Problem 88 - Algebra 1: Concepts and Skills

Question

Evaluate the expression. $$ 6-7 $$

Step-by-Step Solution

Answer

-1

Step 1: Subtract

\(6 - 7 = -1\)

Step 2: Verify

Starting at 6 on the number line and moving 7 units to the left gives \(-1\).

Key Concepts

Negative Numbers

Negative numbers are numbers that are less than zero. They are used to represent quantities that can have opposite directions or values, like debt or below zero temperatures. The most common way to denote a negative number is by placing a minus sign (-) in front of a number.
For instance, in the subtraction exercise you reviewed, the result was -1. This negative sign shows that the result is one unit less than zero.

• Negative numbers extend the number line to the left of zero.
• Every positive number has a negative counterpart.
• When comparing negative numbers, the one with the greater absolute value is actually smaller (e.g., -5 is less than -3).

Understanding these numbers is essential in many areas like finance, where they can represent losses or debts.

Integer Operations

Integer operations include addition, subtraction, multiplication, and division involving whole numbers, which may be positive or negative. Subtraction can often be treated as the addition of a negative number, making integer operations very interconnected.
For the example of the expression 6 - 7:

• Think of subtraction as an operation that finds the difference between two numbers.
• Subtracting 7 from 6 can be viewed as adding -7 to 6, giving a result of -1.

The rules for these operations with negative numbers include:

• Adding two negative numbers results in a negative number.
• Subtracting a negative number from a positive number is like adding the absolute value of the negative number.
• Multiplying or dividing two negative numbers results in a positive number.

These simple rules help in performing and understanding various arithmetic operations that involve both positive and negative integers.

Basic Arithmetic

Basic arithmetic is the foundation of mathematics involving the fundamental operations of addition, subtraction, multiplication, and division. These operations allow us to manipulate numbers to solve a variety of problems.
Subtraction, as seen in the exercise, is one of these core operations. It is the process of finding the difference between two numbers and can be visualized on a number line.
Let's summarize the key points about basic arithmetic with subtraction:

• The subtraction of one number from another is equivalent to adding its negative. For example, 6 - 7 is similar to 6 + (-7).
• Think of subtraction using the number line: start from the first number and move left by the amount of the second number.
• Ensure accuracy in arithmetic by following steps carefully and double-check your results.

Developing a strong grasp of arithmetic is crucial as it lays the groundwork for more advanced mathematical concepts and everyday problem-solving.