How to evaluate a fraction - GRE Quantitative Reasoning

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.

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

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

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

4_x_/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.

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.

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.

To raise $\frac{1}{8}$ to the exponent $\frac{2}{3}$, square $\frac{1}{8}$ and then take the cube root.

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 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:

Factor out 7 from the numerator: $$\frac{7(7^{11}$$$-7^{9}$$)}{7^{11}$$-7^{9}$}

This simplifies to 7.

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:

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:

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:

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

2. Perform the above operations.

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:

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:

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 :

Begin by pulling out like factors in the numerator:

Now rewrite the denominator, since it is a difference of squares:

Cancelling like terms in the numerator and denominator leaves:

To reduce this fraction we need to factor the numerator and find like terms in the denominator to cancel out.

The fraction

can be rewritten as

by factoring.

From here cancel like terms in the numerator and denominator: