Compound Fractions

Help Questions

ACT Math › Compound Fractions

Questions 1 - 6
1

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

2

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

3

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

Explanation

Plugging and into the equation gives:

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

Finally:

4

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

Explanation

Plugging and into the equation gives:

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

Finally:

5

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.

6

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.