CalConverters

Comparing Fractions Calculator

Compare two fractions, mixed numbers, or decimals to see which is less than, greater than, or equal — with LCD, decimal, and cross-multiplication methods shown.

Loading calculator…

How to use this calculator

Type one value into each box — the left value and the right value — using a whole number, fraction, mixed number, or decimal. The calculator converts both to canonical fractions and reports whether the left value is less than (<), greater than (>), or equal to (=) the right value, with the full working shown three different ways below.

Tip: Either box accepts a leading minus sign, like "-1/2" or "-0.75" — negative values compare the same way as positive ones, just flipped on the number line.

Method 1: common denominator (LCD)

Rewrite both fractions over their least common denominator (LCD), then compare numerators directly — once the denominators match, the fraction with the larger numerator is the larger value.

Example: 38\frac{3}{8} vs 512\frac{5}{12}. LCD(8, 12) = 24. Rewrite: 38=924\frac{3}{8} = \frac{9}{24} and 512=1024\frac{5}{12} = \frac{10}{24}. Since 9<109 < 10, 38<512\frac{3}{8} < \frac{5}{12}.

Method 2: convert to decimals

Divide each fraction's numerator by its denominator and compare the resulting decimals directly. A decimal that repeats forever, like 13=0.3333…\frac{1}{3} = 0.3333\ldots, is shown to 6 digits with a trailing "…" so you know it was cut off rather than exact.

Example: −12-\frac{1}{2} vs −13-\frac{1}{3}. −12=−0.5-\frac{1}{2} = -0.5 and −13=−0.333333…-\frac{1}{3} = -0.333333\ldots. Since −0.5-0.5 is farther left on the number line, −12<−13-\frac{1}{2} < -\frac{1}{3}.

Method 3: cross-multiplication

For ab\frac{a}{b} vs cd\frac{c}{d}, multiply diagonally — a×da \times d against b×cb \times c — without ever finding a common denominator:

ab  ?  cd⟺ad  ?  bc\frac{a}{b} \; ? \; \frac{c}{d} \quad\Longleftrightarrow\quad ad \; ? \; bc

Example: 0.60.6 vs 23\frac{2}{3}. First, 0.6=350.6 = \frac{3}{5}. Cross-multiply: 3×3=93 \times 3 = 9 and 5×2=105 \times 2 = 10. Since 9<109 < 10, 0.6<230.6 < \frac{2}{3}.

Tip: All three methods always agree — pick whichever is fastest for the numbers in front of you. Small denominators favor cross-multiplication; "nice" decimals favor the decimal method.

The pitfall: don't compare numerators or denominators directly

It's tempting to glance at two fractions and compare whichever numbers are on top, or on the bottom — but that only works once the fractions share the same denominator (for numerators) or the same numerator (for denominators). 34\frac{3}{4} has a smaller numerator than 58\frac{5}{8}, yet 34=0.75\frac{3}{4} = 0.75 is larger than 58=0.625\frac{5}{8} = 0.625. Always put both values on a common footing — an LCD, a decimal, or a cross product — before comparing.

Worked examples

LeftRightMethod usedResult
3/85/12LCD 24: 9/24 vs 10/243/8 < 5/12
1/22/4Both reduce to 1/21/2 = 2/4
-1/2-1/3Decimal: -0.5 vs -0.333…-1/2 < -1/3
1 1/45/4Mixed number reduces to 5/41 1/4 = 5/4
0.62/3Cross: 9 vs 100.6 < 2/3

Precision note

Every fraction is handled with arbitrary-precision integers (BigInt), never floating-point numbers, so the LCD conversion and the cross-multiplication products are always exact. Only the decimal method has a natural limit — a repeating decimal is shown to 6 digits with "…" rather than continuing forever — but the relation it reports still matches the other two exact methods.

Frequently asked questions

What kinds of values can I compare with this calculator?
Type a whole number ("7"), a simple fraction ("3/8"), a mixed number ("1 1/4"), or a decimal ("0.6") into either box. The calculator converts each one to a canonical fraction before comparing, so any of the four shapes can be compared against any other.
How does the LCD (common denominator) method work?
Find the least common denominator (LCD) of the two fractions, rewrite each one as an equivalent fraction over that LCD, then compare the numerators — whichever numerator is larger belongs to the larger fraction, since both fractions now share the same denominator.
How does the decimal method work?
Divide each fraction's numerator by its denominator to get a decimal, then compare the two decimals directly. This calculator shows up to 6 digits after the decimal point, with an ellipsis ("…") marking a repeating or non-terminating decimal that was cut off, like 13=0.333333…\frac{1}{3} = 0.333333\ldots
How does cross-multiplication work?
For ab\frac{a}{b} vs cd\frac{c}{d}, multiply diagonally: compare a×da \times d against b×cb \times c. If ad<bcad < bc the first fraction is smaller; if ad>bcad > bc it's larger; if ad=bcad = bc the two fractions are equal. This avoids finding an LCD at all.
Why can't I just compare the numerators or denominators directly?
Comparing numerators only works when the denominators already match, and comparing denominators alone tells you nothing about size (a bigger denominator means smaller pieces, not a bigger value). 34\frac{3}{4} has a smaller numerator than 58\frac{5}{8}, yet 34>58\frac{3}{4} > \frac{5}{8} — the fractions must share a common base (a common denominator, a decimal, or a cross product) before any digit-by-digit comparison means anything.
Can this calculator compare negative fractions?
Yes. Type a leading minus sign directly, like "-1/2" or "-0.75". On the number line, more-negative values are smaller, so −12<−13-\frac{1}{2} < -\frac{1}{3} even though 12>13\frac{1}{2} > \frac{1}{3} — flipping the sign of both values reverses the relation.
What happens when the two values are actually equal?
The calculator reports "=" and all three methods agree: the LCD method shows identical numerators over the common denominator, the decimal method shows identical decimals, and cross-multiplication shows ad=bcad = bc. 12\frac{1}{2} and 24\frac{2}{4} are a common example — different-looking fractions with the exact same value.
How is this different from the Ordering Fractions calculator?
This calculator compares exactly two values and reports a single relation (<, >, or =). The Ordering Fractions calculator takes a whole list of values and arranges all of them from smallest to largest in one pass — reach for that one when you have three or more values to rank.

Related calculators