Order of Operations
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ISEE Upper Level: Mathematics Achievement › Order of Operations
A lab order is calculated; evaluate: $(14 + 10) \times(2^2) \div 4 - 3$.
21
24
33
93
Explanation
This question tests ISEE Upper Level Mathematics Achievement by evaluating expressions using the order of operations. The order of operations is a set of rules to determine which operations to perform first in a mathematical expression, typically remembered by PEMDAS: Parentheses, Exponents, Multiplication and Division (left-to-right), Addition and Subtraction (left-to-right). In the given expression $(14 + 10) \times(2^2) \div 4 - 3$, we first calculate within parentheses: $14 + 10 = 24$, then the exponent: $2^2 = 4$, multiply: $24 \times 4 = 96$, divide: $96 \div 4 = 24$, and finally subtract: $24 - 3 = 21$. The correct answer, A (21), results from applying these rules correctly, ensuring that each operation respects the hierarchy. A common mistake, such as choosing B (24), might occur if students forget to subtract the final 3 or misapply the order of operations. To help students master this skill, practice identifying the highest priority operations first and using the PEMDAS acronym to guide the sequence. Encourage students to double-check each step, especially when dealing with complex expressions, to avoid intermediate errors.
In a science experiment, evaluate the materials cost: $40 + (18 \div 3) \times 2^2 - 9$.
47
55
79
95
Explanation
This question tests ISEE Upper Level Mathematics Achievement by evaluating expressions using the order of operations. The order of operations is a set of rules to determine which operations to perform first in a mathematical expression, typically remembered by PEMDAS: Parentheses, Exponents, Multiplication and Division (left-to-right), Addition and Subtraction (left-to-right). In the given expression $40 + (18 \div 3) \times 2^2 - 9$, we first calculate within parentheses: $18 \div 3 = 6$, then the exponent: $2^2 = 4$, multiply: $6 \times 4 = 24$, add: $40 + 24 = 64$, and finally subtract: $64 - 9 = 55$. The correct answer, B (55), results from applying these rules correctly, ensuring that each operation respects the hierarchy. A common mistake, such as choosing A (47), might occur if students perform operations out of order or make arithmetic errors. To help students master this skill, practice identifying the highest priority operations first and using the PEMDAS acronym to guide the sequence. Encourage students to double-check each step, especially when dealing with complex expressions, to avoid intermediate errors.
For a travel meal plan, evaluate: $(9 + 15) \div 3 + 2^3 \times 4 - 10$.
14
18
30
86
Explanation
This question tests ISEE Upper Level Mathematics Achievement by evaluating expressions using the order of operations. The order of operations is a set of rules to determine which operations to perform first in a mathematical expression, typically remembered by PEMDAS: Parentheses, Exponents, Multiplication and Division (left-to-right), Addition and Subtraction (left-to-right). In the given expression $(9 + 15) \div 3 + 2^3 \times 4 - 10$, we first calculate within parentheses: $9 + 15 = 24$, then the exponent: $2^3 = 8$, divide: $24 \div 3 = 8$, multiply: $8 \times 4 = 32$, add: $8 + 32 = 40$, and finally subtract: $40 - 10 = 30$. The correct answer, C (30), results from applying these rules correctly, ensuring that each operation respects the hierarchy. A common mistake, such as choosing B (18), might occur if students misapply the order of operations or make arithmetic errors. To help students master this skill, practice identifying the highest priority operations first and using the PEMDAS acronym to guide the sequence. Encourage students to double-check each step, especially when dealing with complex expressions, to avoid intermediate errors.
For a travel budget, evaluate: $(150 + 90) - 3^2 \times 10 + 48 \div 6$.
158
160
169
211
Explanation
This question tests ISEE Upper Level Mathematics Achievement by evaluating expressions using the order of operations. The order of operations is a set of rules to determine which operations to perform first in a mathematical expression, typically remembered by PEMDAS: Parentheses, Exponents, Multiplication and Division (left-to-right), Addition and Subtraction (left-to-right). In the given expression $(150 + 90) - 3^2 \times 10 + 48 \div 6$, we first calculate the parentheses: $150 + 90 = 240$, then the exponent: $3^2 = 9$, followed by multiplication and division from left to right: $9 \times 10 = 90$ and $48 \div 6 = 8$, giving us $240 - 90 + 8 = 158$. The correct answer, A (158), results from applying these rules correctly, ensuring that each operation respects the hierarchy. A common mistake, such as choosing B (160), might occur if students make arithmetic errors or misapply the order of operations, perhaps by adding before subtracting. To help students master this skill, practice identifying the highest priority operations first and using the PEMDAS acronym to guide the sequence. Encourage students to double-check each step, especially when dealing with complex expressions, to avoid intermediate errors.
A student totals shopping costs; evaluate: $(25 - 9) \times 3 + 2^4 \div 4$.
16
28
52
60
Explanation
This question tests ISEE Upper Level Mathematics Achievement by evaluating expressions using the order of operations. The order of operations is a set of rules to determine which operations to perform first in a mathematical expression, typically remembered by PEMDAS: Parentheses, Exponents, Multiplication and Division (left-to-right), Addition and Subtraction (left-to-right). In the given expression $(25 - 9) \times 3 + 2^4 \div 4$, we first calculate within parentheses: $25 - 9 = 16$, then the exponent: $2^4 = 16$, multiply: $16 \times 3 = 48$, divide: $16 \div 4 = 4$, and finally add: $48 + 4 = 52$. The correct answer, C (52), results from applying these rules correctly, ensuring that each operation respects the hierarchy. A common mistake, such as choosing B (28), might occur if students forget to add the final term or miscalculate the exponent. To help students master this skill, practice identifying the highest priority operations first and using the PEMDAS acronym to guide the sequence. Encourage students to double-check each step, especially when dealing with complex expressions, to avoid intermediate errors.
A student applies discount and tax; evaluate: $60 - (12 \times 2^2) + 30 \div 5$.
12
18
54
96
Explanation
This question tests ISEE Upper Level Mathematics Achievement by evaluating expressions using the order of operations. The order of operations is a set of rules to determine which operations to perform first in a mathematical expression, typically remembered by PEMDAS: Parentheses, Exponents, Multiplication and Division (left-to-right), Addition and Subtraction (left-to-right). In the given expression $60 - (12 \times 2^2) + 30 \div 5$, we first calculate the exponent: $2^2 = 4$, then multiply within parentheses: $12 \times 4 = 48$, divide: $30 \div 5 = 6$, subtract: $60 - 48 = 12$, and finally add: $12 + 6 = 18$. The correct answer, B (18), results from applying these rules correctly, ensuring that each operation respects the hierarchy. A common mistake, such as choosing A (12), might occur if students forget to add the final term or make calculation errors. To help students master this skill, practice identifying the highest priority operations first and using the PEMDAS acronym to guide the sequence. Encourage students to double-check each step, especially when dealing with complex expressions, to avoid intermediate errors.
A recipe is scaled; evaluate: $(6 \times 2^3 + 10) \div 2 - 7$.
22
27
34
41
Explanation
This question tests ISEE Upper Level Mathematics Achievement by evaluating expressions using the order of operations. The order of operations is a set of rules to determine which operations to perform first in a mathematical expression, typically remembered by PEMDAS: Parentheses, Exponents, Multiplication and Division (left-to-right), Addition and Subtraction (left-to-right). In the given expression $(6 \times 2^3 + 10) \div 2 - 7$, we first calculate the exponent: $2^3 = 8$, then multiply: $6 \times 8 = 48$, add within parentheses: $48 + 10 = 58$, divide: $58 \div 2 = 29$, and finally subtract: $29 - 7 = 22$. The correct answer, A (22), results from applying these rules correctly, ensuring that each operation respects the hierarchy. A common mistake, such as choosing B (27), might occur if students forget to subtract the final 7 or make calculation errors in intermediate steps. To help students master this skill, practice identifying the highest priority operations first and using the PEMDAS acronym to guide the sequence. Encourage students to double-check each step, especially when dealing with complex expressions, to avoid intermediate errors.