Problem 61 - Prealgebra

Question

Find each difference. $$-10-(-8)$$

Step-by-Step Solution

Answer

The difference is -2.

Step 1: Identify the Expression

The expression to evaluate is given as \[-10 - (-8)\]. This involves a subtraction of a negative number.

Step 2: Apply Rule for Subtracting Negative Numbers

Remember that subtracting a negative number is the same as adding its opposite. Therefore, \[-10 - (-8)\] becomes \[-10 + 8\].

Step 3: Perform the Addition

Now perform the addition: \[-10 + 8 = -2\]. Here, you add 8 to -10, which moves you closer to zero on the number line but still leaves a negative result.

Key Concepts

Negative Numbers

In mathematics, negative numbers are numbers less than zero. They are represented with a minus sign (-) in front. Understanding negative numbers is crucial because they show things like temperature drops, debt, or below-sea-level elevations.
For example:

• -5 is five units less than 0. It could represent owing $5.
• -3 means three units less than zero. It might indicate a fall of 3 degrees in temperature from freezing point.

Negative numbers can appear in equations, especially in operations involving subtraction and addition. When dealing with them, it's essential to comprehend how they affect calculations. Specifically, when you subtract a negative number, it's equivalent to adding the positive of that number. This happens because two negations make a positive, much like in English when double negatives informally mean a positive.

Number Line

A number line is a visual tool used to represent numbers on a straight, horizontal line. It helps in understanding mathematical concepts, including addition and subtraction of integers.
The number line extends indefinitely in two directions:

• To the right are positive numbers: 1, 2, 3, ...
• To the left are negative numbers: -1, -2, -3, ...

Zero sits in the middle, acting as the dividing point between positive and negative numbers. When solving egin{equation} -10 - (-8) ewline begin{equation} using a number line, begin at -10 (10 units left of zero). Subtracting -8 translates to moving 8 steps to the right since double negatives imply addition. This visual representation helps to see how subtracting a negative number indeed moves you closer to positive numbers. On a number line, it simplifies the concept of "adding" when subtracting a negative number.

Addition of Integers

Adding integers involves combining two whole numbers, whether they're positive or negative. Understanding this concept helps in navigating more complex mathematics efficiently. With integers:

• Adding two positive numbers gives a larger positive number.
• Adding two negative numbers results in a larger negative number.
• Adding a positive and a negative number can yield either a positive or negative sum, depending on the sizes of the numbers involved.

In the exercise egin{equation} -10 + 8 ewline end{equation} we see how adding a positive integer (8) to a negative integer (-10) results in egin{equation}-2. ewline end{equation} It’s like moving right on the number line from -10, advancing 8 steps towards zero, yet remaining in negative territory. Mastering integer addition is key for tackling problems across math disciplines!