### All ACT Math Resources

## Example Questions

### Example Question #1 : How To Find The Solution To A Rational Equation With Lcd

John, Jill, and Jack are splitting a pizza. John eats of the pizza and Jill eats of the pizza. How much of the pizza is left for Jack?

**Possible Answers:**

**Correct answer:**

We can write an equation for the amount of pizza eaten, with as the amount left for Jack.

To solve this equation, we must find the lowest common denominator of and . We can list the multiples of and to find the least common multiple:

We can see that the least common multiple of and is , so we can rewrite each of the fractions with a denominator of .

When we put these fractions back into the equation, we can solve for :

### Example Question #1 : How To Find The Solution To A Rational Equation With Lcd

What is the slope of a line represented by the equation:

**Possible Answers:**

**Correct answer:**

To solve problems where you need to find the slope of a line in a given equation, change the equation so that it matches y-intercept form:

For this equation, first move the 3x over to the other side of the equation.

The equation should now look like this:

Then, divide by 15 to isolate the variable .

Then simplify

Whatever number is before the x in the equation (m) is your slope.

### Example Question #1 : How To Find The Solution To A Rational Equation With Lcd

**Possible Answers:**

0

–2

–1

2

1

**Correct answer:**

2

### Example Question #11 : Linear / Rational / Variable Equations

**Possible Answers:**

*–bm*/(*m*^{2 }+ 1)

*b*/(*m*^{2 }+ 1)

*bm*/(*m*^{2 }+ 1)

*–b*/(*m *+ 1)

–*b*/(*m*^{2 }– 1)

**Correct answer:**

*b*/(*m*^{2 }+ 1)

### Example Question #12 : Linear / Rational / Variable Equations

In the equation below, , , and are non-zero numbers. What is the value of in terms of and ?

**Possible Answers:**

**Correct answer:**