Review of Mathematical Symbols

 

Symbols

 

x and are both used to express multiplication. So 3 x 4 = 12, and 2 3 = 6.

 

Inequality is expressed with the < less than or > greater than sign. Signs are sometimes combined; means greater than or equal to.

 

Absolute value is symbolized by vertical lines surrounding the value, such as a . This means that regardless of the sign of a, its absolute value is positive. -3 = 3.

 

The Greek capital sigma, S, is used to indicate a summation. S ai tells you to add all of the values in a set of as, a1 + a2 + a3 + a4 + ... where the number of a values is not specified.

 

Powers (Exponents)

 

kn is read is k to the n-th power. n is referred to as the exponent, while k is referred to as the base. kn means that you should multiply k by itself n times to get the answer. Squaring, or taking k to the second power, is the most familiar example. 32 = 9. If your calculator has an xy button, you can do the operation quickly. Enter the value of k, then hit the xy button, then enter the value of n, then hit the = button. If your calculator does not have the specialized button, you can still get the desired value by entering the value of k, then hitting the x (multiply) button. Then hit the = button n times.

When you multiply two values that have the same base, such as 32 x 33, you can save some arithmetic by adding the exponents the answer is equal to 35. When you multiply two values that have different bases, you need to find each power separately, then multiply the results. 23 x 33 = 4 x 27 = 108.

Any base to the 0th power, such as 30 or 5000, is equal to 1.

 

Factorial

 

The factorial operation is a shorthand way of expressing the product of a positive integer and all of the integers below it. Its symbol is an exclamation point. 5! = 5 x 4 x 3 x 2 x 1 = 120. 0! is special it is equal to 1.