### All ACT Math Resources

## Example Questions

### Example Question #1 : Algebraic Fractions

Change to a mixed number

**Possible Answers:**

**Correct answer:**

To convert from a fraction to a mixed number we must find out how many times the denominator goes into the numerator using division and the remainder becomes the new fraction.

### Example Question #1 : Algebraic Fractions

What is the average of and ?

**Possible Answers:**

**Correct answer:**

To average, we have to add the values and divide by two. To do this we need to find a common denomenator of 6. We then add and divide by 2, yielding 4.5/6. This reduces to 3/4.

### Example Question #1 : Algebraic Fractions

Which of the following is equivalent to ?

**Possible Answers:**

None of the answers are correct

**Correct answer:**

This problem is solved the same way ½ + 1/3 is solved. For example, ½ + 1/3 = 3/6 + 2/6 = 5/6. Find a common denominator then convert each fraction into an equivalent fraction using that common denominator. The final step is to add the two new fractions and simplify.

### Example Question #1 : Algebraic Fractions

A train travels at a constant rate of meters per second. How many kilometers does it travel in minutes?

**Possible Answers:**

**Correct answer:**

Set up the conversions as fractions and solve:

### Example Question #2 : Algebraic Fractions

Simplify.

**Possible Answers:**

Can't be simplified

**Correct answer:**

To simplify exponents which are being divided, subtract the exponents on the bottom from exponents on the top. Remember that only exponents with the same bases can be simplified

### Example Question #1 : How To Simplify A Fraction

Simplify:

* *

**Possible Answers:**

**Correct answer:**

*x*^{2} – *y*^{2} can be also expressed as (*x* + *y*)(*x* – *y*).

Therefore, the fraction now can be re-written as (*x* + *y*)(*x* – *y*)/(*x* + *y*).

This simplifies to (*x* – *y*).

### Example Question #2 : Algebraic Fractions

Simplify:

**Possible Answers:**

**Correct answer:**

Notice that the term appears frequently. Let's try to factor that out:

Now multiply both the numerator and denominator by the conjugate of the denominator:

### Example Question #1 : Algebraic Fractions

Simplify:

(2*x* + 4)/(*x* + 2)

**Possible Answers:**

*x* + 1

2*x* + 2

2

*x* + 4

*x* + 2

**Correct answer:**

2

(2*x* + 4)/(*x* + 2)

To simplify you must first factor the top polynomial to 2(*x* + 2). You may then eliminate the identical (*x* + 2) from the top and bottom leaving 2.

### Example Question #3 : Algebraic Fractions

Simplify the following expression:

**Possible Answers:**

**Correct answer:**

Factor both the numerator and the denominator:

After reducing the fraction, all that remains is:

### Example Question #1 : How To Simplify A Fraction

Simplify:

**Possible Answers:**

None of the other answers

**Correct answer:**

With this problem the first thing to do is cancel out variables. The x^{2 }can all be divided by each other because they are present in each system. The equation will now look like this:

Now we can see that the equation can all be divided by y, leaving the answer to be: