Simplifying Complex Arithmetic Expressions: A Comprehensive Guide

Mathematics can be daunting for many, but understanding the basics can make it much easier. This guide aims to dissect a complex arithmetic expression and simplify it step-by-step. We'll cover the key principles and provide multiple examples to ensure a thorough understanding.

Understanding the Expression: 57-[42-3 2]

Let's break down the expression: 57-[42-3 2]. This involves nested brackets and arithmetic operations. To simplify this expression, we must follow the order of operations (BODMAS/BIDMAS: Brackets, Orders, Division, Multiplication, Addition, Subtraction).

Step-by-Step Example 1

Expression: 57-[42-3 2]

Evaluate the innermost brackets first: 42-3 2 can be interpreted as 42-(3*2) due to the order of operations. 3*2 6, so the expression becomes 42-6. Calculate 42-6: 36. Now the initial expression is simplified to: 57-[36] Subtract the value in the brackets from 57: 57-36 21.

Step-by-Step Example 2

Expression: 57-[42-32]

Evaluate the innermost brackets first: 42-32 10. Now the expression is simplified to: 57-[10] Subtract: 57-10 47.

Step-by-Step Example 3

Expression: 57-[4×-12]

Evaluate the innermost brackets first: 4×-12 -48. The expression is now simplified to: 57-[-48] Subtract: 57-(-48) 57 48 105.

Step-by-Step Example 4

Expression: 57-[4-1 2]

Evaluate the innermost brackets first: 4-1 2 is interpreted as 4-(1*2) due to the order of operations. 1*2 2, so the expression becomes: 57-[4-2] Calculate 4-2 2. Now the expression is simplified to: 57-[2] Subtract: 57-2 55.

Final Example: Simplifying 57-[42-3 2] Using the Order of Operations

Expression: 57-[42-3 2]

Evaluate the innermost brackets: 42-3 2 can be interpreted as 42-(3*2). 3*2 6, so the expression becomes 42-6. Calculate: 42-6 36. Now the expression is simplified to: 57-[36] Subtract: 57-36 21.

In conclusion, the simplified value of the expression 57-[42-3 2] is 21 following the order of operations.

This comprehensive guide covers various approaches to simplify complex arithmetic expressions, emphasizing the importance of understanding and applying the order of operations (BODMAS/BIDMAS). If you have any questions or need further assistance, please feel free to reach out!