Exercise: Foundational Math
Questions for: Arithmetical BODMAS
A manager is evaluating a sequence of financial adjustments and needs to determine the final value of a calculation.
Evaluate the following mathematical expression:
`20 - 5 + 18 / 3 * 2`
A: 3
B: 18
C: 22
D: 27
Answer: D
1. According to BODMAS/PEMDAS, perform Division and Multiplication from left to right.
First, calculate `18 / 3 = 6`.
The expression becomes: `20 - 5 + 6 * 2`
2. Next, calculate `6 * 2 = 12`.
The expression becomes: `20 - 5 + 12`
3. Perform Addition and Subtraction from left to right.
First, calculate `20 - 5 = 15`.
The expression becomes: `15 + 12`
4. Finally, calculate `15 + 12 = 27`.
Why others are wrong:
A — This result (3) occurs if addition is incorrectly performed before subtraction (`5 + 12 = 17`, then `20 - 17`), violating the left-to-right rule for Addition/Subtraction.
B — This result (18) occurs if multiplication is incorrectly performed before division (`3 * 2 = 6`, then `18 / 6`), violating the left-to-right rule for Division/Multiplication.
C — This result (22) occurs if all operations are performed strictly from left to right without adhering to the BODMAS hierarchy.
A student is evaluating an arithmetic expression following the standard order of operations.
What is the correct value of the expression: `48 / (6 + 2) * 3 - 5^2`?
A: 8
B: -23
C: 7
D: -7
Answer: D
1. **Brackets**: First, evaluate the expression inside the parentheses: `(6 + 2) = 8`.
The expression becomes: `48 / 8 * 3 - 5^2`.
2. **Orders (Exponents)**: Next, calculate the exponent: `5^2 = 25`.
The expression becomes: `48 / 8 * 3 - 25`.
3. **Division and Multiplication** (from left to right):
Perform division: `48 / 8 = 6`.
The expression becomes: `6 * 3 - 25`.
Perform multiplication: `6 * 3 = 18`.
The expression becomes: `18 - 25`.
4. **Subtraction**: Finally, perform the subtraction: `18 - 25 = -7`.
Why others are wrong:
A — This result (8) occurs if the exponent `5^2` is incorrectly calculated as `5 * 2 = 10`, leading to `18 - 10 = 8`.
B — This result (-23) occurs if multiplication `(8 * 3)` is performed before division `(48 / 8)` (violating the left-to-right rule for division and multiplication), leading to `48 / 24 - 25 = 2 - 25 = -23`.
C — This result (7) occurs if the final subtraction `18 - 25` is incorrectly performed as `25 - 18` (reversing the order or making a sign error), yielding a positive value instead of a negative one.
Discuss About this Question.
An individual is calculating the result of a mathematical expression involving several operations.
What is the value of the expression: `18 ÷ 3 + 4 × (7 - 2)`?
A: 26
B: 50
C: 32
D: 15
Answer: A
1. **B**rackets: First, evaluate the expression inside the brackets: `(7 - 2) = 5`.
The expression becomes: `18 ÷ 3 + 4 × 5`.
2. **D**ivision: Next, perform the division from left to right: `18 ÷ 3 = 6`.
The expression becomes: `6 + 4 × 5`.
3. **M**ultiplication: Then, perform the multiplication: `4 × 5 = 20`.
The expression becomes: `6 + 20`.
4. **A**ddition: Finally, perform the addition: `6 + 20 = 26`.
Why others are wrong:
B — Incorrectly performed addition (`6 + 4 = 10`) before multiplication (`10 × 5 = 50`), violating the BODMAS rule.
C — Failed to evaluate the expression inside the brackets first, effectively treating it as `18 ÷ 3 + 4 × 7 - 2`, leading to `6 + 28 - 2 = 32`.
D — Misinterpreted the multiplication operator as an addition operator, calculating `18 ÷ 3 + 4 + (7 - 2)` which equals `6 + 4 + 5 = 15`.
Discuss About this Question.
A technician is calculating the resistance in a complex circuit using the formula: `36 / (4 + 2) * 3 - 5` ohms.
What is the correct resistance value?
A: -12
B: -3
C: 13
D: 28
Answer: C
1. **Brackets (B):** First, calculate the operation inside the brackets: `4 + 2 = 6`.
2. The expression becomes: `36 / 6 * 3 - 5`.
3. **Division (D) and Multiplication (M):** Next, perform division and multiplication from left to right.
* Division: `36 / 6 = 6`.
* The expression becomes: `6 * 3 - 5`.
* Multiplication: `6 * 3 = 18`.
4. The expression becomes: `18 - 5`.
5. **Subtraction (S):** Finally, perform subtraction: `18 - 5 = 13`.
Why others are wrong:
A — This result (-12) occurs if subtraction is performed before multiplication and division from left to right, e.g., `6 * (3 - 5)`.
B — This result (-3) occurs if multiplication is performed before division when division appears first from left to right, e.g., `36 / (6 * 3)`.
D — This result (28) occurs if the brackets are misinterpreted or ignored, performing `(36 / 4) + 2` instead of `36 / (4 + 2)`.
Discuss About this Question.
To accurately solve mathematical expressions, the order of operations, often remembered by the acronym BODMAS/PEMDAS, must be followed strictly. Consider the following expression:
What is the value of `7 + 3 × (12 - 4) ÷ 2`?
A: 58
B: 40
C: 41
D: 19
Answer: D
1. Solve the operation inside the Brackets first: `(12 - 4) = 8`.
The expression becomes: `7 + 3 × 8 ÷ 2`.
2. Perform Multiplication and Division from left to right.
First, `3 × 8 = 24`.
The expression becomes: `7 + 24 ÷ 2`.
3. Next, `24 ÷ 2 = 12`.
The expression becomes: `7 + 12`.
4. Finally, perform the Addition: `7 + 12 = 19`.
Why others are wrong:
A — This result is obtained by performing operations from left to right without respecting BODMAS rules (e.g., `(7 + 3) × 12 - 4) ÷ 2`).
B — This result occurs if addition `(7+3)` is performed before multiplication and division, but brackets are correctly resolved: `(7 + 3) × (12 - 4) ÷ 2 = 10 × 8 ÷ 2 = 40`.
C — This result occurs if the brackets `(12-4)` are ignored, but the remaining BODMAS order (multiplication/division before addition/subtraction) is applied: `7 + (3 × 12) - (4 ÷ 2) = 7 + 36 - 2 = 43 - 2 = 41`.
Discuss About this Question.
Ad Slot (Above Pagination)
Discuss About this Question.