Answer:
[tex]w=\frac{4}{15}[/tex]
Step-by-step explanation:
Given expression:
[tex]\frac{2}{\frac{3}{4}w}=\frac{6}{\frac{3}{5}}[/tex]
To solve for the unknown variable [tex]w[/tex].
Solution:
In order to solve for [tex]w[/tex], we will isolate [tex]w[/tex] on one one side side.
Since the divisor is a fraction, so the expression can be rewritten as:
[tex]2\div\frac{3}{4} w = 6\div \frac{3}{5}[/tex]
In order to divide a number by a fraction, we will take the reciprocal of the divisor and replace division with multiplication.
[tex]2\times \frac{4}{3w}=6\times \frac{5}{3}[/tex]
[tex]\frac{8}{3w}=10[/tex]
Multiplying both sides by [tex]3w[/tex]
[tex]3w.\frac{8}{3w}=10(3w)[/tex]
[tex]8=30w[/tex]
Dividing both sides by 30.
[tex]\frac{8}{30}=\frac{30w}{30}[/tex]
Simplifying fractions by dividing numerator and denominator by their G.C.F.
[tex]\frac{4}{15}=w[/tex]
∴ [tex]w=\frac{4}{15}[/tex] (Answer)
