# SAT Math : How to evaluate a fraction

## Example Questions

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

If  pizzas cost  dollars and  sodas cost  dollars, what is the cost of  pizzas and  sodas in terms of  and ?

Explanation:

If 10 pizzas cost x dollars, then each pizza costs x/10. Similarly, each soda costs y/6. We can add the pizzas and sodas together by finding a common denominator:

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

According the pie chart, the degree measure of the sector representing the number of workers spending 5 to 9 years in the same role is how much greater in the construction industry chart than in the financial industry chart?

Explanation:

Since the values in the pie charts are currently in terms of percentages (/100), we must convert them to degrees (/360, since within a circle) to solve the question. The "5 to 9 years" portion for the financial and construction industries are 18 and 25 percent, respectively. As such, we can cross-multiply both:

18/100 = x/360

x = 65 degrees

25/100 = y/360

y = 90 degrees

Subtract: 90 – 65 = 25 degrees

Alternatively, we could first subtract the percentages (25 – 18 = 7), then convert the 7% to degree form via the same method of cross-multiplication.

### Example Question #12 : How To Evaluate A Fraction

6 contestants have an equal chance of winning a game.  One contestant is disqualified, so now the 5 remaining contestants again have an equal chance of winning.  How much more likely is a contestant to win after the disqualification?

Explanation:

When there are 6 people playing, each contestant has a 1/6 chance of winning.  After the disqualification, the remaining contestants have a 1/5 chance of winning.

1/5 – 1/6 = 6/30 – 5/30 = 1/30.

### Example Question #14 : 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 #15 : 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 #17 : 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 #18 : How To Evaluate A Fraction

Solve:

Explanation:

In order to solve , identify the least common denominator, or LCD.  Multiply the uncommon denominators, and the LCD is 6.

Rewrite the equation.

Multiply by six on both sides of the equation to cancel the denominators.

### Example Question #19 : How To Evaluate A Fraction

Evaluate:

Explanation:

Find the least common denominator, or LCD of  is six.

Rewrite the equation with the correct denominator.

Multiply by six on both sides of the equation and solve for .

### Example Question #20 : How To Evaluate A Fraction

Solve the following: