# ACT Math : Algebraic Fractions

## Example Questions

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### Example Question #1 : Algebraic Fractions

Change to a mixed number

Explanation:

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 ?

Explanation:

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  ?

None of the answers are correct

Explanation:

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?

Explanation:

Set up the conversions as fractions and solve:

### Example Question #2 : Algebraic Fractions

Simplify.

Can't be simplified

Explanation:

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:

Explanation:

x2 – y2 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:

Explanation:

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:

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

x + 1

2x + 2

2

x + 4

x + 2

2

Explanation:

(2x + 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:

Explanation:

Factor both the numerator and the denominator:

After reducing the fraction, all that remains is:

Simplify: