Question

2 over 3/4w= 6 over 3/5

Answer 1

`w=(4)/(15)`

Explanation:

Given expression:

`(2)/((3)/(4)w)=(6)/((3)/(5))`

To solve for the unknown variable
`w`.

Solution:

In order to solve for
`w`, we will isolate
`w` on one one side side.

Since the divisor is a fraction, so the expression can be rewritten as:

`2/(3)/(4) w = 6/ (3)/(5)`

In order to divide a number by a fraction, we will take the reciprocal of the divisor and replace division with multiplication.

`2* (4)/(3w)=6* (5)/(3)`

`(8)/(3w)=10`

Multiplying both sides by
`3w`

`3w.(8)/(3w)=10(3w)`

`8=30w`

Dividing both sides by 30.

`(8)/(30)=(30w)/(30)`

Simplifying fractions by dividing numerator and denominator by their G.C.F.

`(4)/(15)=w`

∴
`w=(4)/(15)` (Answer)