EXPRESSIONS WITH PARENTHESES

•  Whenever you see parentheses in a math problem, you are being asked to solve, you should immediately think, “Parentheses First.”  Parentheses always tell which operation to do first in a number expression. It is important to follow this mathematical rule, because you will get very different answers if you do not

• The placement of the parentheses can change the value of the expression,   so be careful when you are solving. Let’s look at an example. 10 – (4 -2). If you ignore the parentheses, you would just follow the problem from left to right and say that 10 – 4 is 6, and 6 – 2 is 4. However, by applying the parentheses rule you will instead subtract two from four as your first step. This will leave you with 10 – 2, which is 8, not 4.

• The parentheses rule is part of a larger set of math rules that mathematicians decided to use to help normalize the way people all over the world do math so that mathematicians would be using a common vocabulary when they communicate about math. The particular group of rules to which the parentheses rule belongs is called the Order of Operations rules. Some people use the acronym PEMDAS, or the phrase, “Please Excuse My Dear Aunt Sally” to help them remember the order of operations rules. Each letter stands for one action that can be taken on a math expression. The letters go in the order in which you should do each part. The P is for parentheses. We already know that operations in parentheses come first. Next is E for exponents. Exponents are numbers written smaller and up to the right of a regular number. They tell the number of times a number should be used to multiply by itself. Then comes M and D multiply and divide. Whichever one comes first from left to right is done next.  Finally, A and S are for add and subtract. Again, you will do whichever one comes first from left to right first.

• Let’s look at how the orders of operation are applied to this expression:  (4 -2) + 3 x 15 – 4 ÷ 2. Parentheses first, so 4-2 is 2. That leaves us with 2 + 3 x 15 – 4 ÷ 2. There are no exponents, so multiplication and division are next. That means 3 x 15 and 4 ÷ 2 come before any adding or subtracting.  3 x 15 is 45, and 4 ÷ 2 is 2. So now the expression is 2 + 45 – 2. Addition and subtraction are last from left to right, so 2 + 45 is 47, and 47 – 2 is 45.  So remember that when you see parentheses in your math problem, they are telling you where to start. Solve what is inside them, first. Then you can move on  to the other order of operation rules. Knowing where to start is the hard part!
  

Name:__________________________________

Answer the following questions based on the reading passage. Don’t forget to go back to the passage whenever necessary to find or confirm   your answers.

1) Why is it important for mathematicians to have certain mathematical rules that they all follow?

2) How do you know what to do first when you look at a math problem?

3) Should you do multiplication or addition first in a math   problem?

4)  Should you subtract or divide first in a math problem?

5)  Is using a memory tool like PEMDAS helpful for you?  Why or why not?