Help me understand

Question

Find the value of x that solves the following proportion 9/6=x10 Will you plese help me solve this?

Answer 1

Solving this as written  9/6 = x*10, I'm going to use * to mean multiply.

I think the first time you see x it is mysterious. What is x? springs to mind. In this case x = 9/60 = 3/20.

What about getting from 9/6 = x*10 to x = 9/60, how do you get there.

For me I think of x as being all crowded by the 10. Get away from me 10, go over there says x in order to be less crowded. But there are rules. 10 can go to the other side of the equation, but it has to go the bottom not to the top. so that gives you x = 9/(6 times 10) = 9/60. That's what people call cross multiplying, 10 goes ACROSS the equation but from top to bottom.

BUT WHY does 10 have to go to the bottom not to the top?

That's all about what does = mean.

= means;

whatever is on the left side of the equation is EQUAL to whatever is on the right side of the equation.

So to stay equal, to be true to what equal means, whatever you do to the left side you have to do the right side too.

So when x says get away 10, and 10 says "so make me", that means dividing both sides of the equation by 10. When 10 is divided by 10 that is equal to 1 so that makes 10 go away

So the process looks like

(9/6) DIVIDE by 10 = x * 10 DIVIDE by ten

9/(6*10) = x * 1 = x

 

That's a lot of writing and a lot of explaining. So the same thing in more mathematical form looks like

(9/6) * (1/10) =  x * 10 * (1/10)

(9*1)/(6*10) = x * (10/10)

9/60 = x * 1 = x

9/60 = x

 

In words, 10 says so make me go away, so multiply the LEFT & the RIGHT side of the equation by 10's exact nemesis 1/10, and 10 goes away.

 

Or to really focus on what is important, learn what EQUAL really means, and the rest comes from that.

 

Answer 2

Hi Glenda,

Andy Gave you a perfect answer for the problem that you posted, but I wonder if the problem you posted is correct? 9/6 =x10 is not a proportion.

Is the problem 9/6 = x/10?

If so, You can also solve this equation by cross multiplying.

9/6 = x/10

To cross multiply, you multiply the numerator of the fraction on the left (9) by the denominator of the fraction on the right (10) = 90. Then repeat for the denominator on the left side (6) times the numerator on the right (x) = 6x. So,

90 = 6x

We divide both sides by 6 to isolate the variable. 90 divided by 6 = 15. 6x divided by 6 = x. So,

x = 15

It's always good to check your answers as well. You can do this by plugging in your answer for the variable and cross multiplying.

9/6 = 15/10

multiply 9*10 = 90, 6*15 = 90

90 = 90

x = 15 is correct!

Hope this helps!

-Becca M.

 

 

 

Answer 3

When we are given an equation we can change its form by doing identical operations on both sides of the operation. So if we are given the equation 9/6 = x10 we can divide both sides of the equation by 10. Thus we get 9/6 divided by 10 = x10 divided by 10. The left side of the equation simplifies to 9/60 and the right side of the equation simplifies to x. Thus, x = 9/60 or x = 3/20