Question

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

Answer 1

Answer:

$w=\frac{4}{15}$

Step-by-step explanation:

Given expression:

$\frac{2}{\frac{3}{4}w}=\frac{6}{\frac{3}{5}}$

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:

$2\div\frac{3}{4} w = 6\div \frac{3}{5}$

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

$2\times \frac{4}{3w}=6\times \frac{5}{3}$

$\frac{8}{3w}=10$

Multiplying both sides by $3w$

$3w.\frac{8}{3w}=10(3w)$

$8=30w$

Dividing both sides by 30.

$\frac{8}{30}=\frac{30w}{30}$

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

$\frac{4}{15}=w$

∴ $w=\frac{4}{15}$  (Answer)