Problem 49 - Prealgebra

Question

Translate each of the following and simplify the result. Find the difference of \(-5\) and \(-1\)

Step-by-Step Solution

Answer

The difference of -5 and -1 is -4.

Step 1: Translate the Phrase into a Mathematical Expression

The phrase asks us to find the difference of two numbers. The ‘difference’ indicates we need to subtract. We are given the numbers -5 and -1. Therefore, the mathematical expression is \[-5 - (-1)\].

Step 2: Simplify the Expression

We have the expression \[-5 - (-1)\]. Remember that subtracting a negative is the same as adding the positive. Thus, this simplifies to \[-5 + 1\].

Step 3: Perform the Calculation

Now, we simply add the two numbers: \[-5 + 1 = -4\]. This is the result of the subtraction.

Key Concepts

Subtracting Negative Numbers

Understanding how to subtract negative numbers is key in many math problems. When we see a subtraction sign followed by a negative number, it can be initially confusing. But there's a helpful rule to remember:

• Subtracting a negative number is equivalent to adding its positive counterpart.

So, when you encounter an expression like \[-5 - (-1)\], it can be transformed by changing the subtraction of a negative number into an addition: \[-5 + 1\].
This simplification makes the calculation mere simple addition. Remembering this concept can save you time and make working with integers much more manageable.

Mathematical Expressions

A mathematical expression is a combination of numbers, variables, and operators (like addition, subtraction, etc.). In our given problem, we needed to translate a verbal phrase into a mathematical expression.
The phrase "find the difference of \(-5\) and \(-1\)" translates directly into \(-5 - (-1)\).
This step involves identifying the operation (in this case, subtraction) and the numbers involved. Expressions are fundamental in algebra and pre-algebra, serving as a bridge from words to calculations. Mastering their translation is essential for solving more complex problems.

Simplifying Expressions

Simplifying expressions involves reducing them to their simplest form while keeping their value unchanged. In our example, we started with \(-5 - (-1)\).
To simplify, we applied the rule of subtracting a negative number, which turned the expression into \(-5 + 1\).

• First, recognize common simplifications, such as subtraction of negatives turning into addition.
• Second, perform the calculation, which leads us to \(-4\) as the final result.

Understanding simplification helps in seeing patterns and making quick calculations, forming a foundation for future algebraic work.