All SAT Math Resources
Example Questions
Example Question #1 : How To Evaluate A Fraction
Evaluate the following equation when and round your answer to the nearest hundredth.
1. Plug in wherever there is an in the above equation.
2. Perform the above operations.
Example Question #1 : How To Evaluate A Fraction
If then which of the following is equal to ?
To raise to the exponent , square and then take the cube root.
Example Question #3 : How To Evaluate A Fraction
Solve
no solution
0
infinitely many solutions
–1
infinitely many solutions
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 #2 : How To Evaluate A Fraction
Evaluate when x=11. Round to the nearest tenth.
1.9
0.2
0.3
1.8
1.8
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 #4 : How To Evaluate A Fraction
For this question, the following trigonometric identities apply:
,
Simplify:
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 #5 : How To Evaluate A Fraction
If 3x = 12, y/4 = 10, and 4z = 9, what is the value of (10xyz)/xy?
160
360
10
22 1/2
4 1/2
22 1/2
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 #6 : How To Evaluate A Fraction
If , , and , find the value of .
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 #3 : How To Evaluate A Fraction
If and , then which of the following is equal to ?
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 #5 : How To Evaluate A Fraction
Find the value of if and .
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:
Example Question #4 : How To Evaluate A Fraction
Factor out 7 from the numerator:
This simplifies to 7.