Order Of Operations Worksheets With Answers PDF
Order Of Operations Worksheets With Answers PDF provide users with structured practice at three difficulty levels, enabling them to master mathematical operations and enhance their problem-solving skills effectively.
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Order Of Operations Worksheets With Answers PDF – Easy Difficulty
Order Of Operations Worksheets With Answers PDF
Objective: To practice the order of operations using various exercise styles including multiple choice, fill in the blanks, word problems, and true or false.
Instructions: Solve the problems using the order of operations (Parentheses, Exponents, Multiplication and Division (from left to right), Addition and Subtraction (from left to right)). Show your work for full credit.
1. Multiple Choice
Choose the correct answer for each problem.
1. 5 + 3 × 2 – 4 = ?
a) 6
b) 10
c) 8
d) 12
2. 12 ÷ (2 + 4) + 3 = ?
a) 4
b) 5
c) 6
d) 2
3. (8 – 3) × 2 + 6 = ?
a) 10
b) 14
c) 12
d) 18
2. Fill in the Blanks
Complete the equations using the correct numbers or operations.
1. 9 + __ × 3 = 24
2. (7 – __) × 2 = 10
3. __ + 8 ÷ 4 = 3
3. True or False
Determine whether the statement is true or false.
1. 6 + (2 × 3) = 12
True / False
2. 4 × (5 + 1) – 3 = 21
True / False
3. (10 – 2) ÷ 4 + 1 = 3
True / False
4. Word Problems
Read the problems carefully and use the order of operations to find the solution.
1. Sarah has 4 bags of apples. Each bag contains 6 apples. She gives away 8 apples. How many apples does she have left?
2. Tom is making a batch of cookies. He uses 2 cups of flour for each batch and decides to make 3 batches. He then adds 4 cups of sugar. How many cups of ingredients did he use in total?
3. A gardener plants 5 rows of flowers, with each row containing 8 flowers. If 10 flowers bloom, how many flowers are left?
5. Mixed Operations
Solve the following expressions, showing your work.
1. 15 – 3 + 2 × (8 ÷ 4) = ?
2. (5 + 3) × (6 – 4) + 10 = ?
3. 9 × (3 + 5) – 4 = ?
Answers:
1.
1. c) 8
2. b) 5
3. b) 14
2.
1. 5
2. 5
3. 1
3.
1. True
2. True
3. False
4.
1. 4 × 6 – 8 = 24 – 8 = 16 (Sarah has 16 apples left)
2. 2 × 3 + 4 = 6 + 4 = 10 (Tom used 10 cups of ingredients total)
3. 5 × 8 – 10 = 40 – 10 = 30 (There are 30 flowers left)
5.
1. 15 – 3 + 2 × (8 ÷ 4) = 15 – 3 + 2 × 2 = 15 – 3 + 4 = 16
2. (5 + 3) × (6 – 4) + 10 = 8 × 2 + 10 = 16 + 10 = 26
3. 9 × (3 + 5) – 4
Order Of Operations Worksheets With Answers PDF – Medium Difficulty
Order of Operations Worksheets with Answers PDF
Objective: To practice the order of operations (PEMDAS/BODMAS) through a variety of exercises, reinforcing the correct sequence of operations needed to solve mathematical expressions.
Instructions: Solve the following exercises using the correct order of operations. Show your work for each exercise and provide the final answer.
Exercise 1: Order of Operations Problems
Evaluate the following expressions by following the order of operations (Parentheses, Exponents, Multiplication and Division from left to right, Addition and Subtraction from left to right).
1. 3 + 5 × (2 + 6)
2. (4 + 8) ÷ 2 – 3
3. 7 × (6 – 4) + 9
4. 10 + 2^3 × 5 – 3
5. (2 + 3) × (4 + 6 ÷ 2)
Exercise 2: True or False
Determine if the given equations are true or false after applying the order of operations.
1. 5 + 2 × 3 = 11
2. (8 – 3) × 2 + 1 = 11
3. 12 ÷ 4 + 6 × 2 = 18
4. 5 × 5 – 2^3 = 25 – 8
5. (10 ÷ 5) + (3 × 4) = 15
Exercise 3: Fill in the Blanks
Complete the equations below by providing the correct operation symbols (+, −, ×, ÷) to make the equation true. In parentheses, write the numbers that should be used to maintain the order of operations.
1. 2 (___) 3 (___) (4 + 6) = 20
2. 9 (___) (2 × 3) (___) 1 = 20
3. 5 (___) (6 ÷ 2) (___) 1 = 20
4. (12 – 4) (___) 2 (___) (2 × 1) = 12
5. (28 ÷ 7) (___) (3 + 1) (___) 4 = 12
Exercise 4: Word Problems
Use the order of operations to solve the following word problems.
1. A box contains 12 apples. You buy 6 more boxes, each containing 8 apples. After giving away 18 apples, how many apples do you have left?
2. You have $50. You spend $15 on lunch and double the remaining amount to buy a gift. What is the total amount you can spend?
3. A gardener plants 4 rows of flowers. In each row, he plants 7 flowers. After 6 flowers die, how many flowers are still growing?
4. A baker makes 30 cupcakes. He sells 5 of them each day for 3 days. How many remain after that period?
5. In a classroom, there are 24 students. If 3 groups of students go on a field trip and each group consists of 4 students, how many students are left in the classroom?
Answers to Exercises
Exercise 1:
1. 3 + 5 × 8 = 3 + 40 = 43
2. 12 ÷ 2 – 3 = 6 – 3 = 3
3. 7 × 2 + 9 = 14 + 9 = 23
4. 10 + 8 × 5 – 3 = 10 + 40 – 3 = 47
5. 5 × (4 + 3) = 5 × 7 = 35
Exercise 2:
1. True
2. True
3. False
Order Of Operations Worksheets With Answers PDF – Hard Difficulty
Order Of Operations Worksheets With Answers PDF
1. **Exercise 1: Solve the following expressions using the order of operations (PEMDAS/BODMAS). Show your work.**
a. 8 + 2 × 5 – 3
b. (6 + 4) ÷ 2 × (3 – 1)
c. 9 – 3 × (2 + 1) + 6 ÷ 2
d. 15 – (5 × 2) + 8 ÷ 4
e. (3 + 5) × (4 – 2) + 6
2. **Exercise 2: Fill in the blanks with the correct answers for the following expressions. Use parentheses where necessary.**
a. 7 + 3 × ___ = 16
b. (4 + ___) × 2 = 24
c. 12 ÷ (___ – 2) = 3
d. ___ × (5 – 3) + 9 = 15
e. (3 + ____) ÷ 2 = 6
3. **Exercise 3: Write a short paragraph explaining the order of operations and why it is important in mathematics. Include an example using a complex expression.**
4. **Exercise 4: Create 5 unique expressions that represent the order of operations correctly. Then, swap expressions with a partner to solve for each other’s problems.**
Example:
a. ___
b. ___
c. ___
d. ___
e. ___
5. **Exercise 5: Application Problems. Use the order of operations to solve these word problems.**
a. A gardener has 50 plants. He plants 12 more and then sells 13. If he decides to buy 9 more plants, how many does he have now?
b. A recipe requires 3 cups of flour. Each cup weighs 200 grams. If 2 cups are used for a batch of cookies and 1 cup is used for a cake, how much flour is remaining in grams?
6. **Exercise 6: Challenge yourself by solving these multi-step problems. Include all steps in your solution.**
a. (5 + 3) × (12 ÷ 4) – 7
b. 6 × (6 – 4) + (10 ÷ 2) × 2
c. (2 × 3) + (8 ÷ 4) × (10 – 5)
7. **Answers Section: Write down the answers for each problem and expression from Exercises 1-6. Be sure to check your work carefully.**
a.
b.
c.
d.
e.
Each exercise is designed to challenge your understanding of the order of operations. Refer back to the PEMDAS/BODMAS rules as needed, and ensure that you explain your thought process for each problem. Remember to practice good mathematical notation and clearly show all your work when you are solving problems.
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How to use Order Of Operations Worksheets With Answers PDF
Order Of Operations Worksheets With Answers PDF can be incredibly helpful in reinforcing mathematical concepts, but choosing the right one to match your knowledge level is crucial for effective learning. First, assess your current understanding of the order of operations—familiarize yourself with the acronym PEMDAS (Parentheses, Exponents, Multiplication and Division, Addition and Subtraction) to determine if you need basic practice or if advanced problems are more appropriate. Look for worksheets that categorize problems by difficulty; many resources provide tiered options, allowing you to start with simpler equations and gradually progress to more complex ones. As you tackle the topic, begin with a quick review of the rules, then choose a worksheet that starts slightly below your comfort zone to reinforce foundational skills before moving up. Make sure to work through the problems methodically; read each question carefully, apply the order of operations step-by-step, and use the answer key provided in the PDF to check your work, correcting any mistakes to solidify your understanding. Lastly, if you find certain types of problems particularly challenging, take notes or create additional practice sessions to build confidence and mastery in those areas.
Engaging with the Order Of Operations Worksheets With Answers PDF offers a multitude of benefits that can significantly enhance a learner’s mathematical understanding. Firstly, these worksheets provide a structured way to practice and master the order of operations, a foundational concept essential for solving complex mathematical problems. By completing the worksheets, individuals can assess their skill level through immediate feedback, as the included answers allow for self-evaluation and correction of misunderstandings. This iterative learning process not only reinforces knowledge but also builds confidence in tackling more advanced topics. Additionally, the worksheets cater to various difficulty levels, enabling learners to progressively challenge themselves and see measurable improvement over time. Ultimately, by dedicating time to these resources, students can solidify their math skills, cultivate a love for problem-solving, and prepare themselves for future academic success, making the Order Of Operations Worksheets With Answers PDF a vital tool in any educational arsenal.