Algebra I

Pre-Algebra Skills: Order Of Operations

Order Of Operations - PEMDAS

1) Simplify anything in Parentheses.

2) Simplify any Exponents.

3) Multiplication or Division (from left to right).

4) Addition or Subtraction (from left to right).

Using the order of operations, simplify:

1. 7-4+6

Using the order of operations (PEMDAS- Parenthesis, exponents, multiplication/division, addition/subtraction) what step do we take first in this problem?

We see that nothing is in parenthesis { ( ) }. There are no exponents ( x^2). There are no multiplication or division symbols (x or *, / ). There are, however, addition and subtraction symbols (+, -).

When using PEMDAS, we want to go in the order of the problem. Add or subtract from left to right. Since we see subtraction first, we will subtract.

So, in 7-4+6,  we will first do 7-4 which is 3. Now we are left with 3+6 which is 9.

2. 7-(4+6)

In this problem, we have parenthesis. So, we will start by simplifying whatever is in the parenthesis. (4+6) would simplify to 10. So now we are left with 7-10. There are no exponents, and nothing to add or divide, so we move on to subtracting. When we subtract 10 from 7, you should remember that we can always go below zero (0) and into our negative numbers. Now 7-10 will be -3. 

Because there is nothing left to simplify, -3 is our final answer.

3. 8/(4*2)

This problem might look tricky, but do not worry. Remember that / is our division symbol and * is our multiplication symbol. x also means to multiply, however we tend to use * more often in algebra and higher levels of math to solve the confusion of whether x means to multiply or if it is a variable.

So, look through the order of operations and find out what we have to do first.

We see the we have parenthesis. (4*2)=8. Now we will rewrite the problem with what we have left which is: 8/8. What is 8 divided by 8? 1.

Now try these problems by yourself:

4. 5^2+3(4+6*3)

5. (5-2^3)+8/4*3

Take your time with these problems, check your work for minor errors, and remember: you got this!!

Answers:

4. 91

5. 3

Didn't get the right answers? I'll review them and explain the process below.

5. 5^2+3(4+6*3)

In this problem we have parenthesis. So we will focus on the inside of that first. We will multiply 6*3 and get 18. (4+18) is 22. Now we have 5^2+3(22). Now we will focus on the exponent. 5^2=25. This is basically a simpler way of saying 5*5. So now we are left with 25+3(22). When a number is directly on the outside of a parenthesis, such as this problems 3(22) it means we multiply the two. So 3*22=66. Our problem is now 25+66 which will simplify to 91.

6. (5-2^3)+8/4*3

We have parenthesis, so we look at that portion of the problem first. There is an exponent inside, so first we solve -2^3 and we get -8. Now we have (5-8)+8/4*3. Next we subtract 8 from 5 and we get -3. Now our problem is -3+8/4*3. What do we do next? We simplify 8/4 and get 2. -3+2*3. Multiply. 2*3=6. Now we have -3+6. -3+6=3.

3 is our final answer.

Now solve these:

7. 7[(18-6)-6]

8. John is 15 years old. John's mom takes him and his younger sister to a football game. Tickets are $22 for adults and $16 for children (18 and under). What is the total cost of the tickets?

Take your time with these problems and use PEMDAS.

Answers:

7. 42

8. $54

That's all for this section! I hope this helped some! If you have any questions, comments, or concerns, please comment below and/or message me privately!