X:2 13/36= 27/85 : 1/4

To solve this equation, we can start by simplifying the given fractions.

First, let's simplify 13/36.

To simplify this fraction, we need to find a common factor that can divide both the numerator (13) and the denominator (36). Since neither 13 nor 36 can be divided evenly by a common factor, we can't simplify it further.

Now, let's simplify 27/85.

To simplify this fraction, we can also look for a common factor that can divide both the numerator (27) and the denominator (85). The greatest common divisor (GCD) of 27 and 85 is 1, so we can't simplify this fraction either.

Lastly, let's simplify 1/4.

This fraction is already in its simplest form. The numerator (1) and the denominator (4) don't have any common factors other than 1.

Now, let's substitute the simplified fractions back into the equation.

x:2 = 27/85 : 1/4

Using the division property of fractions, we can rewrite the equation as:

x/2 = (27/85) * (4/1)

Multiplying fractions is done by multiplying the numerators and multiplying the denominators. So, we get:

x/2 = (27 * 4) / (85 * 1)

x/2 = 108/85

To solve for x, we'll multiply both sides of the equation by 2:

(x/2) * 2 = (108/85) * 2

x = (108/85) * 2

Now, we can multiply the fractions:

x = (108 * 2) / 85

x = 216/85

Therefore, the value of x is 216/85.