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Cross multiplication actually makes solving problems with two fractions much easier! Learn the steps you need to take in this lesson and you’ll see just how easy it is to cross multiply.

Steps to Solve

Your cross multiplication of fractions problems will always look something like this:

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Problem 1
cross multiplication


You have two fractions and a variable that you need to solve somewhere.To solve such a problem, use these steps.

Step 1:

Multiply the left numerator with the right denominator. This is your left side of your equation.For the above problem, you get 3 * 12 = 36. This is the left side of the equation (36 = ?).

Step 2:

Multiply the left denominator with the right numerator. This is the right side of your equation.

Continuing with our problem, you get 4 * x = 4x. This is the right side of the equation (36 = 4x).

Step 3:

Solve for x. Divide as necessary.Now you have an equation 36 = 4x that you can solve for x. To solve for x, you divide by the 4 that is currently being multiplied with the x. You divide both sides by the 4.

You get 36 / 4 = 4x / 4.

Solution

After doing the last step, you finish by dividing both sides by 4. You get 9 = x.

So your answer is x = 9. And you are done!Just to recap, you found your answer by multiplying the numerator on the left side with the denominator on the right side. This is your left side. Your right side of the equation comes from multiplying the denominator on the left side with the numerator on the right side.

More Examples

Let’s try some more so you can see how easy it is.Solve.


Problem 2
cross multiplication


Step 1:

Multiplying the left numerator with the right denominator, you get 12 * 5 = 60.

Step 2:

Multiplying the left denominator with the right numerator, you get x * 2 = 2x. Your equation now is 60 = 2x.

Step 3:

Solving for x, you now divide by 2 on both sides. You get 60 / 2 = 2x / 2 which becomes 30 = x. And you are done! Your solution is x = 30.

Let’s do one more!Again, solve:

Problem 3
cross multiplication


Step 1:

43 * x = 43x

Step 2:

6 * 11 = 66. 43x = 66.

Step 3:

43x / 43 = 66 / 43. This becomes x = 66 / 43 since it’s already as simplified as it can get.

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