### All ACT Math Resources

## Example Questions

### Example Question #1 : Operations And Fractions

Solve for *x* where

**Possible Answers:**

**Correct answer:**

To solve this, subtract 1 1/2 from both sides. Convert to common denominators.

4 1/3 – 1 1/2 = 4 2/6 – 1 3/6.

In order to subtract, you'll want to "borrow" from the 4 2/6. Rewrite 4 2/6 as 3 8/6 and then subtract 1 3/6 from this. Your solution is 2 5/6. Most calculators will also do these calculations for you.

### Example Question #6 : Operations And Fractions

Solve for :

**Possible Answers:**

**Correct answer:**

Begin by isolating your variable:

Next, you need to find the common denominator. For the left side of your equation, it is . For the right, it is . This means that you need to rewrite as follows:

Now, simplify and combine terms:

You can further simplify the left side:

Next, multiply both sides by . This gives you:

### Example Question #11 : Operations And Fractions

Simplify:

**Possible Answers:**

**Correct answer:**

First, you must convert your fractions to the common denominator of :

Next, do your subtraction:

Next, you must be very careful. Notice how you must handle your subtractions in order to maintain the correct distribution of signs:

Now, carefully distribute for each group:

Next, simplify:

Factor out the common in the numerator:

There is still a common , but that does not help you get your fraction into the form found in the answers.

### Example Question #2 : How To Subtract Fractions

Choose the answer which best solves the equation below:

**Possible Answers:**

**Correct answer:**

To solve this equation, you must first make sure that both fractions have a common denominator.

In this case the common denominator will be 12:

Then you perform your operation:

### Example Question #3 : How To Subtract Fractions

If John has slices of an slice pizza left over, and he eats of them, what fraction of the pizza does he have left over?

**Possible Answers:**

**Correct answer:**

To find this answer, first you need to set up your equation:

And you need to get rid of the decimal in the numerator. We can do this by multiplying each fraction by 2/2.

Then solve for your answer:

### Example Question #11 : Operations And Fractions

What common number can you add to the numerator and denominator of to get ?

**Possible Answers:**

**Correct answer:**

Set up an equation where you add the same unknown number (x) to both the numerator and the denominator of the original fraction, and set the equation equal to .

Cross-multiply the fractions to simplify.

Now, solve for x.