# Fractions Solve for Unknown

## Calculator Use

Solve equivalent and inequivalent fractions for one unknown value. This calculator will calculate 1 unknown variable to solve the proportion between 2 fractions. Some people 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 variable X 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:

If we multiply both sides by 1 using the denominators from the other side of the equation we get:

Note that this doesn't change anything, because multiplying anything by 1 doesn't change its value. So now we have:

If we said \( \frac{3}{4} = \frac{3}{4} \), or \( \frac{a}{4} = \frac{b}{4} \), 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:

Which is the result of cross multiplying our original equation:

## 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/

**Cite this content, page or calculator as:**

Furey, Edward "Fractions Solve for Unknown"; from *http://www.calculatorsoup.com* - Online Calculator Resource.