# GRE Arithmetic - Fractions

GRE math questions that measure your knowledge of fractions are generally straight forward. However, because many people have not done such "simple" math in many years, it turns out that such simple questions often morph into rather difficult ones.

In a fraction, x/y, the x is the numerator and the y is the denominator; the fraction x/y can also be defined as 'x divided by y.' Dividing both the numerator and denominator by the same number does not change the value of the fraction, and for any one fraction, there are many other equivalent fractions. For example, 2/3 is equivalent to 6/9, 1/9 is equivalent to 2/18, and 2/3445 is equivalent to 4/6890. To add or subtract fractions with the same denominator, simply add or subtract the numerator and keep the denominator.

For example, consider the following:

Solve 2/6 + 3/21

Here's how you should approach the problem:

- The two denominators are 6 and 21. Thus, the prime factors of 6 are 2 and 3, and the prime factors of 21 are 3 and 7, and so the unique denominators are 2, 3 and 7.
- Multiply the unique denominators to get the LCD, 42.
- Rewrite both fractions so that the denominator is the LCD, and so 2/6 = 14/42, and 3/21 = 6/42. All that we've done is rewrite both fractions so they have the same denominator, the LCD.
- Now, the addition of the two fractions is easy: 14/42 + 6/42 = 20/42.

A fraction can also be expressed as a **mixed number**, which combines an integer and a fraction. For example, 14/5 is equivalent to 5/5 + 5/5 + 4/5 = 1 + 1 + 4/5, which can be written as 2 and 4/5. You have to know how to quickly convert between mixed numbers and fractions, and vice-versa, because on the GRE you'll be presented with equations and numbers in both formats.