Problem 99 - Prealgebra and Introductory Algebra

Question

Subtract. $$-95-(-28)$$

Step-by-Step Solution

Answer

-67

Step 1: Identify the Double Negatives

In this problem, you have to deal with a double negative situation. In mathematics, when you have a double negative (subtracting a negative number), it is equivalent to addition.

Step 2: Simplify the Double Negatives Into an Addition Problem

When we simplify the double negatives (-95 - (-28)) it becomes (-95 + 28), because subtracting a negative number is equivalent to adding a positive number.

Step 3: Perform the Addition Operation

When you add -95 with +28, you get -67 because you are basically moving up 28 units from -95 on the number line.

Key Concepts

Understanding Double Negatives

When you see a subtraction of a negative number, like \(-(-28)\), it might seem a bit tricky at first. However, there's a simple rule to remember:

• A double negative, essentially, means a positive.
• Think of it as reversing a reversal.

So when the exercise shows \(-95 - (-28)\), the double negatives \(- -\) become a positive, changing the problem to \(-95 + 28\). This transformation makes it easier to work with as you then solve the two numbers as an addition problem.

Exploring Integer Operations

Integer operations involve the basic mathematical functions of adding, subtracting, multiplying, or dividing whole numbers which include negatives. Negative integers are below zero and behave differently than positive integers in operations:

• While switching directions is typical with double negatives, each integer operation keeps its own unique logic.
• Understanding how these work together is key to performing arithmetic with integers.

When adding or subtracting, it's crucial to pay mind to signs which deeply affect the resulting calculation outcome. Handling integer operations correctly sets the foundation for more complex math problems.

Mastering Addition and Subtraction of Integers

To master integer addition and subtraction, it helps to visualize them on a number line. Let's dissect the modified problem: \(-95 + 28\). Start at -95 and move to the right 28 units. Addition moves you up the number line, while subtraction moves you down:

• When adding, if both integers are negative, the sum is negative.
• If you add a positive number to a negative number like here, think of the positive number as moving up towards zero.
• The operation involves finding the difference between the numbers and determining the direction based on their signs.

The exercise simplifies to this conceptual approach bringing us to the result \(-67\). Using these strategies helps in understanding how the calculation flows smoothly.