Fractions comparison calculator
Calculator compares two fractions and tells you if they are equal or different. If given fractions are different, the calculator will let you know which one is greater, which one is smaller and what is the difference between them.

First fraction
Second fraction

# Result - which fraction is greater (lower)?

First fractionSecond fraction
 3 8
<
 12 16

# Result - why this fraction is greater (lower)?

Your fractions are NOT equal (have different values), because:
L = 3 · 16 = 48
R = 12 · 8 = 96
L ≠ R

## The first method of comparison (common denominator)

First fraction
 3 8
is smaller than second one
 12 16
, because:

L=
 3 8
=
 3 ·2 8 ·2
=
 6 16

R=
 12 16

The numerator of first fraction is lower, so L<R.

## The second method of comparison (common numerator)

First fraction
 3 8
is smaller than second one
 12 16
, because:

L=
 3 8
=
 3 ·4 8 ·4
=
 12 32

R=
 12 16

The denominator of first fraction is greater, so L<R.
Fractions differ by
 3 8
, because:

StepsIIIIIIIVV
Operations
 12 16
-
 3 8
=
 12 16
-
 3 8
=
 12 16
-
 6 16
=
 6 16
=
 6 16
=
 3 8

# How to check if given fractions are equal?

Sometimes we don't need to know which fraction is the greater or smaller one - we just want to know if those two fractions are equal or not. There is another simple rule:
• Two fractions are equal if numerator of first fraction multiplied by denominator of second one is equal to numerator of second fraction multiplied by denominator of first one. In pure math formula:
$\dfrac{A}{B} = \dfrac{C}{D}, \text{ if } A \times D = C \times B$

# How to test, which of the given fractions is the bigger one (smaller one)?

• If both fractions have same denominator, then the fraction, which has bigger nominator is the bigger one.
ⓘ Example: Fraction 3/4 is bigger than 1/4, because has bigger numerator:
$\dfrac{3}{\fbox{4}} > \dfrac{1}{\fbox{4}} \text{, because } 3 > 1 \text{ (common denominator)}$

• If both fractions have same numerator, then the fraction, which has lower denominator is the bigger one.
ⓘ Example: Fraction 1/4 is bigger than 1/5, because has lower denominator:
$\dfrac{\fbox{1}}{4} > \dfrac{\fbox{1}}{5} \text{, because } 4 < 5 \text{ (common numerator)}$

• If none of the above took place, then we need to bring fraction to common numerator or common denominator form by expanding or reducing them.

# How to compute the difference beetwen fractions?

• Sometimes, when we already know, which of the fractions is the greater one and which one is smaller, we want to compute difference beetwen them. In other words we want to know how much one fraction is greater than another one.
• To compute difference beetwen two fractions we need to subtract smaller fraction from bigger one. In order to do this we need to follow general subract rules i.e. we need perform below steps:
• I. Convert input fractions into improper form. If your fractions do not contain wholes part, then this step is unnecessary and can be skipped.
• II. Find common denominator. If input fractions already have common denominator, this step can be skipped.
• III. Perform subtraction. In this step, calculla subtracts nominators and saves denominator without changes.
• IV. Get wholes part out of result. This step is needed only if result is improper fraction i.e. its nominator is greater than denominator.
• V. Simplify result (convert fraction to the simplest form).