When analyzing the expression 5 + 2 × (3 + 4), what should be done first?

When analyzing the expression 5 + 2 × (3 + 4), what should be done first?

• A. Add 5 and 2
• B. Multiply 2 by 3
• C. Calculate the expression within parentheses
• D. Add all the numbers directly

Answer: (C)

The correct approach to analyzing the expression 5 + 2 × (3 + 4) starts with calculating the expression within the parentheses. According to the order of operations, often remembered by the acronym PEMDAS (Parentheses, Exponents, Multiplication and Division, Addition and Subtraction), any calculations inside parentheses should be performed first. In the expression, (3 + 4) is contained in parentheses, so it should be evaluated before any other operations. This evaluation yields 7. After calculating within the parentheses, the expression simplifies to 5 + 2 × 7. From there, multiplication and addition can be performed following the order of operations. Therefore, understanding that parentheses take priority in calculations determines why calculating the expression within parentheses is the correct first step in resolving the entire mathematical expression.

The correct approach to analyzing the expression 5 + 2 × (3 + 4) starts with calculating the expression within the parentheses. According to the order of operations, often remembered by the acronym PEMDAS (Parentheses, Exponents, Multiplication and Division, Addition and Subtraction), any calculations inside parentheses should be performed first.

In the expression, (3 + 4) is contained in parentheses, so it should be evaluated before any other operations. This evaluation yields 7. After calculating within the parentheses, the expression simplifies to 5 + 2 × 7. From there, multiplication and addition can be performed following the order of operations.

Therefore, understanding that parentheses take priority in calculations determines why calculating the expression within parentheses is the correct first step in resolving the entire mathematical expression.