Math Help: PEMDAS

06/22/2015
The order of operations was developed by mathematicians long ago to make it easier to communicate their equations. If you do not follow the order of operations in solving a mathematical equation, and simply solve from left to right as you would read a text, you may arrive at an incorrect answer. PEMDAS (Parentheses, Exponents, Multiplication and Division, Addition and Subtraction) is a mnemonic device for remembering the order of operations in a mathematical equation so that you can avoid mistakes. Let’s walk through those steps using the following equation: 3^(4-2)x((4+6)/5)-1.

P=Parentheses

The first step in solving an equation is to always first complete the operations within parentheses, the P in PEMDAS. In our example equation, we see three sets within parentheses. The first, (4-2), is straightforward and becomes (4-2)=2. The second is a little more complicated because there are two sets of parentheses. If this is the case, go to the innermost set within the parentheses, in this case (4+6). Since 4+6=10, we then arrive at (10/5) which equals 2. After the first step, our equation looks like this: 3^2x2-1.

E=Exponents

The next letter in PEMDAS is E for exponents. Exponents tell how many times to use a number in a multiplication. If the exponent is 2, or squared, you should multiply the number by itself twice. If the exponent is 3, or cubed, the number should be multiplied by itself three times. After we have cleared up all the parentheses, we move on to exponents and square roots. We see one exponent in our equation: 3^2=9. Now our equation is as follows: 9x2-1.

MD=Multiplication and Division

The MD in PEMDAS go together because all multiplication and division are done in this third step as you come to it from left to right. In our equation, 9x2=18, so now we have 18-1.