Problem 25 - Algebra 1: Concepts and Skills

Question

Find the difference. $$ -2.2-(-1) $$

Step-by-Step Solution

Answer

-1.2

Step 1: Analyze the Problem

The problem is asking to find the difference between two numbers, -2.2 and -1. Both numbers are negative. The operation to be applied is subtraction, and additionally, the problem contains a double negative situation here which should be treated as a positive. Therefore, the basic arithmetic operation turns into \( -2.2 + 1 \).

Step 2: Perform the Arithmetical Operation

The equation is reduced to \( -2.2 + 1 \). Now proceed by performing the addition. The sum of -2.2 and 1 gives -1.2.

Step 3: State the Solution

After performing the addition, we find that the difference between -2.2 and -1 is -1.2.

Key Concepts

Negative Numbers

Negative numbers are numbers that are less than zero. They are often used to represent losses, debts, or temperatures below freezing. Understanding how to work with negative numbers can help you solve many real-world problems.

When you look at a number line, negative numbers are positioned to the left of zero. For example, if zero is at the center, numbers like -1, -2, -3, and so on extend indefinitely to the left.

• Negative numbers when added to positive numbers can affect the result based on their magnitude.
• Subtracting a negative number can lead to an increase in value, due to the "opposites attract" behavior in arithmetic.
• If you multiply or divide a negative number with a positive number, the result is negative.

Working with negative numbers may seem confusing at first, but with practice, you'll handle them with ease.

Arithmetic Operations

Arithmetic operations include addition, subtraction, multiplication, and division. They are the building blocks of mathematics and help us solve all sorts of problems. Here, we focus on subtraction and addition, which are directly relevant to the exercise.

In subtraction, you find the difference between two numbers. If you subtract a larger number from a smaller number, the result will be negative. When dealing with the problem \(-2.2 - (-1)\), subtraction is being applied. However, due to the double negative, it turns into addition \((-2.2 + 1)\).

• Additive Inverse: Subtraction involves the concept of the additive inverse, where subtracting a negative is like adding a positive.
• Order of Operations: When performing arithmetic operations, follow the order PEMDAS – Parentheses, Exponents, Multiplication and Division (from left to right), Addition and Subtraction (from left to right).

These operations lay the foundation for solving more complex problems across various fields.

Double Negatives

Double negatives occur when two negative signs are present next to each other in a mathematical expression. This concept can appear tricky, but it follows a straightforward rule: two negatives make a positive.

Consider an expression like \(a - (-b)\). In this expression, the two negatives (the subtraction and the negative of \(-b\)) transform the operation into addition \(a + b\). This happens because subtracting a negative number is equivalent to adding its positive counterpart.

• Double negatives "cancel out," turning subtraction into addition.
• Always look out for parentheses indicating implicit negations, such as subtraction before a negative number.
• Remember to simplify expressions by removing double negatives whenever possible to avoid errors.

Grasping the concept of double negatives helps in simplifying and solving various arithmetic expressions smoothly.