Understanding the Math Problem

The question asks us to find the value of a given mathematical expression. The expression involves several operations: multiplication, addition, subtraction, and squaring numbers. To solve this accurately, we need to follow the correct order of operations.

Step-by-Step Calculation Explained

To evaluate the expression \(62.5 \times 2 + 1100 - (16)^2 + (30)^2\), we must follow the order of operations, often remembered by acronyms like BODMAS or PEMDAS.

• B/P: Brackets/Parentheses first
• O/E: Orders/Exponents (like squares and cubes) next
• DM: Division and Multiplication (from left to right)
• AS: Addition and Subtraction (from left to right)

Let's break down the calculation step-by-step:

Step 1: Evaluate the terms within parentheses and exponents (Orders/Exponents).

We have two terms with exponents:

• \((16)^2 = 16 \times 16\). Let's calculate this.
• \((30)^2 = 30 \times 30\). Let's calculate this.

Calculation:

• \(16 \times 16 = 256\)
• \(30 \times 30 = 900\)

Now substitute these values back into the expression:

\(62.5 \times 2 + 1100 - 256 + 900\)

Step 2: Perform Multiplication.

Next, we look for multiplication in the expression:

• \(62.5 \times 2\)

Calculation:

• \(62.5 \times 2 = 125\)

Substitute this value back into the expression:

\(125 + 1100 - 256 + 900\)

Step 3: Perform Addition and Subtraction (from left to right).

Now we have only addition and subtraction remaining. We perform these operations from left to right.

• First, add 125 and 1100: \(125 + 1100 = 1225\)
• The expression is now: \(1225 - 256 + 900\)
• Next, subtract 256 from 1225: \(1225 - 256 = 969\)
• The expression is now: \(969 + 900\)
• Finally, add 900 to 969: \(969 + 900 = 1869\)

Final Result Calculation

Following the order of operations (BODMAS/PEMDAS), the step-by-step calculation is:

• Evaluate powers: \(16^2 = 256\), \(30^2 = 900\). The expression becomes \(62.5 \times 2 + 1100 - 256 + 900\).
• Evaluate multiplication: \(62.5 \times 2 = 125\). The expression becomes \(125 + 1100 - 256 + 900\).
• Perform addition/subtraction from left to right:
• \(125 + 1100 = 1225\)
• \(1225 - 256 = 969\)
• \(969 + 900 = 1869\)

The final value of the expression is 1869.

Revision Table: Key Mathematical Operations

Additional Information on Order of Operations

The order of operations is crucial in mathematics to ensure that everyone gets the same result when evaluating an expression. Without a standard order, the result could be ambiguous.

The acronyms BODMAS (Brackets, Orders, Division/Multiplication, Addition/Subtraction) and PEMDAS (Parentheses, Exponents, Multiplication/Division, Addition/Subtraction) help remember this order. Remember that Division and Multiplication have equal priority and should be done from left to right as they appear. Similarly, Addition and Subtraction have equal priority and are done from left to right.

In this problem, evaluating the squares \((16^2\) and \(30^2)\) before multiplication \((62.5 \times 2)\) is correct because exponents (Orders) come before Multiplication in the order of operations. Then, the addition and subtraction are performed from left to right.