All ACT Math Resources
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?
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 #2 : 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?
None of the other answers
Plugging and into the equation gives:
Create a common denominator by multiplying by in the numerator and denominator:
Example Question #3 : How To Find A Solution To A Compound Fraction
What does equal?
Simplify the numerator first: .
Then, simplify the denominator: .
Next, you have to do , which is the same as , when solved for and simplified.