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Subtraction is one of the four basic arithmetic operations in mathematics. It involves taking one number away from another. The number you are subtracting from is called the 'minuend,' and the number you are subtracting is called the 'subtrahend.' The result of the subtraction is known as the 'difference.'

In the given exercise, the phrase '45 decreased by 20' indicates that we need to perform subtraction. Here, 45 is the minuend, and 20 is the subtrahend. The goal is to find the difference between these two numbers.

Understanding the terms and the operation can make it easier to quickly identify what needs to be done in a problem. Remember, words like 'decreased by,' 'less,' and 'minus' suggest subtraction in a math problem.

A mathematical expression is a combination of numbers, symbols, and operators that represent a mathematical relationship or value. In simple terms, it’s like a math sentence that can be solved or simplified.

For the exercise, we translated the phrase '45 decreased by 20' into the mathematical expression: 45 - 20.

The translation of words into a mathematical expression follows a set of rules or conventions. For subtraction, keywords like 'decreased by' help us identify what operation to use and how to set up our expression. In this case, the phrase directly translates into the arithmetic operation of subtraction.

Knowing how to write a proper mathematical expression from a word problem is crucial. It ensures you have a clear and correct path to solving the problem. Practice turning word problems into expressions to get comfortable with the process.

Simplification refers to making a mathematical expression easier to understand or solve. This usually involves performing the operations indicated in the expression.

In our exercise, the mathematical expression was 45 - 20. To simplify, we perform the subtraction: 45 minus 20 equals 25.

Simplifying expressions is about breaking down the problem into smaller, manageable steps.

Here's a small checklist to simplify any mathematical expression:

• Identify the operators (like +, -, *, /)
• Perform the operations in the correct order (follow the rules like BODMAS/BIDMAS)
• Write down the simplified result (check for any further simplification)

By following these steps, you make the problem easier to handle and come to the correct solution methodically. Remember, simplification helps in understanding and solving complex expressions effectively.