# ACT Math : How to find a solution to a compound fraction

## Example Questions

### Example Question #1 : How To Find A Solution To A Compound Fraction

John's shadow is six feet long, and Mary's shadow is five feet long. If John is four feet tall, which of the following is closest to Mary's height in inches?

Explanation:

First we set up a proportion. Mary's shadow (5 feet) to John's shadow (6 feet) is equal to Mary's height (x feet) to John's height (4 feet), i.e. 5 / 6 = x / 4.

Solve for x by first cross-mulitplying: 20 = 6x.

Divide both sides by 6: x = 20 / 6 feet

Multiply by 12 to find this height in inches: 20 * 12 / 6 = 20 * 2 = 40 inches

### Example Question #1 : How To Find A Solution To A Compound Fraction

When two resistors ( and ) are added together in a parallel circuit to create an equivalent single resistor, the equivalent resistor () has a resistance defined by the following equation:

If  and , what does  equal?

Explanation:

Plugging  and  into the equation gives:

Create a common denominator by multiplying  by  in the numerator and denominator:

Finally:

### Example Question #2 : How To Find A Solution To A Compound Fraction

What does  equal?

Explanation:

Simplify the numerator first: .

Then, simplify the denominator: .

Next, you have to do , which is the same as , when solved for and simplified.