## Parentheses, Brackets, and Braces in Math Expressions

#### Aligned To Common Core Standard:

**Grade 5 Operations** - 5.OA.1

What is the Purpose of Parentheses, Brackets, and Braces in Math Expressions -
When you are doing mathematics problems, you will come across many symbols that are important for solving these problems. Similar is the case for parentheses, brackets and braces; which are used many times in prealgebra and algebra. That is why it is necessary for you to understand what each of these symbols is used for.
**Parentheses ()** - Parentheses which are denoted by round brackets are used to group numbers, variables or both within a problem. It tells us the order of operations in a single operation. For example, take the problem 9 + (6 - 5) x 3, Normally, the problem will begin with the multiplication operation. However, here because of the parentheses, the subtraction will be solved first. Parentheses can also be used to multiply numbers. Like 2 x 5 can be also be written as (2)(5).
**Brackets []** - Brackets are also used for grouping variables and numbers together. Usually, in a single problem, parentheses are solved first and then brackets.
**Braces {}** - Braces are used just like brackets and parentheses, i.e. to group numbers and variables. However, braces are solved after the parentheses and the braces. Braces are also used in sets for discussing a set of elements.
Let us look at an example, 5 - {3[5 - 2(3-1)] ÷ 3}. We will now discuss the problem at every step.

5 - {3[5 - 2(3-1)] ÷ 3}, 5 - 3{[5-2(2)] ÷ 3} - Multiplying 2 and 2, 5 - {3[5 - 4]) ÷ 3} -Subtracting 4 from 5, 5 - {3(1) ÷ 3} = 5 - {3 ÷ 3} - Dividing 3 with 3 between the braces, 5 - 1 = 4. These worksheets and lessons will help you learn the different meanings and uses of parentheses, brackets, and braces in expressions.

### Printable Worksheets And Lessons

- Working with Parentheses Step-by-step Lesson- Here are two problems that we walk you through. One has a single parenthesis and then when hit you with a set of them to work with.
- Guided Lesson - Now, we break out all the funky brackets, and then we even ask you where you would like the brackets.
- Guided Lesson Explanation - I tried to flesh out the problems for you step by step. If I did a poor job, please hit me with an email.
- Practice Worksheet - Ten problems for you to sort through and complete.
- Matching Worksheet - Match the order of operations problems to their final answer.

#### Homework Sheets

These are designed to help remind students of the skill and provide them a great deal of practice. I made plenty.

- Homework 1 - Complete the following problems. Make sure to review your order of operations.
- Homework 2 - Breakdown the parentheses first. You will need to complete it through.
- Homework 3 - Exponents make there way in here. Note if exponent is inside or outside. It makes a big difference.
- Homework 4 - Division is pretty popular on this sheet.
- Homework 5 - For the most part, these are three step problems.
- Homework 6 - Folded brackets might be new to students.

#### Practice Worksheets

These problems are well spaced out to provide you with plenty of work room.

- Practice 1 - PEMDAS appears. It is spelled out for you on this worksheet.
- Practice 2 - If you see a bracket, that is where the problem begins.
- Practice 3 - If you have an exponent outside of a parentheses, you must perform the operation within the parentheses before applying the exponent.
- Practice 4 - Follow PEMDAS out in the bracket first.
- Practice 5 - Lots of room to work here. Note the outside operation that needs to take place.
- Practice 6- You will need the room for your vision while solving the problems.

#### Math Skill Quizzes

These are all in direct sync with the skills that students will see on any and all national exams.

- Quiz 1 - The first three are in bold Arial font for vision help.
- Quiz 2 - Note the position of the exponents within each exercise.
- Quiz 3 - In most cases you will need to focus bracket and break it down within the problem.
- Quiz 4 - Standard Arial font is used for integers here and on.
- Quiz 5 - The integers are much larger on this quiz, but not found in
**bold**. - Quiz 6 - These are the longest problems of all.