Math worksheet for evaluating expressions with parentheses, brackets, and braces, designed for practice in order of operations.
Math worksheet titled "Evaluate Expressions With Parentheses, Brackets, & Braces" featuring six problems involving nested parentheses, brackets, and braces for students to solve.
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Show Answer Key & Explanations
Step-by-step solution for: Order of Operations Worksheets - Math Monks
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Show Answer Key & Explanations
Step-by-step solution for: Order of Operations Worksheets - Math Monks
To solve the given problems, we need to carefully evaluate each expression step by step, following the order of operations (PEMDAS/BODMAS: Parentheses/Brackets, Exponents/Orders, Multiplication and Division, Addition and Subtraction).
\[ 2\{2[24 + 4(23 - 14) - 25]\} \]
1. Solve the innermost parentheses:
\[ 23 - 14 = 9 \]
So the expression becomes:
\[ 2\{2[24 + 4 \cdot 9 - 25]\} \]
2. Perform the multiplication:
\[ 4 \cdot 9 = 36 \]
So the expression becomes:
\[ 2\{2[24 + 36 - 25]\} \]
3. Perform the addition and subtraction inside the brackets:
\[ 24 + 36 = 60 \]
\[ 60 - 25 = 35 \]
So the expression becomes:
\[ 2\{2[35]\} \]
4. Perform the multiplication inside the braces:
\[ 2 \cdot 35 = 70 \]
So the expression becomes:
\[ 2\{70\} \]
5. Perform the final multiplication:
\[ 2 \cdot 70 = 140 \]
Answer:
\[ \boxed{140} \]
---
\[ 2\{10[12 + 4(20 - 10) + 30]\} \]
1. Solve the innermost parentheses:
\[ 20 - 10 = 10 \]
So the expression becomes:
\[ 2\{10[12 + 4 \cdot 10 + 30]\} \]
2. Perform the multiplication:
\[ 4 \cdot 10 = 40 \]
So the expression becomes:
\[ 2\{10[12 + 40 + 30]\} \]
3. Perform the addition inside the brackets:
\[ 12 + 40 = 52 \]
\[ 52 + 30 = 82 \]
So the expression becomes:
\[ 2\{10[82]\} \]
4. Perform the multiplication inside the braces:
\[ 10 \cdot 82 = 820 \]
So the expression becomes:
\[ 2\{820\} \]
5. Perform the final multiplication:
\[ 2 \cdot 820 = 1640 \]
Answer:
\[ \boxed{1640} \]
---
\[ \{3 \times [(9 - 3)^2 - (21 - 19) \times 4]\} \div 2 \]
1. Solve the innermost parentheses:
\[ 9 - 3 = 6 \]
\[ 21 - 19 = 2 \]
So the expression becomes:
\[ \{3 \times [6^2 - 2 \times 4]\} \div 2 \]
2. Perform the exponentiation:
\[ 6^2 = 36 \]
So the expression becomes:
\[ \{3 \times [36 - 2 \times 4]\} \div 2 \]
3. Perform the multiplication:
\[ 2 \times 4 = 8 \]
So the expression becomes:
\[ \{3 \times [36 - 8]\} \div 2 \]
4. Perform the subtraction inside the brackets:
\[ 36 - 8 = 28 \]
So the expression becomes:
\[ \{3 \times 28\} \div 2 \]
5. Perform the multiplication inside the braces:
\[ 3 \times 28 = 84 \]
So the expression becomes:
\[ 84 \div 2 \]
6. Perform the division:
\[ 84 \div 2 = 42 \]
Answer:
\[ \boxed{42} \]
---
\[ 10\{3[25 - 6(22 - 19) + 11]\} \]
1. Solve the innermost parentheses:
\[ 22 - 19 = 3 \]
So the expression becomes:
\[ 10\{3[25 - 6 \cdot 3 + 11]\} \]
2. Perform the multiplication:
\[ 6 \cdot 3 = 18 \]
So the expression becomes:
\[ 10\{3[25 - 18 + 11]\} \]
3. Perform the addition and subtraction inside the brackets:
\[ 25 - 18 = 7 \]
\[ 7 + 11 = 18 \]
So the expression becomes:
\[ 10\{3[18]\} \]
4. Perform the multiplication inside the braces:
\[ 3 \cdot 18 = 54 \]
So the expression becomes:
\[ 10\{54\} \]
5. Perform the final multiplication:
\[ 10 \cdot 54 = 540 \]
Answer:
\[ \boxed{540} \]
---
\[ 2 \times \{76 - [(15 - 9)^2 - (5^2 - 3 \times 7)]\} \]
1. Solve the innermost parentheses:
\[ 15 - 9 = 6 \]
\[ 5^2 = 25 \]
\[ 3 \times 7 = 21 \]
So the expression becomes:
\[ 2 \times \{76 - [6^2 - (25 - 21)]\} \]
2. Perform the exponentiation:
\[ 6^2 = 36 \]
So the expression becomes:
\[ 2 \times \{76 - [36 - (25 - 21)]\} \]
3. Perform the subtraction inside the innermost brackets:
\[ 25 - 21 = 4 \]
So the expression becomes:
\[ 2 \times \{76 - [36 - 4]\} \]
4. Perform the subtraction inside the brackets:
\[ 36 - 4 = 32 \]
So the expression becomes:
\[ 2 \times \{76 - 32\} \]
5. Perform the subtraction inside the braces:
\[ 76 - 32 = 44 \]
So the expression becomes:
\[ 2 \times 44 \]
6. Perform the final multiplication:
\[ 2 \times 44 = 88 \]
Answer:
\[ \boxed{88} \]
---
\[ 11^2 - \{3 \times [8 - (5^2 - 19)]\} \]
1. Solve the innermost parentheses:
\[ 5^2 = 25 \]
So the expression becomes:
\[ 11^2 - \{3 \times [8 - (25 - 19)]\} \]
2. Perform the subtraction inside the innermost brackets:
\[ 25 - 19 = 6 \]
So the expression becomes:
\[ 11^2 - \{3 \times [8 - 6]\} \]
3. Perform the subtraction inside the brackets:
\[ 8 - 6 = 2 \]
So the expression becomes:
\[ 11^2 - \{3 \times 2\} \]
4. Perform the exponentiation:
\[ 11^2 = 121 \]
So the expression becomes:
\[ 121 - \{3 \times 2\} \]
5. Perform the multiplication inside the braces:
\[ 3 \times 2 = 6 \]
So the expression becomes:
\[ 121 - 6 \]
6. Perform the subtraction:
\[ 121 - 6 = 115 \]
Answer:
\[ \boxed{115} \]
---
1. \(\boxed{140}\)
2. \(\boxed{1640}\)
3. \(\boxed{42}\)
4. \(\boxed{540}\)
5. \(\boxed{88}\)
6. \(\boxed{115}\)
Problem 1:
\[ 2\{2[24 + 4(23 - 14) - 25]\} \]
1. Solve the innermost parentheses:
\[ 23 - 14 = 9 \]
So the expression becomes:
\[ 2\{2[24 + 4 \cdot 9 - 25]\} \]
2. Perform the multiplication:
\[ 4 \cdot 9 = 36 \]
So the expression becomes:
\[ 2\{2[24 + 36 - 25]\} \]
3. Perform the addition and subtraction inside the brackets:
\[ 24 + 36 = 60 \]
\[ 60 - 25 = 35 \]
So the expression becomes:
\[ 2\{2[35]\} \]
4. Perform the multiplication inside the braces:
\[ 2 \cdot 35 = 70 \]
So the expression becomes:
\[ 2\{70\} \]
5. Perform the final multiplication:
\[ 2 \cdot 70 = 140 \]
Answer:
\[ \boxed{140} \]
---
Problem 2:
\[ 2\{10[12 + 4(20 - 10) + 30]\} \]
1. Solve the innermost parentheses:
\[ 20 - 10 = 10 \]
So the expression becomes:
\[ 2\{10[12 + 4 \cdot 10 + 30]\} \]
2. Perform the multiplication:
\[ 4 \cdot 10 = 40 \]
So the expression becomes:
\[ 2\{10[12 + 40 + 30]\} \]
3. Perform the addition inside the brackets:
\[ 12 + 40 = 52 \]
\[ 52 + 30 = 82 \]
So the expression becomes:
\[ 2\{10[82]\} \]
4. Perform the multiplication inside the braces:
\[ 10 \cdot 82 = 820 \]
So the expression becomes:
\[ 2\{820\} \]
5. Perform the final multiplication:
\[ 2 \cdot 820 = 1640 \]
Answer:
\[ \boxed{1640} \]
---
Problem 3:
\[ \{3 \times [(9 - 3)^2 - (21 - 19) \times 4]\} \div 2 \]
1. Solve the innermost parentheses:
\[ 9 - 3 = 6 \]
\[ 21 - 19 = 2 \]
So the expression becomes:
\[ \{3 \times [6^2 - 2 \times 4]\} \div 2 \]
2. Perform the exponentiation:
\[ 6^2 = 36 \]
So the expression becomes:
\[ \{3 \times [36 - 2 \times 4]\} \div 2 \]
3. Perform the multiplication:
\[ 2 \times 4 = 8 \]
So the expression becomes:
\[ \{3 \times [36 - 8]\} \div 2 \]
4. Perform the subtraction inside the brackets:
\[ 36 - 8 = 28 \]
So the expression becomes:
\[ \{3 \times 28\} \div 2 \]
5. Perform the multiplication inside the braces:
\[ 3 \times 28 = 84 \]
So the expression becomes:
\[ 84 \div 2 \]
6. Perform the division:
\[ 84 \div 2 = 42 \]
Answer:
\[ \boxed{42} \]
---
Problem 4:
\[ 10\{3[25 - 6(22 - 19) + 11]\} \]
1. Solve the innermost parentheses:
\[ 22 - 19 = 3 \]
So the expression becomes:
\[ 10\{3[25 - 6 \cdot 3 + 11]\} \]
2. Perform the multiplication:
\[ 6 \cdot 3 = 18 \]
So the expression becomes:
\[ 10\{3[25 - 18 + 11]\} \]
3. Perform the addition and subtraction inside the brackets:
\[ 25 - 18 = 7 \]
\[ 7 + 11 = 18 \]
So the expression becomes:
\[ 10\{3[18]\} \]
4. Perform the multiplication inside the braces:
\[ 3 \cdot 18 = 54 \]
So the expression becomes:
\[ 10\{54\} \]
5. Perform the final multiplication:
\[ 10 \cdot 54 = 540 \]
Answer:
\[ \boxed{540} \]
---
Problem 5:
\[ 2 \times \{76 - [(15 - 9)^2 - (5^2 - 3 \times 7)]\} \]
1. Solve the innermost parentheses:
\[ 15 - 9 = 6 \]
\[ 5^2 = 25 \]
\[ 3 \times 7 = 21 \]
So the expression becomes:
\[ 2 \times \{76 - [6^2 - (25 - 21)]\} \]
2. Perform the exponentiation:
\[ 6^2 = 36 \]
So the expression becomes:
\[ 2 \times \{76 - [36 - (25 - 21)]\} \]
3. Perform the subtraction inside the innermost brackets:
\[ 25 - 21 = 4 \]
So the expression becomes:
\[ 2 \times \{76 - [36 - 4]\} \]
4. Perform the subtraction inside the brackets:
\[ 36 - 4 = 32 \]
So the expression becomes:
\[ 2 \times \{76 - 32\} \]
5. Perform the subtraction inside the braces:
\[ 76 - 32 = 44 \]
So the expression becomes:
\[ 2 \times 44 \]
6. Perform the final multiplication:
\[ 2 \times 44 = 88 \]
Answer:
\[ \boxed{88} \]
---
Problem 6:
\[ 11^2 - \{3 \times [8 - (5^2 - 19)]\} \]
1. Solve the innermost parentheses:
\[ 5^2 = 25 \]
So the expression becomes:
\[ 11^2 - \{3 \times [8 - (25 - 19)]\} \]
2. Perform the subtraction inside the innermost brackets:
\[ 25 - 19 = 6 \]
So the expression becomes:
\[ 11^2 - \{3 \times [8 - 6]\} \]
3. Perform the subtraction inside the brackets:
\[ 8 - 6 = 2 \]
So the expression becomes:
\[ 11^2 - \{3 \times 2\} \]
4. Perform the exponentiation:
\[ 11^2 = 121 \]
So the expression becomes:
\[ 121 - \{3 \times 2\} \]
5. Perform the multiplication inside the braces:
\[ 3 \times 2 = 6 \]
So the expression becomes:
\[ 121 - 6 \]
6. Perform the subtraction:
\[ 121 - 6 = 115 \]
Answer:
\[ \boxed{115} \]
---
Final Answers:
1. \(\boxed{140}\)
2. \(\boxed{1640}\)
3. \(\boxed{42}\)
4. \(\boxed{540}\)
5. \(\boxed{88}\)
6. \(\boxed{115}\)
Parent Tip: Review the logic above to help your child master the concept of order of operations with parentheses worksheet.
