Question

For Exercises \(1-74,\) simplify. $$-8 \div 2+4$$

Short answer

Answer: The simplified form of the given expression is 0.

Step-by-step solution

Perform the division

First, perform the division operation in the expression: $$-8 \div 2 = -4$$ So now, our simplified expression is: $$-4 + 4$$

Perform the addition

Finally, perform the addition operation in the simplified expression: $$-4 + 4 = 0$$ The simplified expression is 0.

Key concepts

Order of Operations

When solving math problems, especially in algebra, it's important to follow the order of operations. This ensures that you solve the problem correctly and systematically. The order of operations is often remembered by the acronym PEMDAS:

• Parentheses
• Exponents
• Multiplication and Division (from left to right)
• Addition and Subtraction (from left to right)

In this problem, there are two operations: division and addition. The order of operations tells us to perform division before addition, which is why we start by dividing \(-8 \div 2\). Remembering the correct order of operations is crucial for simplifying expressions accurately.

Division

Division is a way of breaking down a number into equal parts. In this exercise, we perform the division as the first operation according to the order of operations rules. When we divide \(-8\) by \(2\), we need to consider the sign. Since \(-8\) is negative and \(2\) is positive, dividing them gives a negative result:

• \(-8 \div 2 = -4\)

This step breaks down the numerator \(-8\) into equal parts, resulting in \(-4\). Being comfortable with division helps simplify expressions correctly.

Addition

After performing division, the next step is to do addition, as outlined in the order of operations. Addition combines numbers together. In our simplified expression, we have \(-4\) and \(4\). When you add a negative number to a positive number of the same magnitude, such as \(-4 + 4\), the numbers cancel each other out and result in zero:

• \(-4 + 4 = 0\)

Understanding addition, especially when dealing with negative numbers, helps transition smoothly from step to step when simplifying expressions.

Simplifying Expressions

Simplifying expressions is all about reducing them to their simplest form. This often makes calculations easier and helps you see the structure of a problem more clearly. In our exercise, we started with \(-8 \div 2 + 4\). With the help of the order of operations, dividing first and then adding, we reached the simplest form:

• Original: \(-8 \div 2 + 4\)
• Simplified: \(0\)

By understanding how to simplify expressions, you can solve math problems more efficiently and with greater accuracy. Simplification is a fundamental skill in prealgebra and lays the foundation for more advanced math concepts.