# ACT Math : Algebraic Fractions

## Example Questions

### Example Question #11 : How To Evaluate A Fraction

Simplify:

Explanation:

Begin by simplifying the numerator.

has a common denominator of .  Therefore, we can rewrite it as:

Now, in our original problem this is really is:

When you divide by a fraction, you really multiply by the reciprocal:

### Example Question #11 : How To Evaluate A Fraction

Simplify:

Explanation:

Begin by simplifying the numerator and the denominator.

Numerator

has a common denominator of .  Therefore, we have:

Denominator

has a common denominator of .  Therefore, we have:

Now, reconstructing our fraction, we have:

To make this division work, you multiply the numerator by the reciprocal of the denominator:

### Example Question #16 : How To Evaluate A Fraction

Simplify:

None of the other answer choices are correct.

Explanation:

Recall that dividing is equivalent multiplying by the reciprocal.  Therefore, ((x - 4) / (1 / 2)) / (1 / (x + 4)) = ((x - 4) * 2)  *  (x + 4) / 1.

Let's simplify this further:

(2x – 8) * (x + 4) = 2x2 – 8x + 8x – 32 = 2x2 – 32

### Example Question #13 : How To Evaluate A Fraction

Solve for :

Explanation:

Begin by isolating the variables:

Now, the common denominator of the variable terms is . The common denominator of the constant values is . Thus, you can rewrite your equation:

Simplify:

Cross-multiply:

Simplify:

Finally, solve for :

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

Evaluate when x=11. Round to the nearest tenth.

0.2

1.9

1.8

0.3

1.8

Explanation:

Wherever there is an x, plug in 11 and perform the given operations. The numerator will be equal to 83 and the denominator will be equal to 46. 83 divided by 46 is equal to 1.804… and since the second decimal place is not greater than or equal to 5, the first decimal place stays the same when rounding so the final answer is 1.8.

### Example Question #1 : How To Find Inverse Variation

Find the inverse equation of:

Explanation:

To solve for an inverse, we switch x and y and solve for y. Doing so yields:

### Example Question #2 : How To Find Inverse Variation

Find the inverse equation of  .

Explanation:

1. Switch the  and  variables in the above equation.

2. Solve for :

### Example Question #3 : How To Find Inverse Variation

When ,  .

When .

If  varies inversely with , what is the value of  when ?

Explanation:

If  varies inversely with .

1. Using any of the two  combinations given, solve for :

Using :

2. Use your new equation  and solve when :

### Example Question #2 : Algebraic Fractions

 x y

If  varies inversely with , what is the value of ?

Explanation:

An inverse variation is a function in the form:  or , where  is not equal to 0.

Substitute each  in .

Therefore, the constant of variation, , must equal 24. If  varies inversely as must equal 24. Solve for .

### Example Question #5 : How To Find Inverse Variation

Two numbers  and  vary inversely, and  when . If this is true, what is the value of  when ?