Fractions - GRE Quantitative Reasoning

To simplify a complex fraction, simply invert the denomenator and multiply by the numerator:

Multiplying the numerator by the reciprocal of the denominator for each term we get:

Since we have a common denominator we can now add these two terms.

Although you could look for the common denominator of the fraction as it has been written, it is probably easiest to rewrite the fraction in slightly simpler terms. Thus, recall that you can rewrite your fraction as:

Using the rule for dividing fractions, you can rewrite your expression as:

Then, you can multiply each set of fractions, getting:

This makes things very easy, for then your value is:

For this problem, begin by rewriting the complex fraction, using the rule for dividing fractions:

This is much easier to work on. Cancel out the s and the and the , this gives you:

, which is merely . Thus, your problem is:

The common denominator is , so you can rewrite this as:

Let us first get our value for the percentage of the first fraction. 20% of 2/7 is found by multiplying 2/7 by 2/10 (or, simplified, 1/5): (2/7) * (1/5) = (2/35)

Our addition is therefore (2/35) + (1/4). There are no common factors, so the least common denominator will be 35 * 4 or 140. Multiply the numerator and denominator of 2/35 by 4/4 and the numerator of 1/4 by 35/35.

This yields:

(8/140) + (35/140) = 43/140, which cannot be reduced.

Simplify expressions inside parentheses first: and

Now we have:

Add them by finding the common denominator (LCM of 4, 2, and 3 = 12) and then multiplying the top and bottom of each fraction by whichever factors are missing from this common denominator:

Start by looking at Quantity A. The common denominator for this expression is . To calculate this, you perform the following multiplications:

This is the same as:

, or

This is the same as Quantity B. They are equal!

Begin by converting both top and bottom into non-mixed fractions:

So now we have:

In order to divide, take the fraction on the bottom, flip it, and multiply it by the fraction up top:

Multiply straight across:

Now reduce the fraction. Both top and bottom are divisible by 9 (an easy way to tell this is to see that in the original fractions we are multiplying both 9 and 18 are divisible by 9), so reduce each side by a factor of 9:

The answer is .

It is best to figure out what each of the leaks are per hour. We can figure this out by adding together the two fractional rates of leaking. For the first leak, we can do this as follows:

This is the same as:

For the second leak, we use the same sort of procedure:

Thus, our two leaks combined are:

The common denominator for these is ; thus, we can solve:

Now, our equation can be set up:

, where is the time it will take for the cistern to be emptied.

Multiply by on both sides:

Solve for :

Divide by :

Begin by simplifying the left side of the equation. You can do this by multiplying the numerator of the fraction by the reciprocal of its denominator:

Now, we know that our equation is:

Multiply both sides by and you get:

Thus, by taking the square root of both sides, you get:

Among your answers, is the only one that matches these.

Let's make the two quantities look the same.

Quantity A: 120 miles / 5 gallons = 24 miles / gallon

Quantity B: 25 miles / gallon

Quantity B is greater.

In order to solve quantitative comparison problems, you must first deduce whether or not the problem is actually solvable. Since this consists of finding the solution to an -coordinate on a line where nothing too complicated occurs, it will be possible.

Thus, your next step is to solve the problem.

Since and , you can plug in the -value and solve for :

Plug in y:

Add 2 to both sides:

Divide by 3/4. To divide, first take the reciprocal of 3/4 (aka, flip it) to get 4/3, then multiply that by 5/3:

Make the improper fraction a mixed number:

Now that you have what x equals, you can compare it to Quantity B.

Since is bigger than 2, the answer is that Quantity A is greater

Remember that when you divide by a fraction, you multiply by the reciprocal of that fraction. Therefore, this division really is:

At this point, it is merely a matter of simplification and finishing the multiplication:

To begin with, most students find it easy to remember that...

From this, you can apply the rule of division of fractions. That is, multiply by the reciprocal:

Therefore,

Since nothing needs to be reduced, this is your answer.

One remote is defective for every 199 non-defective remotes.

First, compute the new number of philosophy books. This will be .

The ratio of philosophy books to history books is thus:

This can be reduced by dividing the numerator and the denominator by :

Therefore, the ratio is .

27 of the 72 cars are 4-wheel drive, we can write this as a proportion.

The proportion of the 4-wheel drive cars to the total number of vehicles.

Therefore, to find the proportion of 2-wheel drive cars is,

Therefore the ratio of 2-wheel drive:4-wheel drive vehicles is 5:3.

Begin by making your life easier: presume that there are papers on the desk. Immediately, we know that there are paper clips. Now, if there are papers, you know that there also must be greeting cards. Technically you figure this out by using the ratio:

By cross-multiplying you get:

Solving for , you clearly get .

(Many students will likely see this fact without doing the algebra, however. The numbers are rather simple.)

Now, this means that our desk has on it:

papers

paper clips

greeting cards

Therefore, you have total items. Based on this, your ratio of paper clips to total items is:

, which is the same as .

To begin, you need to do a simple addition to find the total number of flowers in the garden:

Now, the ratio of petunias to the total number of flowers in the garden can be represented by a simple division of the number of petunias by . This is:

Next, reduce the fraction by dividing out the common from the numerator and the denominator:

This is the same as .

To begin, you need to calculate how many students are taking Old Norse. This is:

Now, the ratio of students taking Old Norse to students taking Greek is the same thing as the fraction of students taking Old Norse to students taking Greek, or:

Next, just reduce this fraction to its lowest terms by dividing the numerator and denominator by their common factor of :

This is the same as .