Problem 59 - Beginning and Intermediate Algebra

Question

Find each difference. $$ -8-6 $$

Step-by-Step Solution

Answer

-14

Step 1: Interpret the Problem

Understand the expression \( -8 - 6 \). This means we are subtracting 6 from -8.

Step 2: Simplify the Expression

Subtracting a positive number from a negative number makes the result more negative. \( -8 - 6 \) is equivalent to \( -8 + (-6) \).

Step 3: Combine the Values

Combine \( -8 \) and \( -6 \): \( -8 + (-6) = -14 \).

Key Concepts

negative numbers

Negative numbers are numbers less than zero. We often see them with a minus sign (-) before the number. It's important to understand that negative numbers represent values below zero.
For example: -1, -5, and -10 are all negative numbers.
When you work with negative numbers, the rules can be a bit different than with positive numbers. Let's break it down:

• When you add a negative number, you move to the left on the number line.
• When you subtract a positive number from a negative number, you also move left.
• The further left you go, the 'more negative' the number becomes.

Understanding negative numbers is crucial when performing various types of integer operations, like the subtraction problem we started with.

integer operations

Integer operations involve basic math tasks like addition, subtraction, multiplication, and division, but with whole numbers (integers). Integers include both positive numbers, negative numbers, and zero.
Let's focus on subtraction of integers:

• Subtracting a positive number from a positive number is straightforward, for example: 10 - 4 = 6.
• Subtracting a positive number from a negative number makes the result more negative, like in our exercise: -8 - 6.
• To solve, convert the problem to adding a negative number: -8 - 6 is the same as -8 + (-6).

Performing these operations correctly is about recognizing how each move affects the number. As you keep practicing, these steps will become second nature.

simplifying expressions

Simplifying expressions means reducing them to their simplest form. This helps make it easier to see what is really going on in a math problem.
For our exercise, let's simplify:

• Start with the expression: -8 - 6.
• Understanding subtraction here, rewrite it as: -8 + (-6).
• Combine the two negative values: -8 and -6.
• When you add two negative numbers, the values combine to make a larger negative number: -8 + (-6) = -14.

By simplifying, you break down the problem and make it easier to solve. This practice is essential not just in solving homework problems but also in developing a better understanding of mathematical concepts.