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We're asked to solve the proportion
8/36 is equal to 10/n.
So we need to figure out what n is.
And the easiest way to do this is to multiply both sides of
this equation by both denominators.
So if we multiply both sides of this equation by
n, what do we get?
The whole purpose of doing that is so that this n in the
denominator will cancel out with this n, which is
essentially in the numerator.
You can view this as n/1.
So if you do that, the left-hand side of our equation
becomes 8/36 times n, or you can even view it as 8n/36
because you can really do this as n/1.
So the left-hand side becomes 8n/36.
And then that will be equal to 10/n times n/1.
This n and that n cancel out, and you're left with
10/1, or just 10.
Now we can multiply both sides of this equation.
To really get rid of that 36 in the denominator, we can
multiply both sides by 36, or you can imagine, by 36/1.
Either way.
36/1 is the same thing as 36.
This 36 cancels out with that 36.
And on the left-hand side, we have 8n, and on the right-hand
side is equal to 10 times 36 is 360.
Now to solve for n, we can just divide both sides of this
equation by 8.
So if you divide that side by 8, and that side by 8, the
left-hand side, the 8's will cancel out, and you are left
with n is equal to 360 divided by 8, and then we can figure
out what that actually is.
8 goes into 360.
So 8 is divisible not into 3, it's divisible
into 36 four times.
4 times 8 is 32.
Subtract.
6 minus 2 is 4.
3 minus 3 is nothing.
Bring down the 0.
8 goes into 40 exactly five times.
5 times 8 is 40, and then you have no remainder.
So n is equal to 360/8, which is the exact same thing as 45.
So going back to our original proportion, we now solved for
n, and we know that 8/36 is the same exact thing as 10/45.