# SAT Math : How to evaluate a fraction

## Example Questions

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

Evaluate the following equation when  and round your answer to the nearest hundredth.

Explanation:

1. Plug in  wherever there is an  in the above equation.

2. Perform the above operations.

### Example Question #243 : Algebra

Mary walked to school at an average speed of 2 miles per hour and jogged back along the same route at an average speed of 6 miles per hour. If her total traveling time was 1 hour, what was the total number of miles in the round trip?

Explanation:

Since Mary traveled 3 times as quickly coming from school as she did going to school (6 miles per hour compared to 2 miles per hour), we know that Mary spent only a third of the time coming from school as she did going. If x represents the number of hours it took to get to school, then x/3 represents the number of hours it took her to return.

Knowing that the total trip took 1 hour, we have:

x/3 = 1

4x/3 = 1

= 3/4

So we know it took Mary 3/4 of an hour to travel to school (and the remaining 1/4 of an hour to get back).

Remembering that distance =  rate * time, the distance Mary traveled on her way to school was (2 miles per hour) * (3/4 of an hour) = 3/2 miles. Furthermore, since she took the same route coming back, she must have traveled 3/2 of a mile to return as well.

Therefore, the the total number of miles in Mary's round trip is 3/2 miles + 3/2 miles = 6/2 miles = 3 miles.

### Example Question #2 : How To Evaluate A Fraction

If then which of the following is equal to ?

Explanation:

To raise  to the exponent , square  and then take the cube root.

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

Solve

infinitely many solutions

no solution

0

–1

infinitely many solutions

Explanation:

The common denominator of the left side is x(x–1). Multiplying the top and bottom of 1/x by (x–1) yields

Since this statement is true, there are infinitely many solutions.

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

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

1.9

0.3

0.2

1.8

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 #861 : Algebra

For this question, the following trigonometric identities apply:

,

Simplify:

Explanation:

To begin a problem like this, you must first convert everything to  and  alone. This way, you can begin to cancel and combine to its most simplified form.

Since  and , we insert those identities into the equation as follows.

From here we combine the numerator and denominators of each fraction together to easily see what we can combine and cancel.

Since there is a  in the numerator and the denominator, we can cancel them as they divide to equal 1. All we have left is , the answer.

### Example Question #253 : Algebra

If 3x = 12, y/4 = 10, and 4z = 9, what is the value of (10xyz)/xy?

10

360

160

1/2

22 1/2

22 1/2

Explanation:

Solve for the variables, the plug into formula.

x = 12/3 = 4

y = 10 * 4 = 40

z= 9/4 = 2 1/4

10xyz = 3600

Xy = 160

3600/160 = 22 1/2

### Example Question #2 : How To Evaluate A Fraction

If  , , and , find the value of .

Explanation:

In order to solve , we must first find the values of , and  using the initial equations provided. Starting with :

Then:

Finally:

With the values of , and  in hand, we can solve the final equation:

### Example Question #862 : Algebra

If    and , then which of the following is equal to

Explanation:

In order to solve , first substitute the values of  and  provided in the problem:

Find the Least Common Multiple (LCM) of the fractional terms in the denominator and find the equivalent fractions with the same common denominator:

Finally, in order to divide by a fraction, we must multiply by the reciprocal of the fraction:

### Example Question #4 : How To Evaluate A Fraction

Find the value of  if  and .

Explanation:

In order to solve for , first substitute  into the equation for :

Then, find the Least Common Multiple (LCM) of the two fractions and generate equivalent fractions with the same denominator:

Finally, simplify the equation:

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