, but the rule is that the fraction closer to zero is larger. −1/2 is greater than −2/3 because −0.5 is to the right of −0.667 on the number line.