GRE Arithmetic - Number operations

The basic arithmetic number operations are Addition, Subtraction, Multiplication, and Division. You absolutely must be fully familiar with these concepts in order to do well on the math section of the GRE. In fact, you should be very good at these concepts, because even the easier math questions on the GRE require you to utilize one -- and often several -- of these number operations as you work towards the answer.

If two or more numbers are added, the result is called the Sum. If a number is subtracted from another number, the result is called the Difference. If two or more numbers are multiplied, the result is called the Product. If one number is divided by another, then the result is called the Quotient. A less-used term on the GRE is Reciprocal, and you can expect this term to appear on harder questions. Reciprocal means the 'inverse' of a number, which is formed by dividing 1 by that number.

For example, the reciprocal of 4 is 1 divided by 4, or 1/4. You need to be familiar with this terminology because on the GRE you will be asked to find the sum, product, quotient, etc., and you will need to know what operation to apply to arrive at the correct answer. To add the numbers of the same sign, just add the numbers and keep the same sign. To add numbers with unlike signs, take the absolute values of both numbers. Then, subtract the smaller number from the larger number, and then retain the sign of the number with the larger absolute value. For example:

-32 + 22
|-32| = 32 and |22| = 22
32-22 = 10
retain the minus to get -10

If you need to subtract positive and negative numbers, remember that the subtraction sign changes the sign of the number being subtracted, so just make the subtraction sign change and then use the rule to add numbers with unlike signs. If you want to multiply and divide positive and negative numbers, just do the usual multiplication or division, and then apply the rules in the following table.

The following table summarizes the resulting sign if you divide or multiply two numbers:

The sign of the two numbers being multiplied or divided The resulting sign
Both numbers are negative Positive
Both numbers are positive Positive
One number is negative, the other is positive Negative


Test Tip If you have an even amount of negative numbers, then the product of those numbers is positive. If you have an odd amount of negative numbers, then the product of those numbers is negative. This is an often-tested concept on the GRE, so be ready! For example,
(-1)(-2)(-5) = -10
(-1)(-2)(-5)(-2) = 20