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Simplifying expressions is an important skill in mathematics that involves reducing an expression to its simplest form. This process helps in understanding and interpreting mathematical expressions better. In this exercise, we have the expression \(8 - 18\). To simplify, we calculate the subtraction.

Simplification usually involves applying basic arithmetic operations - addition, subtraction, multiplication, and division - to make the expression easier to manage or solve.

• Identify the operation: Here it's subtraction.
• Perform the operation: Subtract 18 from 8, which gives us -10.

Any further steps depend on additional operations or terms in the expression, but in this example, once the subtraction is done, we reach the simplified form \(-10\). Simplifying expressions keeps calculations neat and helps in focusing on solving more complex equations easily.

Negative numbers are numbers with a value less than zero. They are usually represented with a minus sign (-) before them. Understanding how to work with negative numbers is essential, especially in subtraction operations as demonstrated in this exercise.

When you have an expression like \(8 - 18\), the result, \(-10\), is a negative number. This tells us that 18 is more than 8 by 10 units, and hence the outcome is negative.

• Significance of negative numbers: They help in representing values below zero, such as temperatures or debts.
• Operations involving negatives: When subtracting and the initial number is smaller, the outcome is negative. For instance, from \(8 - 18 = -10\).

Handling negative numbers properly is crucial for accurate calculations, ensuring you interpret mathematical expressions correctly.

Writing mathematical expressions correctly ensures that numerical problems are accurately conveyed and solved. This exercise asked us to write "8 decreased by 18," which translates to the expression \(8 - 18\).

To write expressions, remember these key steps:

• Identify the numbers involved: In this case, 8 and 18.
• Determine the operation: 'Decreased by' indicates subtraction.
• Write the expression: Arrange the numbers and operation as \(8 - 18\).

Being precise in expression writing is essential as it dictates the direction of solving the problem.
Creating correct expressions bridges the gap between a word problem and its numerical solution, forming the foundation of successful problem solving in mathematics.