Question

What is the value of the expression (-8/9) divided by (-2/3) x (-4 1/2) ?

options

a). -6
b). -8/27
c). 8/27
d). 6

Answer 1

B)
`x=-(8)/(27)`

Explanation:

`-(8)/(9)=-(2)/(3)x(-4(1)/(2))`

• To start things off, lets convert any mixed numbers like
  `-4(1)/(2)` into improper fractions. In this case
  `-4(1)/(2)` as an improper fraction is
  `-(9)/(2)`.

`-(8)/(9)=-(2)/(3)x(-(9)/(2))`

• Now let's multiply
  `-(2)/(3)x` by
  `-(9)/(2)`. When multiplying fractions, all you need to do is multiply the numerators and denominators separately. Your final answer should be
  `(18)/(6)x`.
• *Note: a negative times a negative is a positive, so that's why we now have an even number in front of
  `x` instead of a negative number.

`-(8)/(9)=(18)/(6)x`

• Now we want to isolate
  `x`, so we'll have to divide
  `-(8)/(9)` by
  `(18)/(6)`, but dividing these two fractions seems like a pain. To make things a bit easier, let's turn our improper fraction into a whole number. To change this improper fraction into a whole number, we should ask ourselves what times
  `6` is equal to
  `18`? In this case, the answer is 3, so
  `(18)/(6)` is actually the same thing as the whole number
  `3`.
• *Note: In general, keeping fractions as either improper fractions or whole numbers will make doing math easier. Avoid mixed numbers like
  `-4(1)/(2)` when trying to do math and simply change improper fractions into mixed numbers once you have your final solution.

`-(8)/(9)=3x`

• Now divide
  `-(8)/(9)` by
  `3`. Think of it as multiplying the denominator of
  `-(8)/(9)` by
  `3`.

`-(8)/(27)=x`