If you're seeing this message, it means we're having trouble loading external resources on our website.

If you're behind a web filter, please make sure that the domains *.kastatic.org and *.kasandbox.org are unblocked.

## Algebra basics

### Course: Algebra basics>Unit 3

Lesson 7: Writing & solving proportions

# Worked example: Solving proportions

Learn the reasoning behind solving proportions. We'll put some algebra to work to get our answers, too. Created by Sal Khan and Monterey Institute for Technology and Education.

## Want to join the conversation?

• In the first example on how to find the proportion, Sal said to multiply 8x10/8 to get 10. He said he made the calculation on his head, but I wonder what steps should I follow to get that answer? The 10/8 looks obvious after he gave it away but if he hadn't I don't think I could have find it on my own. At least I don't know how to do it at the moment. •   Well, let's see...we're basically asking 8 times what = 10, right? So, in algebra terms, 8 x n = 10 or 8n = 10. Divide both sides by 8 to get the n by itself and you get n = 10/8. Does that make sense?
• Is there any easier way to do it? Like a way without using common core? Because this is way to confusing! •   In that first example that Sal gave you, try checking for fractions to simplify first. You can see that the first fraction `8/36` simplifies to `2/9`.
``2       10--  =   --9        n``

Now, we need to ask ourselves this question: "2 times what equals 10?" And to answer that question, 2 times 5 equals 10. So, we now know to multiply 5 on the denominator of the first fraction to find n. 9 times 5 equals 45, so `n = 45`.

There is another way: it's to cross-multiply and then solve the equation. But you won't learn about solving equations until much later in Pre-Algebra: https://www.khanacademy.org/math/pre-algebra/pre-algebra-equations-expressions/pre-algebra-intro-equations/v/variables-expressions-and-equations

Let's use Sal's example again:
``2       10--  =   --9        n``

Try drawing an 'X' with your fingers on the proportion above. That's how we'll cross-multiply it. The equation will ultimately look like this: `2 ⋅ n = 10 ⋅ 9`. Simplify the equation and you get: `2n = 90`. To solve it, you just divide 2 on both sides:
``2n = 90÷2 = ÷2n = 45``

I hope this helped!
• Did anyone else hear breathing in between while he was talking? :( • i don't even know what he said during those whole 7 minutes • Is there anytime the answer is 0? • confused • I was doing the "Solving Proportions" and the question was like "12/7 = k/8", and whatever I did I kept getting 13.7142857143, but it was wrong. I don't understand. • The video is a bit confusing, and I'm struggling to transfer this to solving the questions for "Solving Proportions". For example in the question:

4/z = 12/5
I understand that you begin by multiplying by z.
z * 4/z = 12/5*z
--> 4 = 12/5*z

After this, the solution set asks you to multiply both sides by 5/12, the opposite fraction of the right side. Why is that?
And how does multiplying a fraction with its opposite give you one? • This concept is based upon the Inverse Property of Multiplication that says:
Any number multiplied by its reciprocal = 1
For example: 12/5 * 5/12 = 60/60 = 1

If you find it easier, you can do cross multiplication. This is where you multiply along each diagonal of the proportion.
4/z = 12/5
12(z) = 4(5)
12z = 20
Then, divide by 12: z = 20/12 = 5/3

Hope this helps.
• That was a little confusing.. • Err... Did Sal show 5 different ways of solving one problem? • Yes he told many ways and some of them were confusing. The simplest way I think is Cross multiplication. Here's how to do it.

Lets take a number 3/12=4/X

1. First cross multiply the digits i.e, multiply 12 x 4 and 3 x X
2. 12 x 4 = 48 and 3 x X = 3X
3.Next, According to question 3/12=4/X so, 48 will be equal to 3X
4.48=3X
5. Now I need to find the value for X So in order to isolate X I need to divide 3X by 3 (In order to find the value for X)
6. 48= [4X/3] If I divide one side by 3 then I must also divide the other side by 3 (That is the rule of the Equation).
So, we get [48/3]=[3X/3]
7. Next lets solve it 48/3 is 16 and 3X/3 is X
8. Now we get 16=X
9. Finally, the X value is 16
10. So X=16

Hope this helps. Feel free to Comment me if you have any questions :)