ISEE Lower Level Mathematics Achievement Flashcards: Order Of Operations

What this deck covers

This deck focuses on Order Of Operations, giving you a quick way to review the definitions, rules, and examples that matter most for ISEE Lower Level Mathematics Achievement.

How to use these flashcards

Work through these flashcards in short sessions. Try to answer each prompt before flipping the card, then revisit any cards you miss until the explanation feels automatic.

Flashcard 1: What is the value of $\frac{1}{2} \times 12 + 3$?

Answer: $9$. Multiplication precedes addition: compute $\frac{1}{2} \times 12$ first, then add 3.

Flashcard 2: What is the value of $(36 \div 3)^2$?

Answer: $144$. Parentheses prioritize the division, then square the result.

Flashcard 3: What is the value of $36 \div 3^2$?

Answer: $4$. Exponents precede division: compute $3^2$ first, then divide 36 by that.

Flashcard 4: What is the value of $4 \times (2^3 - 5)$?

Answer: $12$. Parentheses require evaluating the exponent and subtraction inside first, then multiplying by 4.

Flashcard 5: What is the value of $6 + \frac{8}{4} \times 3$?

Answer: $12$. Division and multiplication precede addition and are done left to right: $\frac{8}{4} \times 3$, then add to 6.

Flashcard 6: What does it mean to evaluate $+$ and $-$ from left to right in an expression?

Answer: Do $+$ and $-$ in the order they appear, moving left to right. Addition and subtraction share precedence and are evaluated in sequence from left to right as they occur in the expression.

Flashcard 7: What is the correct order of operations for $+,-,\times,\div$, parentheses, and exponents?

Answer: Parentheses, exponents, multiply/divide left to right, add/subtract left to right. Follows the PEMDAS rule: parentheses first, then exponents, multiplication and division from left to right, and addition and subtraction from left to right.

Flashcard 8: What is the value of $3 + 4 \times 2$?

Answer: $11$. Multiplication precedes addition, so compute $4 \times 2$ first, then add 3.

Flashcard 9: What is the value of $4^3 \div 8$?

Answer: $8$. Exponents precede division: compute $4^3$ first, then divide by 8.

Flashcard 10: What is the value of $18 \div (3 \times 2)$?

Answer: $3$. Parentheses require multiplying inside first, then dividing 18 by that result.

Flashcard 11: What is the value of $24 \div 6 + 2 \times 3$?

Answer: $10$. Division and multiplication precede addition and are done left to right: $24 \div 6$ and $2 \times 3$, then add the results.

Flashcard 12: What is the value of $\frac{1}{2} \times (12 + 3)$?

Answer: $\frac{15}{2}$. Parentheses take priority: add inside first, then multiply by $\frac{1}{2}$.

Flashcard 13: What is the value of $10 - 2 \times (3 + 1)$?

Answer: $2$. Parentheses are evaluated first, then multiplication, followed by subtraction.

Flashcard 14: What is the value of $3 + 2[5 - (1 + 1)]$?

Answer: $9$. Innermost parentheses first, then brackets as implied multiplication, followed by addition.

Flashcard 15: What is the value of $2(7 + 3)$?

Answer: $20$. Parentheses are evaluated first, followed by the implied multiplication.

Flashcard 16: What is the value of $24 \div (6 + 2) \times 3$?

Answer: $9$. Parentheses are evaluated first, then division, followed by multiplication left to right.

Flashcard 17: What is the value of $(3 + 4) \times 2$?

Answer: $14$. Parentheses take priority, so add inside first, then multiply by 2.

Flashcard 18: What is the value of $10 - 2 \times 3 + 1$?

Answer: $5$. Multiplication precedes addition and subtraction: compute $2 \times 3$ first, then 10 minus that plus 1 left to right.

Flashcard 19: What is the value of $2 \cdot 7 + 3$?

Answer: $17$. Multiplication precedes addition, so compute $2 \cdot 7$ first, then add 3.

Flashcard 20: What does it mean to evaluate $\times$ and $\div$ from left to right in an expression?

Answer: Do $\times$ and $\div$ in the order they appear, moving left to right. Multiplication and division share precedence and are evaluated in sequence from left to right as they occur in the expression.

Flashcard 21: What is the value of $5^2 - 3 \times 4$?

Answer: $13$. Exponents precede multiplication and subtraction: compute $5^2$ first, then $3 \times 4$, and subtract from 25.

Flashcard 22: What is the value of $18 \div 3 \times 2$?

Answer: $12$. Division and multiplication are performed left to right: divide 18 by 3 first, then multiply by 2.

Flashcard 23: What is the value of $(5^2 - 3) \times 4$?

Answer: $88$. Parentheses prioritize the subtraction after the exponent, then multiply the result by 4.

Flashcard 24: What is the value of $(6 + \frac{8}{4}) \times 3$?

Answer: $24$. Parentheses prioritize the addition after division, then multiply the result by 3.

Flashcard 25: What is the value of $8 - 3^2 + 4$?

Answer: $3$. Exponents precede addition and subtraction: compute $3^2$ first, then perform 8 minus that plus 4 left to right.