6th Grade mixed operations made easy: Free printable worksheets

Mixed operations are problems that involve more than one arithmetic operation. For example, 3 + 4 x 5 is a mixed operation problem that involves addition and multiplication. Mixed operations are important for practice in 6^th Grade because they help students develop their number sense, mental math skills, and problem-solving abilities.

They also prepare students for more advanced math topics like fractions, decimals, percentages, algebra, and geometry. By practicing with Mathskills4kids 6^th Grade mixed operations made easy, students will be able to:

• Apply the order of operations (PEMDAS) correctly and consistently
• Simplify expressions with parentheses, brackets, and exponents
• Perform calculations with positive and negative numbers
• Estimate and check the reasonableness of their answers
• Communicate their mathematical thinking clearly and logically

Students will encounter four types of mixed operations in 6th grade: addition, subtraction, multiplication, and division. Each type has rules and strategies that students need to know and apply. Here are some examples of each type of mixed operation:

• Addition: Adding two or more numbers together. For example, 12 + 7 + 5 = 24.
• Subtraction: Taking away one number from another. For example, 20 - 8 - 4 = 8.
• Multiplication: Repeated addition of the same number. For example, 3 x 4 = 3 + 3 + 3 + 3 = 12.
• Division: Splitting a number into equal parts or groups. For example, 12 ÷ 3 = 4.

One of the best ways to practice and master mixed operations is to use worksheets. Worksheets are printable or digital sheets that contain a set of problems for students to solve. Worksheets can help students:

• Review and reinforce what they have learned in class
• Practice their skills independently and at their own pace
• Identify their strengths and weaknesses
• Monitor their progress and improvement
• Prepare for tests and quizzes

 

Worksheets for grade 6 mixed operations can be found online or in books. They can vary in difficulty, format, and content. Some worksheets may focus on one type of mixed operation, while others may include a mix of all four types. Some worksheets may provide hints or examples, while others may require students to figure out the problems independently. Some worksheets may have multiple-choice or fill-in-the-blank questions, while others may have open-ended or word problems.

To solve mixed operation problems, we must follow the order of operations, i.e., a set of rules that tells which operation to do first. The order of operations is:

• Parentheses: Do the calculations inside parentheses first.
• Exponents: Calculate the powers or roots next.
• Multiplication and Division: Do these operations from left to right.
• Addition and Subtraction: Do these operations from left to right.

 

Here are some examples of how to apply the order of operations to solve mixed operation problems.

Example 1: 3 x (4 + 5) - 6 ÷ 2

Solution:

• First, do the calculation inside the parentheses: 4 + 5 = 9
• Then, multiply by 3: 3 x 9 = 27
• Next, divide by 2: 6 ÷ 2 = 3
• Finally, subtract from 27: 27 - 3 = 24

The answer is 24.

 

Example 2: (2 x 3)² + (4 - 1)³

Solution:

• First, do the calculations inside the parentheses: 2 x 3 = 6 and 4 - 1 = 3
• Then, raise to the power of 2 and 3: 6² = 36 and 3³ = 27
• Finally, add them together: 36 + 27 = 63

The answer is 63.

To have an idea of what grade 6 mixed operation problems look like, here are some examples from Mathskills4kids.com:

Example 1: Simplify the expression: (8 - 2) x (5 + 3) ÷ (4 -1)

 

Solution:

Step 1: Apply the order of operations (PEMDAS): Parentheses first.

(8 - 2) x (5 + 3) ÷ (4 -1)

= (6) x (8) ÷ (3)

Step 2: Apply the order of operations (PEMDAS): Exponents next. There are no exponents in this expression.

(6) x (8) ÷ (3)

Step 3: Apply the order of operations (PEMDAS): Multiplication and division from left to right.

(6) x (8) ÷ (3)

= 48 ÷ 3

Step 4: Apply the order of operations (PEMDAS): Addition and subtraction from left to right. There are no addition or subtraction in this expression.

48 ÷ 3

= 16

Answer: 16

 

Example 2: Evaluate the expression: -3 x (-2) + 4 x (-1)

Solution:

Step 1: Apply the order of operations (PEMDAS): Parentheses first. There are no parentheses in this expression.

-3 x (-2) + 4 x (-1)

Step 2: Apply the order of operations (PEMDAS): Exponents next. There are no exponents in this expression.

-3 x (-2) + 4 x (-1)

Step 3: Apply the order of operations (PEMDAS): Multiplication and division from left to right.

-3 x (-2) + 4 x (-1)

= 6 + (-4)

Step 4: Apply the order of operations (PEMDAS): Addition and subtraction from left to right.

6 + (-4)

= 2

Answer: 2

Please, encourage your students to try these exercises to practice their skills in solving mixed operation problems. They can check their answers at the end of this article.

1. (5 + 7) x (8 - 3)
2. (9 - 4)² + (6 x 2)³
3. (12 ÷ 4) x (3 + 5) - (7 - 2)
4. (10 - 6) x (4 + 2)²
5. (8 x 3) ÷ (2 + 4) + (5 - 1)
6. (7 x 5) - (6 + 4)²
7. (9 + 3) ÷ (6 - 2) x (4² - 1)
8. (5 x 4)³ - (8 ÷ 2)²
9. (6 + 2) x (7 - 3) + (9 ÷ 3)²
10. (8 - 4)³ + (10 ÷ 2) x (5 +1)

Here are some tips to help 6^th graders master mixed operations.

• Review the order of operations and memorize it.
• Use parentheses to group the calculations that need to be done first.
• Use a calculator or a pencil and paper to check your work.
• Practice with different types of problems, such as word problems, fractions, decimals, and negative numbers.
• Challenge yourself with more complex problems that involve multiple steps and operations.