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Fractions Solve for [unknown] Calculator
(solving equivalent fractions)
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Equation:
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About this Calculator

This calculator will calculate 1 unknown variable to solve the proportion between 2 fractions.  Some people just refer to this as solving equivalent fractions but it also solves for inequalities.

Enter 3 values and 1 unknown. For example, enter X/45 = 1/15. This calculator will solve for X.

How to solve for X variable in fractions

We solve for X by cross multiplying and solving the equation for X

For Example: Given the equation 4/10 = X/15 solve for X.

Cross multiplying we get
4 * 15 = 10 * X

Solving the equation for X we get
X = (4 * 15) / 10

Simplifying we get
X = 6

Plugging 4 back into the original equation
4/10 = 6/15

Checking our answer, since multiplying anything by 1 doesn't change its value and 3/3 = 1 and 2/2 = 1,
4/10 * 3/3 = 12/30
6/15 * 2/2 = 12/30
since these are equal it is true that X = 4 in our equation.

Why does cross multiplying fractions work?

Cross multiplying works because we are really just multiplying both sides of the equation by 1.  Since multiplying anything by 1 doesn't change its value we will have an equivalent equation.

    For example, let's look at this equation:
    
         A   C
         - = - 
         B   D
    
    If we multiply both sides by 1 using the denominators from the other side
    of the equation we get:
    
         A   D   C   B
         - * - = - * - 
         B   D   D   B
    
    Note that this doesn't change anything, because multiplying anything 
    by 1 doesn't change its value.  So now we have
    
         A*D     B*C
         ---  =  --- 
         B*D     B*D
    
    If we said 3/4 = 3/4 or A/4 = B/4, you could then say 3 = 3 or A = B.
    Since the denominators are also the same here, B*D, we can remove them and say that
    
         A*D = B*C, which is the result of cross multiplying our original equation
    
         A   C
         - X -
         B   D

References/ Additional Reading

Cross Multiply from Math Is Fun at http://www.mathsisfun.com/

Cross-Multiplication from Ask Dr. Math at http://mathforum.org/

Cross Products from Ask Dr. Math at http://mathforum.org/