# GMAT Math : Understanding fractions

## Example Questions

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### Example Question #1 : Understanding Fractions

If  and , which of the following is the smallest?

Explanation:

It can be solved by calculating all five answers:

The smallest is .

### Example Question #1 : Fractions

What is % of 18?

15

12

8

12

10

12

Explanation:

We need to convert this percentage into a fraction.  This is one of the conversions you should remember.

% = 0.666666 =

### Example Question #3 : Understanding Fractions

Which of the following is less than ?

Explanation:

It's easiest to convert the fractions into decimals.

Therefore, the correct answer is 0.25.

### Example Question #4 : Understanding Fractions

Given that  and , what is the range of possible values for ?

Explanation:

To get the smallest possible , subtract the greatest possible  from the smallest possible ; this is .

To get the greatest possible , subtract the smallest possible  from the greatest possible ; this is  .

### Example Question #5 : Understanding Fractions

If  and , then evaluate .

It cannot be determined from the information given.

It cannot be determined from the information given.

Explanation:

Either  or

But without further information, it is impossible to tell which is true. Therefore, the correct choice is that it cannot be determined from the information given.

### Example Question #6 : Understanding Fractions

Galactic Bounty Hunters, Inc has two departments: Trainees and Veterans.  If on an average week, the each member of the Trainee department arrests  as many criminals as each member of the Veteran department, but the Veteran department has  as many members as the Trainee department, what fraction of the arrests were made by the members of the Veteran department?

Explanation:

What we want to do is pick numbers for the number of arrests made during the week and for the number of members in each department.

Let's take the number of arrests first.  Let's say each Trainee arrests 3 criminals.  Then, since the Trainees make 3/5 the number of arrests the Veterans make, we have:

So, each Veteran would arrest 5 criminals.

Next, we know that there are 1/3 as many Veterans as Trainees.  There if we have 3 Trainees, then we have 1 Veteran.

Using this information we can create the following equation for total arrests made by each department:

Where  is the number of Trainee arrests times the number of Trainees and  is the number of Veteran arrests times the number of Veterans

We're almost done.  Since we have 3 Trainees, and each arrests 3 criminals, the total number of Trainee arrests is 9.

Since we have 1 Veteran, and each arrests 5 criminals, the total number of Veteran arrests is 5.

The total number of arrests is

The fraction of the arrests made by the Veterans is:

### Example Question #7 : Understanding Fractions

Find the result and simplify the following expression:

Explanation:

We start by simplifying the denominators:

and

We know that:

Then we put both fractions to the same denominator, and don't forget to simplify the fraction:

### Example Question #8 : Understanding Fractions

Which of the following is false?

Explanation:

is false because is not displaying the correct way to add two fractions together. When adding fractions we must find a common denominator before adding the numerators.

For example, if , then the above expression would read

This we know is absurd!

### Example Question #9 : Understanding Fractions

What is the least common denominator of the following fractions?

Explanation:

The least common denominator (LCD) is the lowest common multiple of the denominators.

Multiples of 5: 5, 10, 15, 20, 25, 30, 35, 40, 45, 50

Multiples of 15: 15, 30, 45, 60, 75, 90,105,120, 135, 150

Multiples of 3: 3, 6, 9, 12, 15, 18, 21, 24, 27, 30

The least common denominator is 15.

### Example Question #151 : Algebra

What value must  take in order for the following expression to be greater than zero?

Explanation:

is such that:

Add  to each side of the inequality:

Multiply each side of the inequality by :

Multiply each side of the inequality by :

Divide each side of the inequality by :

You can now change the fraction on the right side of the inequality to decimal form.

The correct answer is , since k has to be less than  for the expression to be greater than zero.

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