ISEE Upper 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 Upper 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 $18 \div (3 \times 2)$?

Answer: $3$. Parentheses are evaluated first, computing $3 \times 2$ inside, then dividing 18 by the result.

Flashcard 2: What is $-3^2$ (no parentheses around $-3$)?

Answer: $-9$. The negative sign applies after the exponent, so compute $3^2$ first, then negate it.

Flashcard 3: What is $7 - \{3 + [2 \times (4 - 1)]\}$?

Answer: $-2$. Innermost parentheses and brackets are evaluated step-by-step, starting with $(4-1)$, then multiplication, addition, and finally subtraction.

Flashcard 4: What is $(8 - 3) \times 2$?

Answer: $10$. Parentheses take precedence, so subtract inside first, then multiply by 2.

Flashcard 5: What is $\frac{3}{4} + \frac{1}{2}$?

Answer: $\frac{5}{4}$. Addition of fractions requires a common denominator, so convert $\frac{1}{2}$ to $\frac{2}{4}$ before adding.

Flashcard 6: State the order of operations for evaluating expressions (use the standard PEMDAS order).

Answer: Parentheses, Exponents, Multiply/Divide (L to R), Add/Subtract (L to R). This sequence follows the PEMDAS rule, ensuring operations are performed in the correct precedence to evaluate expressions accurately.

Flashcard 7: What is $24 \div (6 + 2) \times 5$?

Answer: $15$. Parentheses are evaluated first, then division and multiplication left to right.

Flashcard 8: What is $5 - (2 - 7)$?

Answer: $10$. Parentheses are evaluated first, and subtracting a negative is equivalent to addition.

Flashcard 9: What does it mean to evaluate addition and subtraction from left to right in an expression?

Answer: Compute $+$ and $-$ in the order they appear, left to right. Addition and subtraction share the same precedence level and are evaluated sequentially from left to right after multiplication and division.

Flashcard 10: What is $8 - 3 \times 2$?

Answer: $2$. Multiplication precedes subtraction, so compute $3 \times 2$ first, then subtract from 8.

Flashcard 11: What is $8 \div \frac{1}{2} - 3$?

Answer: $13$. Division precedes subtraction, so compute $8 \div \frac{1}{2}$ first, then subtract 3.

Flashcard 12: What is $18 \div 3 \times 2$?

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

Flashcard 13: What is $6(2) - 3^2$?

Answer: $3$. Implied multiplication and exponent are computed before subtraction, with $3^2$ taking precedence over multiplication.

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

Answer: $18$. Innermost parentheses are evaluated first, then brackets imply multiplication by 3.

Flashcard 15: What does it mean to evaluate multiplication and division from left to right in an expression?

Answer: Compute $\times$ and $\div$ in the order they appear, left to right. Multiplication and division share the same precedence level and are evaluated sequentially from left to right before addition and subtraction.

Flashcard 16: What is $2^3 + 1$?

Answer: $9$. Exponents precede addition, so compute $2^3$ first, then add 1.

Flashcard 17: What is $4 + 2(3 + 1)$?

Answer: $12$. Parentheses are evaluated first, then implied multiplication, followed by addition.

Flashcard 18: What is $\frac{2^3 \times 3}{4}$?

Answer: $6$. Exponents precede multiplication, which precedes division, so compute $2^3$ first, then multiply by 3, and divide by 4.

Flashcard 19: What is $(-3)^2$?

Answer: $9$. Parentheses include the negative sign with the base, so square -3 directly.

Flashcard 20: What is $\frac{1}{2} \times 8 + 3$?

Answer: $7$. Multiplication precedes addition, so compute $\frac{1}{2} \times 8$ first, then add 3.

Flashcard 21: What is $\left(\frac{2}{3}\right)^2 \times 9$?

Answer: $4$. Exponents are evaluated first inside parentheses, then multiplication by 9.

Flashcard 22: What is $24 \div 6 + 2 \times 5$?

Answer: $14$. Division and multiplication are performed left to right before addition, treating the expression as $(24 \div 6) + (2 \times 5)$.

Flashcard 23: What is $2 + 3 \times (4 - 6)$?

Answer: $-4$. Parentheses are evaluated first, then multiplication before addition.

Flashcard 24: What is $\left(\frac{3}{4} + \frac{1}{2}\right) \times 4$?

Answer: $5$. Parentheses are evaluated first by adding the fractions, then multiplying the sum by 4.