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what is 4/9 y=16

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6 Answers

(4/9)*y = 16.

1. Multiply each side by (9/4) to get the y by itself. 

[9/4]*(4/9)*y = [9/4]*16

2. [9/4]*(4/9) = 1, so we can replace that with 1. 

1*y = [9/4]*16

3. Simplify the right side and left side. 

y = 144/4 = 36

 

 

4/9y=16

Fractions confuse many people.  A Fraction is a division problem.  4/9 is the same as saying 4 divided by 9.  Since multiplication is the opposite of division we can remove the fraction by multiplying 9  to each term [9(4/9y)= 9(16)

9X 4y/9= 4y; 9 X 16 = 144

4y= 144

y = 36

I like Uzair Q's answer the best, but lets give a more general answer and use the correct vocabulary. The equation we are considering is a faction multiplied by a variable on the left side. To clear this faction and get the variable by itself, we multiply by the reciprocal fraction. This is the same effect as the first two answers but think it is clearer because the left hand side immediately becomes our variable Y only, and then all that we have to do is the calculations on the right hand side.

So, once again, the fraction 9/4 is chosen because it is the reciprocal of 4/9. If our original fraction were 2/5, we would multiply by 5/2, if 7/3, we would multiply by 3/7.  Multiplying any fraction by it's reciprocal will result in 1. One times the variable is just the variable itself. therefore the fraction clears.

Follow these steps:

1.  Multiply each side of the equation by the denominator of the variable, in this case, 9.

        (9)*(4/9)y = (16)*(9).  In the left side, the 9/9 is 1.  The result will be: 4y = 144

2.  Divide each side of the equation by the coefficient of y, in this casem 4.

      (4y) / 4 = 144 / 4.  In the left side, 4/4 is 1, for that reason the equation will be y = 144/4.

3.  y = 144 / 4 = 36

4.  y = 36

  • Divide both sides of the equation (4/9) y  = 16 by the fration (4/9). Why? Because in Math we're allowed to do so, as long as we're not dividing by zero!  We write  [(4/9) y] / (4/9) = [ 16 ] / (4/9).
  • y stands alone on the left side because (4/9) divided by (4/9) equals 1.
  •  Looking at what happens to the right side, recall that to divide by a fraction (4/9) is the same as to multiply by that fraction flipped over, that means the numerator becomes the denominator and the denominator becomes the numerator! We write y = 16 x (9/4) . Your calculator will show 36 after computation.
  • The solution to the initial equation is y = 36

First, try to get rid of any factors in front of y. If 4/9 of something equals 16, then 4 units of something will be 9 times larger, that is, 16*9, right? So, we multiplied both parts by 9 to obtain equation 4y=16*9=144. Now, by the same logic, if 4 units of something is 144, then one unit will be 4 times less than 144. You now can complete the problem yourself, I will leave this last calculation for you to do.

Overall, we multiplied both parts by 9 and divided by 4. In other words, we multiplied both parts by 9/4 or divided both parts by 4/9--these are just two different ways to say the same thing! In general, if you have equation a*x=b and a≠0, then you divide both parts by a to get x=b/a, whatever the number a is. 4/9 is as good a number for the coefficient in front of x as any other number. So we divide 16 by 4/9, that is 16:4/9. In order to divide a number by a simple fraction p/q, one can multiply by the reciprocal fraction, q/p. So 16:4/9 becomes 16*9/4. The rest shall be easy.

Hope it helps.