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Difficulty: MediumOrder of Operations

Arrange the following mathematical operations in the exact sequence they must be performed to correctly evaluate the expression below:

40−[2×(3+4)2]÷740 - [2 \times (3 + 4)^2] \div 7
  1. 1Add the numbers inside the innermost parentheses
  2. 2Apply the exponent of 2
  3. 3Multiply the squared result by 2
  4. 4Divide the value of the brackets by 7
  5. 5Subtract the quotient from 40

Answer

The correct sequence is: Add the numbers inside the innermost parentheses, apply the exponent of 2, multiply the squared result by 2, divide the value of the brackets by 7, and finally subtract the quotient from 40.
Evaluating the expression following the Order of Operations (PEMDAS) requires these steps in sequence:
1) Add (3 + 4) inside the parentheses.
2) Square that sum.
3) Multiply the squared value by 2 to clear the brackets.
4) Divide that result by 7.
5) Subtract the quotient from 40.

Step-by-Step Solution

1
Identify the innermost grouping symbols (parentheses) and perform the addition.
40−[2×(7)2]÷740 - [2 \times (7)^2] \div 7
Parentheses (P) are evaluated first in the order of operations.
2
Evaluate the exponent applied to the innermost group.
40−[2×49]÷740 - [2 \times 49] \div 7
Exponents (E) are evaluated immediately after parentheses.
3
Complete the operations inside the brackets by performing multiplication.
40−[98]÷740 - [98] \div 7
The brackets act as secondary grouping symbols and must be fully simplified to a single value.
4
Perform the division located outside the brackets.
40−1440 - 14
Between division and subtraction, division (D) always takes precedence.
5
Perform the final subtraction.
2626
Subtraction (S) is evaluated last.

Key Concept

Order of Operations (PEMDAS)
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Topics

Order of Operations

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