Solving One-Step Equations

Lets take a look at the expression 2 + 8 6 2. John and Sarah both simplified the expression, but they got two different answers. Although their work is different, they are both convinced that they are correct.

Johns Work: Sarahs Work:2 + 8 6 2 2 + 8 6 210 6 2 2 + 8 3

4 2 10 3 2 7

Different AnswersHomePreviousNextTo avoid getting different answers when simplifying the same expression (like with John and Sarah), mathematicians have agreed on an order for doing operations. There are essentially 4 steps that we follow to simplify expressions.

Order of OperationsStep 1: Perform any operation(s) inside grouping symbols (grouping symbols include parentheses ( ), brackets [ ], or absolute value signs||). Note: If there are more than one set of grouping symbols, then start with the innermost set. Step 2: Simplify powers (get rid of the exponents).Step 3: Multiply and divide in order from left to right.Step 4: Add and Subtract in order from left to right. PreviousHomeNext

You Did It!Following the order of operations (PEMDAS), parentheses come first. That means that we need to start by looking at the expression inside of the parentheses (7 16). If we think of this as a new expression, we follow the steps following the parentheses (EMDAS). This means that we start by simplifying the power 7.Back to QuestionNext QuestionHomeQuestion 5What is the simplest form of the expression 40 2 3?

a.

b.

c.

2234228HomePrevious QuestionAdditional Resources and Tutorialshttp://www.wisc-online.com Instruction as well as practice problems are provided for extra helphttp://www.learnalberta.ca Test your knowledge of the steps that you need to follow to simplify an expressionhttp://www.funbrain.com For those that are up for a challenge, see if you can arrange these numbers to get the answer shown using the order of operationshttp://www.hippocampus.org Click on Algebra then, Number Operations and follow along with an interactive tutorial of the order of operationshttp://www.mathgoodies.com Read about and practice using the order of operations to simplify expressionshttp://www.free-training-tutorial.com Test your skills with several of these different games

HomeHelpful TipsA common technique for remembering the order of operations is to simplify each step to one word and use the abbreviation PEMDAS.

ParenthesesExponents Multiply DivideAddSubtract

You can remember PEMDAS by thinking of the phrase Please Excuse My Dear Aunt Sally.

Left to RightLeft to RightPreviousHomeNextOrder of OperationsGoing back to our original expression 2 + 8 6 2, lets use the order of operations to find out who (John or Sarah) found the correct answer.

Step 1: There are no parentheses or grouping symbols, so we skip this step and go on to the next. Step 2: There are no exponents, so we skip this step. Step 3: We now multiply/divide from left to right. This means that the first thing we need to do is 6 2, which gives us an answer of 3. So, when we re-write the expression, we replace 6 2 with 3 to get 2 + 8 3.Step 4: We now add/subtract from left to right. So, we are going to start by doing the computation 2 + 8, which gives us 10. If we re-write the expression we now have 10 3. When we subtract, we get a final answer of 7.

Since we ended up with a final answer of 7, Sarah was correct.

ParenthesesExponentsMultiply/DivideAdd/SubtractPreviousHomeOrder of OperationsExample 2:

Problem: 25 8 2 + 3

Solution: 25 8 2 + 9 25 16 + 9

9 + 9

18The simplest name for the numerical expression 25 8 2 + 3 is 18.

Parentheses: No parenthesesExponents: 3 = 33 = 9Multiply/Divide (Left to Right): 82 = 16Add/Subtract (Left to Right): First, 25 16 = 9 Then, 9 + 9 = 18

PreviousHomeNextOrder of OperationsExample 3:

Problem: 3 + |1 2|

Solution: 3 + 1 4

The simplest name for the numerical expression 3 + |1 2| is 4.

Parentheses: The absolute value signs are treated as grouping symbols, like parentheses. 1 2 = -1 and the absolute value of -1 is 1. Exponents: No exponentsMultiply/Divide (Left to Right): No multiplication or divisionAdd/Subtract (Left to Right): 3 + 1 = 4

PreviousHomeNextOrder of OperationsExample 4:

Problem: 6[13 2 (4 + 1)]

Solution: 6(13 2 5) 6 (13 10) 6 3

18The simplest name for the numerical expression 6[13 2 (4 + 1)] is 18.

Parentheses: There are two sets of grouping symbols, so we start with the innermost 4 + 1 = 5. Then, go to the second set of parentheses. Treat what is inside (13 2 5) like a new expression. To simplify, follow the remaining steps (EMDAS). Exponents: There are no exponents Multiply/Divide: 2 5 = 10. Add/Subtract: 13 10 = 3. We have taken care of what is in the parentheses and are left with the remaining expression 6 3. We can now move on to the step below.Exponents: No exponents in 6 3Multiply/Divide (Left to Right): 6 3 = 18Add/Subtract (Left to Right): No addition or subtraction

PreviousHomeNextOrder of OperationsExample 5:Problem: 9 + [4 (10 9)]

Solution: 9 + (4 1) 9 + (4 1) 9 + 3

9 + 27

36The simplest name for the numerical expression 9 + [4 (10 9)] is 36.

Parentheses: There are two sets of grouping symbols, so we start with the innermost 10 9 = 1. Then, go to the second set of parentheses. Treat what is inside (4 - 1) like a new expression. To simplify, follow the remaining steps (EMDAS). Exponents: 1 = 1 Multiply/Divide: No multiplication or division Add/Subtract: 4 1 = 3We have taken care of what is in the parentheses and are left with the remaining expression 9 + 3. We can now move on to the step below.Exponents: 3 = 3 3 3 = 9 3 = 27Multiply/Divide (Left to Right): No multiplication or divisionAdd/Subtract (Left to Right): 9 + 27 = 36

PreviousHome

Nice Work!Following the order of operations (PEMDAS), parentheses come first. Since we have two sets of parentheses, we simplify the expression in the innermost set first. That means that we would start with 7 + 4.Back to QuestionNext QuestionHome

Keep Trying!Remember, 3 is the same as 3 3Back to QuestionHome