Solve for w 2/w=0.4/0.7

$\frac{2}{w} = \frac{0.4}{0.7}$

Step 1

Divide $0.4$ by $0.7$ .

$\frac{2}{w} = 0.\overline{571428}$

Step 2

Find the LCD of the terms in the equation.

Finding the LCD of a list of values is the same as finding the LCM of the denominators of those values.

$w, 1$

The LCM of one and any expression is the expression.

$w$

Step 3

Multiply each term in $\frac{2}{w} = 0.\overline{571428}$ by $w$ to eliminate the fractions.

Multiply each term in $\frac{2}{w} = 0.\overline{571428}$ by $w$ .

$\frac{2}{w} w = 0.\overline{571428} w$

Simplify the left side.

Cancel the common factor of $w$ .

Cancel the common factor.

$\frac{2}{w} w = 0.\overline{571428} w$

Rewrite the expression.

$2 = 0.\overline{571428} w$

Step 4

Solve the equation.

Rewrite the equation as $0.\overline{571428} w = 2$ .

$0.\overline{571428} w = 2$

Divide each term in $0.\overline{571428} w = 2$ by $0.\overline{571428}$ and simplify.

Divide each term in $0.\overline{571428} w = 2$ by $0.\overline{571428}$ .

$\frac{0.\overline{571428} w}{0.\overline{571428}} = \frac{2}{0.\overline{571428}}$

Simplify the left side.

Cancel the common factor of $0.\overline{571428}$ .

Cancel the common factor.

$\frac{0.\overline{571428} w}{0.\overline{571428}} = \frac{2}{0.\overline{571428}}$

Divide $w$ by $1$ .

$w = \frac{2}{0.\overline{571428}}$

Simplify the right side.

Divide $2$ by $0.\overline{571428}$ .

$w = 3.5$