Simplifying Mathematical Expressions: Step-by-Step Solution

To simplify a mathematical expression like the one given, we must follow the correct order of operations. This order is often remembered by acronyms like BODMAS or PEMDAS.

• B/P: Brackets or Parentheses
• O/E: Orders or Exponents (powers, square roots)
• DM: Division and Multiplication (from left to right)
• AS: Addition and Subtraction (from left to right)

The expression we need to simplify is:

\(166 \times 4 - 52 \times 5 + 232 \div 8 - 4800 \div 15\)

Let's break down the simplification process using the order of operations.

Step 1: Perform Division Operations

Following the BODMAS/PEMDAS rule, we first perform the division operations present in the expression, working from left to right.

• Calculate \(232 \div 8\):
• \(232 \div 8 = 29\)
• Calculate \(4800 \div 15\):
• \(4800 \div 15 = 320\)

Now, substitute these results back into the expression:

\(166 \times 4 - 52 \times 5 + 29 - 320\)

Step 2: Perform Multiplication Operations

Next, we perform the multiplication operations, again working from left to right.

• Calculate \(166 \times 4\):
• \(166 \times 4 = 664\)
• Calculate \(52 \times 5\):
• \(52 \times 5 = 260\)

Substitute these results back into the expression:

\(664 - 260 + 29 - 320\)

Step 3: Perform Addition and Subtraction Operations

Finally, we perform the addition and subtraction operations from left to right.

• Calculate \(664 - 260\):
• \(664 - 260 = 404\)
• Now add 29 to the result:
• \(404 + 29 = 433\)
• Finally, subtract 320:
• \(433 - 320 = 113\)

Final Result of Simplification

After performing all the operations in the correct order, the simplified value of the expression \(166 \times 4 - 52 \times 5 + 232 \div 8 - 4800 \div 15\) is 113.

Revision Table: Order of Operations Summary

Additional Information on Mathematical Simplification

Understanding the order of operations is crucial for accurately simplifying mathematical expressions. Without it, performing operations in a different order would likely lead to an incorrect result. The BODMAS/PEMDAS rule provides a standard approach to ensure consistency in calculations.

This rule applies to any mathematical expression, regardless of its complexity. It ensures that everyone simplifying the same expression arrives at the same unique answer.

Remember that multiplication and division have equal priority and should be performed from left to right as they appear. Similarly, addition and subtraction have equal priority and are also performed from left to right.