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.
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.
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
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/