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# 1/3y=18 ????

Hi Grace,

Let's begin by writing out our equation:  1 / 3y = 18

First, we want to get rid of the fraction on the left side of the equation by multiplying both sides of the equation by the denominator (3y), which will cancel out the denominator (3y):

(3y) (1 / 3y) = (3y)(18) which gives us:  1 = 54y

Now we need to get rid of the 54 in front of the y on the right side of the equation to get our value for y.

We can do this by dividing both sides of the equation by 54 which will cancel out the multiplication by 54 on the right side:

1 / 54 = 54y / 54 which gives us our answer for y:  y = 1 / 54

I trust this explanation will help you understand how we solved our equation.

Regards, Jordan.

1 = 54y

I'm unsure of whether the problem is   1/(3y) = 18    OR if it is    (1/3)y = 18

But in either case, you have an unknown variable (y) that you are looking to solve for. So your goal is to set the equation equal to this variable (i.e., y= ), and you do so by isolating y to one side of the equation. I will work out both equations to help you understand.

If the problem looks like the first equation above..... 1/(3y) = 18 ....then the first step is to multiply both sides of the equation by 3y.

(3y) * (1/(3y)) = (3y) * (18)     ==>     1 = 54y

Then divide both sides of the equation by 54 to solve for y.

(1) / (54) = (54y) / (54)     ==>     1/54 = y

Thus,   y = 1/54

If the problem looks like the second equation.... (1/3)y = 18 ....then, to solve for y, simply multiply both sides of the equation by 3.

(3) * ((1/3)y) = (3) * (18)      ==>      y = 54

Thus,    y = 54

Okay, y is a variable. That means you want your final solution to say y = whatever because you are trying to say what the value of y is. So we need to get the y all by itself. Whenever there is a number attached to the variable you can multiply by the reciprocal of that number to get rid of it. In this case you have 1/3 atached to y. The reciprocal is just the same thing upside down which is 3/1 or 3. This works because 1/3 * 3/1 equals 1, right? so that would turn 1/3y into 1y which is just what we mean when we say y. The next thing to know is that whatever you do to one side of the equation you have to do to the other side. So...

1/3y = 18

3 * 1/3y = 18 * 3 multiply each side by 3 to get rid of the 1/3 attached to the y

so the result is

y = 18*3

which works out to

y = 54

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