Order of Operations - ISEE Upper Level: Mathematics Achievement
Card 1 of 24
State the order of operations for evaluating expressions (use the standard PEMDAS order).
State the order of operations for evaluating expressions (use the standard PEMDAS order).
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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.
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.
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What does it mean to evaluate multiplication and division from left to right in an expression?
What does it mean to evaluate multiplication and division from left to right in an expression?
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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.
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.
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What is $8 - 3 \times 2$?
What is $8 - 3 \times 2$?
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$2$. Multiplication precedes subtraction, so compute $3 \times 2$ first, then subtract from 8.
$2$. Multiplication precedes subtraction, so compute $3 \times 2$ first, then subtract from 8.
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What is $(8 - 3) \times 2$?
What is $(8 - 3) \times 2$?
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$10$. Parentheses take precedence, so subtract inside first, then multiply by 2.
$10$. Parentheses take precedence, so subtract inside first, then multiply by 2.
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What is $18 \div 3 \times 2$?
What is $18 \div 3 \times 2$?
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$12$. Division and multiplication are performed left to right, so divide 18 by 3 first, then multiply by 2.
$12$. Division and multiplication are performed left to right, so divide 18 by 3 first, then multiply by 2.
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What is $18 \div (3 \times 2)$?
What is $18 \div (3 \times 2)$?
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$3$. Parentheses are evaluated first, computing $3 \times 2$ inside, then dividing 18 by the result.
$3$. Parentheses are evaluated first, computing $3 \times 2$ inside, then dividing 18 by the result.
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What is $2^3 + 1$?
What is $2^3 + 1$?
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$9$. Exponents precede addition, so compute $2^3$ first, then add 1.
$9$. Exponents precede addition, so compute $2^3$ first, then add 1.
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What is $-3^2$ (no parentheses around $-3$)?
What is $-3^2$ (no parentheses around $-3$)?
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$-9$. The negative sign applies after the exponent, so compute $3^2$ first, then negate it.
$-9$. The negative sign applies after the exponent, so compute $3^2$ first, then negate it.
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What is $(-3)^2$?
What is $(-3)^2$?
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$9$. Parentheses include the negative sign with the base, so square -3 directly.
$9$. Parentheses include the negative sign with the base, so square -3 directly.
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What is $4 + 2(3 + 1)$?
What is $4 + 2(3 + 1)$?
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$12$. Parentheses are evaluated first, then implied multiplication, followed by addition.
$12$. Parentheses are evaluated first, then implied multiplication, followed by addition.
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What is $6(2) - 3^2$?
What is $6(2) - 3^2$?
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$3$. Implied multiplication and exponent are computed before subtraction, with $3^2$ taking precedence over multiplication.
$3$. Implied multiplication and exponent are computed before subtraction, with $3^2$ taking precedence over multiplication.
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What is $24 \div 6 + 2 \times 5$?
What is $24 \div 6 + 2 \times 5$?
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$14$. Division and multiplication are performed left to right before addition, treating the expression as $(24 \div 6) + (2 \times 5)$.
$14$. Division and multiplication are performed left to right before addition, treating the expression as $(24 \div 6) + (2 \times 5)$.
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What is $24 \div (6 + 2) \times 5$?
What is $24 \div (6 + 2) \times 5$?
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$15$. Parentheses are evaluated first, then division and multiplication left to right.
$15$. Parentheses are evaluated first, then division and multiplication left to right.
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What is $\frac{1}{2} \times 8 + 3$?
What is $\frac{1}{2} \times 8 + 3$?
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$7$. Multiplication precedes addition, so compute $\frac{1}{2} \times 8$ first, then add 3.
$7$. Multiplication precedes addition, so compute $\frac{1}{2} \times 8$ first, then add 3.
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What is $8 \div \frac{1}{2} - 3$?
What is $8 \div \frac{1}{2} - 3$?
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$13$. Division precedes subtraction, so compute $8 \div \frac{1}{2}$ first, then subtract 3.
$13$. Division precedes subtraction, so compute $8 \div \frac{1}{2}$ first, then subtract 3.
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What is $\frac{3}{4} + \frac{1}{2}$?
What is $\frac{3}{4} + \frac{1}{2}$?
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$\frac{5}{4}$. Addition of fractions requires a common denominator, so convert $\frac{1}{2}$ to $\frac{2}{4}$ before adding.
$\frac{5}{4}$. Addition of fractions requires a common denominator, so convert $\frac{1}{2}$ to $\frac{2}{4}$ before adding.
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What is $\left(\frac{3}{4} + \frac{1}{2}\right) \times 4$?
What is $\left(\frac{3}{4} + \frac{1}{2}\right) \times 4$?
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$5$. Parentheses are evaluated first by adding the fractions, then multiplying the sum by 4.
$5$. Parentheses are evaluated first by adding the fractions, then multiplying the sum by 4.
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What is $2 + 3 \times (4 - 6)$?
What is $2 + 3 \times (4 - 6)$?
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$-4$. Parentheses are evaluated first, then multiplication before addition.
$-4$. Parentheses are evaluated first, then multiplication before addition.
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What is $5 - (2 - 7)$?
What is $5 - (2 - 7)$?
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$10$. Parentheses are evaluated first, and subtracting a negative is equivalent to addition.
$10$. Parentheses are evaluated first, and subtracting a negative is equivalent to addition.
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What is $3[2 + (5 - 1)]$?
What is $3[2 + (5 - 1)]$?
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$18$. Innermost parentheses are evaluated first, then brackets imply multiplication by 3.
$18$. Innermost parentheses are evaluated first, then brackets imply multiplication by 3.
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What is $7 - {3 + [2 \times (4 - 1)]}$?
What is $7 - {3 + [2 \times (4 - 1)]}$?
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$-2$. Innermost parentheses and brackets are evaluated step-by-step, starting with $(4-1)$, then multiplication, addition, and finally subtraction.
$-2$. Innermost parentheses and brackets are evaluated step-by-step, starting with $(4-1)$, then multiplication, addition, and finally subtraction.
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What is $\frac{2^3 \times 3}{4}$?
What is $\frac{2^3 \times 3}{4}$?
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$6$. Exponents precede multiplication, which precedes division, so compute $2^3$ first, then multiply by 3, and divide by 4.
$6$. Exponents precede multiplication, which precedes division, so compute $2^3$ first, then multiply by 3, and divide by 4.
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What is $\left(\frac{2}{3}\right)^2 \times 9$?
What is $\left(\frac{2}{3}\right)^2 \times 9$?
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$4$. Exponents are evaluated first inside parentheses, then multiplication by 9.
$4$. Exponents are evaluated first inside parentheses, then multiplication by 9.
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What does it mean to evaluate addition and subtraction from left to right in an expression?
What does it mean to evaluate addition and subtraction from left to right in an expression?
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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.
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.
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