What does evaluate mean in math fractions

A variable is a letter, for example x, y or z, that represents an unspecified number.

$$6+x=12$$

To evaluate an algebraic expression, you have to substitute a number for each variable and perform the arithmetic operations. In the example above, the variable x is equal to 6 since 6 + 6 = 12.

If we know the value of our variables, we can replace the variables with their values and then evaluate the expression.

Example

Calculate the following expression for x=3 and z=2

$$6z+4x=\: ?$$

Solution: Replace x with 3 and z with 2 to evaluate the expression.

$$6z+4x=\: ?$$

$$6\cdot {\color{blue} 2}+ 4\cdot {\color{blue} 3}=?$$

$$\: \, 12+12=24$$

Video lesson

Evaluate the following expression for x = 2, y = 5 and z = 4

$$4x+(7-z)-6y$$

All GRE Math Resources

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

Correct answer:

Explanation:

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

2. Perform the above operations.

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?

Correct answer:

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 + x/3 = 1

3x/3 + 1x/3 = 1

4x/3 = 1

x  = 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.

If then which of the following is equal to ?

Correct answer:

Explanation:

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

Solve   

Possible Answers:

no solution

0

infinitely many solutions

–1

Correct answer:

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. 

Evaluate 

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.

For this question, the following trigonometric identities apply:

,

Simplify:

Correct answer:

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. 

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

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

If  , , and , find the value of .

Correct answer:

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:

If    and , then which of the following is equal to ? 

Correct answer:

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:

Find the value of  if  and .

Correct answer:

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:

All GRE Math Resources

What is evaluate in math example?

What do evaluate mean in math?

How do you evaluate a fraction in simplest form?