Question

proportion problem


$\frac{8}{9}$ = $\frac{w - 2}{6}$

Answer 1

Answer: w=66/9

Step-by-step explanation: 8/9=w-2/6

8(6)=9(w-2)

48 =9w-18

48+18=9w

66=9w

w=66/9

or w=7(3/9)

Answer 2

It is assumed here that the problem targets on what the value of w is in this proportion.

Answer:

$\\ w = 7\frac{1}{3} = 7 + \frac{1}{3} = 7.3333333333...$

Step-by-step explanation:

We need to solve the problem so the value of w equals the proportion on both sides. To achieve this, we can apply the following:

Step 1: multiply each side of the equation by 6

$\\ \frac{8}{9} = \frac{w-2}{6}$

$\\ \frac{8}{9}*6 = \frac{w-2}{6}*6$

$\\ \frac{8*6}{9} = \frac{6*(w-2)}{6}$

$\\ \frac{8*6}{9} = (w-2)*\frac{6}{6}$

$\\ \frac{8*6}{9} = (w-2)*1$

$\\ \frac{8*6}{9} = w-2$

Step 2: add 2 to both sides

$\\ \frac{8*6}{9} = w-2$

$\\ \frac{8*6}{9} + 2 = w-2+2$

$\\ \frac{8*6}{9} + 2 = w$

Finally, we get an answer that can be expressed with fractions

$\\ w = \frac{8*6}{9} + 2$

$\\ w = 8*\frac{6}{9} + 2$

Simplifying the fraction $\\ \frac{6}{9} = \frac{2}{3}$

$\\ w = 8*\frac{2}{3} + 2$  

$\\ w = \frac{8*2}{3} + 2$  

$\\ w = \frac{16}{3} + 2$

To show the result as a fraction, we can rewrite 16 as 16= 9 + 6 + 1. Then

$\\ w = \frac{9 + 6 + 1}{3} + 2$

$\\ w = \frac{9}{3} + \frac{6}{3} + \frac{1}{3} + 2$

$\\ w = 3 + 2 + \frac{1}{3} + 2$

$\\ w = 7 + \frac{1}{3} = 7.3333333333...$

Then

$\\ w = 7\frac{1}{3}$

We can prove this substituting this value in the proportion given at the beginning of the question.

$\\ \frac{8}{9} = \frac{w-2}{6}$

$\\ \frac{8}{9} = \frac{7 + \frac{1}{3} -2}{6}$

$\\ \frac{8}{9} = \frac{5 + \frac{1}{3}}{6}$

$\\ \frac{8}{9} = \frac{\frac{15+1}{3}}{6}$

$\\ \frac{8}{9} = \frac{16}{18}$

$\\ \frac{8}{9} = \frac{8}{9}$