Simplify each numerical expression....

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Key Concepts

Finding Common Denominators

When adding or subtracting fractions, it is necessary to convert them to equivalent fractions with the same denominator. This step simplifies the process by allowing the direct addition or subtraction of the numerators while maintaining the common denominator.

Handling Negative Numbers

Working with negative numbers in expressions is crucial, as it affects the direction and magnitude of the result. This concept involves correctly applying the negative sign during operations, especially when subtracting or adding negative fractions, to avoid errors in the final simplified expression.

Order of Operations

This concept dictates the sequence in which parts of an arithmetic expression should be evaluated. When working with expressions involving multiple operations such as parentheses, addition, and subtraction, it is essential to perform the calculations inside the parentheses first before handling the operations outside.

Fraction Arithmetic

Understanding fraction arithmetic is central to manipulating and simplifying expressions involving fractions. This includes adding, subtracting, multiplying, and dividing fractions, which often requires aligning the fractions by finding a common denominator.

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