Evaluate (-12)(0.5)+(-4(2+8))/-5

Solution:

Step 1: Simplify the expression.

Step 1.1

Combine $2$ and $8$ to get $10$. $\left(-12\right) \cdot 0.5 + \frac{-4 \cdot (2 + 8)}{-5}$

Step 1.2

Calculate $-4$ times $10$. $\left(-12\right) \cdot 0.5 + \frac{-4 \cdot 10}{-5}$

Step 2: Simplify each term.

Step 2.1

Compute $-12$ times $0.5$. $-6 + \frac{-40}{-5}$

Step 2.2

Divide $-40$ by $-5$. $-6 + 8$

Step 3: Combine the results.

Add $-6$ and $8$ together to get the final answer. $2$

Knowledge Notes:

The problem involves evaluating a mathematical expression that contains both addition and division of negative numbers. Here are the relevant knowledge points:

1. Order of Operations: When solving mathematical expressions, the order of operations must be followed. This is often remembered by the acronym PEMDAS, which stands for Parentheses, Exponents, Multiplication and Division (from left to right), and Addition and Subtraction (from left to right).

2. Negative Numbers: When multiplying or dividing two negative numbers, the result is positive. When adding a negative number to a positive number, you subtract the absolute value of the negative number from the positive number.

3. Multiplication and Division: These operations are performed from left to right. Multiplication is finding the product of two numbers, while division is the process of determining how many times one number is contained within another.

4. Addition: This is the process of combining two or more quantities to find their total.

5. Simplification: This involves performing all possible operations within an expression to reduce it to its simplest form or a single numerical value.

In the given problem, we first simplify the expression inside the parentheses $(2+8)$, then perform the multiplication and division operations, and finally, we add the results to get the final answer. The use of Latex in rendering mathematical expressions ensures clarity and precision in the presentation of the solution.