Question

Proportion problem



`(8)/(9)` =
`(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(1)/(3) = 7 + (1)/(3) = 7.3333333333...`

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

`\\ (8)/(9) = (w-2)/(6)`

`\\ (8)/(9)*6 = (w-2)/(6)*6`

`\\ (8*6)/(9) = (6*(w-2))/(6)`

`\\ (8*6)/(9) = (w-2)*(6)/(6)`

`\\ (8*6)/(9) = (w-2)*1`

`\\ (8*6)/(9) = w-2`

Step 2: add 2 to both sides

`\\ (8*6)/(9) = w-2`

`\\ (8*6)/(9) + 2 = w-2+2`

`\\ (8*6)/(9) + 2 = w`

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

`\\ w = (8*6)/(9) + 2`

`\\ w = 8*(6)/(9) + 2`

Simplifying the fraction
`\\ (6)/(9) = (2)/(3)`

`\\ w = 8*(2)/(3) + 2`

`\\ w = (8*2)/(3) + 2`

`\\ w = (16)/(3) + 2`

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

`\\ w = (9 + 6 + 1)/(3) + 2`

`\\ w = (9)/(3) + (6)/(3) + (1)/(3) + 2`

`\\ w = 3 + 2 + (1)/(3) + 2`

`\\ w = 7 + (1)/(3) = 7.3333333333...`

Then

`\\ w = 7(1)/(3)`

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

`\\ (8)/(9) = (w-2)/(6)`

`\\ (8)/(9) = (7 + (1)/(3) -2)/(6)`

`\\ (8)/(9) = (5 + (1)/(3))/(6)`

`\\ (8)/(9) = ((15+1)/(3))/(6)`

`\\ (8)/(9) = (16)/(18)`

`\\ (8)/(9) = (8)/(9)`