Order of Operations Flashcards

Cheatsheet Content

### Flashcard 1 **Question:** Simplify $3 \times [ (10 - 4) \div 2 + 5 ]$ **Answer:** 1. Innermost Parentheses: $10 - 4 = 6$ 2. Division inside brackets: $6 \div 2 = 3$ 3. Addition inside brackets: $3 + 5 = 8$ 4. Multiplication: $3 \times 8 = 24$ **Result:** 24 ### Flashcard 2 **Question:** Simplify $\frac{4^2 + (5 \times 2 - 3)}{7}$ **Answer:** 1. Parentheses (multiplication): $5 \times 2 = 10$ 2. Parentheses (subtraction): $10 - 3 = 7$ 3. Exponents: $4^2 = 16$ 4. Numerator addition: $16 + 7 = 23$ 5. Division: $23 \div 7 \approx 3.2857$ (or leave as $\frac{23}{7}$) **Result:** $\frac{23}{7}$ ### Flashcard 3 **Question:** Simplify $2 \times \{ 15 - [ 3 \times (8 - 6) ] \} + 1$ **Answer:** 1. Innermost Parentheses: $8 - 6 = 2$ 2. Multiplication inside brackets: $3 \times 2 = 6$ 3. Subtraction inside braces: $15 - 6 = 9$ 4. Multiplication: $2 \times 9 = 18$ 5. Addition: $18 + 1 = 19$ **Result:** 19 ### Flashcard 4 **Question:** Simplify $( \sqrt{49} + 3^2 ) \div (10 - 2 \times 3)$ **Answer:** 1. First Parentheses (square root): $\sqrt{49} = 7$ 2. First Parentheses (exponent): $3^2 = 9$ 3. First Parentheses (addition): $7 + 9 = 16$ 4. Second Parentheses (multiplication): $2 \times 3 = 6$ 5. Second Parentheses (subtraction): $10 - 6 = 4$ 6. Division: $16 \div 4 = 4$ **Result:** 4 ### Flashcard 5 **Question:** Simplify $100 \div 5^2 \times (12 - 8) - 15$ **Answer:** 1. Exponents: $5^2 = 25$ 2. Parentheses: $12 - 8 = 4$ 3. Division: $100 \div 25 = 4$ 4. Multiplication: $4 \times 4 = 16$ 5. Subtraction: $16 - 15 = 1$ **Result:** 1 ### Flashcard 6 **Question:** Simplify $( -5 )^2 + 3 \times ( -2 )^3 - 10 \div 5$ **Answer:** 1. Exponent 1: $(-5)^2 = 25$ 2. Exponent 2: $(-2)^3 = -8$ 3. Multiplication: $3 \times (-8) = -24$ 4. Division: $10 \div 5 = 2$ 5. Addition/Subtraction (from left to right): $25 - 24 - 2 = 1 - 2 = -1$ **Result:** -1 ### Flashcard 7 **Question:** Simplify $1 - [ 2 + \{ 3 - ( 4 - 5 ) \} ]$ **Answer:** 1. Innermost Parentheses: $4 - 5 = -1$ 2. Subtraction inside braces: $3 - (-1) = 3 + 1 = 4$ 3. Addition inside brackets: $2 + 4 = 6$ 4. Subtraction: $1 - 6 = -5$ **Result:** -5 ### Flashcard 8 **Question:** Simplify $6 \times \frac{1}{2} - ( \frac{3}{4} + \frac{1}{4} )^2 + 7$ **Answer:** 1. Parentheses (addition): $\frac{3}{4} + \frac{1}{4} = \frac{4}{4} = 1$ 2. Exponent: $1^2 = 1$ 3. Multiplication: $6 \times \frac{1}{2} = 3$ 4. Subtraction: $3 - 1 = 2$ 5. Addition: $2 + 7 = 9$ **Result:** 9 ### Flashcard 9 **Question:** Simplify $ [ (18 \div 3) + 2 ]^2 \div \sqrt{64} - 5 $ **Answer:** 1. Innermost Parentheses (division): $18 \div 3 = 6$ 2. Addition inside brackets: $6 + 2 = 8$ 3. Exponent: $8^2 = 64$ 4. Square root: $\sqrt{64} = 8$ 5. Division: $64 \div 8 = 8$ 6. Subtraction: $8 - 5 = 3$ **Result:** 3 ### Flashcard 10 **Question:** Simplify $10 \times [ 4^2 - ( 20 - 2 \times 5 ) ] + 3$ **Answer:** 1. Innermost Parentheses (multiplication): $2 \times 5 = 10$ 2. Subtraction inside brackets: $20 - 10 = 10$ 3. Exponent: $4^2 = 16$ 4. Subtraction inside brackets: $16 - 10 = 6$ 5. Multiplication: $10 \times 6 = 60$ 6. Addition: $60 + 3 = 63$ **Result:** 63