Question

Evaluate the expression. \(-29.4-(-8)+4\)

Short answer

-17.4

Step-by-step solution

Simplify Negative of Negative

Simplify the part of the expression where there is a negative of a negative number. In this case, it is '-(-8)'. This can be simplified as '+8', since subtracting a negative number is the same as adding a positive number. So, the expression becomes -29.4 + 8 + 4.

Perform Addition

Now, add together the numbers. Start by adding -29.4 and 8. This gives you -21.4. Then add this result to 4, thus -21.4 + 4.

Final Result

Finally, perform the last addition to get the final result. The expression -21.4 + 4 equals -17.4.

Key concepts

Simplifying Expressions

When it comes to simplifying expressions, the goal is to make the expression as straightforward as possible. This often involves combining like terms, using the distributive property, or, as in our exercise, dealing with negatives in a strategic way. For instance, simplifying the negative of a negative, like in the expression \( -(-8) \), is a common step. As we see, this becomes \( +8 \), since two negatives make a positive.

In simplifying expressions that include multiple negative signs, it's important to pay close attention to the order of operations, also known as PEMDAS (Parentheses, Exponents, Multiplication and Division (from left to right), Addition and Subtraction (from left to right)). Remember that simplification is all about making an expression easier to understand and solve, which is vital for confidently tackling more complex algebraic problems.

Adding Negative Numbers

The concept of adding negative numbers can sometimes be counterintuitive. To simplify the process, think of each negative number as a debt and positive numbers as assets. When you 'add' a debt, you are actually increasing the amount you owe, thus going further into the negative. However, if you subtract a debt (which looks like adding a negative), you're effectively reducing the amount you owe, or moving into the positive territory.

For example, in the expression \( -29.4-(-8)+4 \) from our exercise, evaluating \( -(-8) \) is the same as subtracting a debt, which adds to our total (or in this case, reduces our overall 'debt'). Adding negative numbers requires careful attention to signs to avoid mistakes and reach the correct solution.

Arithmetic Operations

In essence, all of algebra rests on the foundation of basic arithmetic operations: addition, subtraction, multiplication, and division. Becoming proficient in these operations, especially when dealing with both positive and negative numbers, is essential for success in algebra.

When these operations are combined in expressions, it's crucial to follow the correct order of operations. For instance, our initial expression in the exercise not only involved adding a negative number, but also required that we add and subtract multiple numbers in sequence. We started with the most immediate operation (removing a negative sign) before smoothly moving on to the additions. By systematically performing each arithmetic operation with careful attention to signs and order, we arrived at the expression's final, simplified form. Remember, practice is key to mastering these operations and becoming adept at evaluating any algebraic expression you encounter.