Simplify $(3 \times 22) \div 6+[28-(4)^2]=?$
A) 32
B) 55
C) 46
D) 23
Answer (1)
Perform the multiplication: 3 × 22 = 66 .
Perform the division: 66 \tdiv 6 = 11 .
Calculate the exponent: ( 4 ) 2 = 16 .
Perform the subtraction and addition: 11 + ( 28 − 16 ) = 11 + 12 = 23 .
The simplified expression is 23 .
Explanation
Understanding the Problem We are asked to simplify the expression ( 3 × 22 ) \tdiv 6 + [ 28 − ( 4 ) 2 ] = ? . To do this, we will follow the order of operations (PEMDAS/BODMAS).
Multiplication First, we calculate the multiplication within the parentheses: 3 × 22 = 66 .
Division Next, we perform the division: 66 \tdiv 6 = 11 .
Exponent Now, we calculate the exponent: ( 4 ) 2 = 4 × 4 = 16 .
Subtraction Then, we perform the subtraction within the brackets: 28 − 16 = 12 .
Addition Finally, we add the results from the division and the subtraction: 11 + 12 = 23 .
Final Answer Therefore, the simplified expression is equal to 23.
Examples
Understanding order of operations is crucial in many real-life scenarios, such as calculating expenses or determining the outcome of a series of actions. For instance, if you're calculating the total cost of items with discounts and taxes, following the correct order ensures you get the accurate final amount. Imagine you buy 3 items costing $22 each, get a group discount reducing the total by a factor of 6, and then have to pay a fixed additional fee of $28 minus the square of $4 for shipping and handling. The expression we solved mirrors this situation, ensuring you calculate the correct final cost.
