Solving for Y: How does this problem work out to become 77/5?

Question

I'm doing a problem where I solve for Y

My initial problem was :

y-9=4/5(x+8)

 

I know I have to distribute and then add on 9, but i'm confused on how 4/5 eventually becomes 77\5.

 

The answer to the problem is y=4/5x+77/5

 

Answer 1

y - 9 = (4/5)(x + 8)

5(y - 9) = 4(x + 8)       multiply both sides by 5

5y - 45 = 4x + 32         distribute

5y = 4x + 77               add 45 to both sides

y = 4x/5 + 77/5           divide both sides by 5

Answer 2

With the fraction of (4/5), you may multiply by 5, then later divide by 5.

Or, you may distribute first, then work with improper fractions.

  y - 9 = 4/5(x+8)

  y - 9 = (4/5)x + (4/5)8           [distribute first]

  y = (4/5)x +32/5 +45/5        [add 9 = 45/5 to both sides]

  y = (4/5)x + 77/5                [combine fractions]

Answer 3

When you distribute the 4/5 you multiply 4/5 by 8. When multiplying fractions you multiply numerators together and denominators together. so you have 4/5 * 8/1 which is (4*8)/(5*1) = 32/5. The next step is to add nine to both sides of the equation. Since you are adding a fraction and a whole number you have to have a common denominator so 9 becomes 45/5. 32/5 + 45/5 = 77/5.