Problem 17 - Prealgebra and Introductory Algebra

Question

Add. $$3+(-5)$$

Step-by-Step Solution

Answer

The answer is -2.

Step 1: Understand the Question

The question asks to 'add' a negative number to a positive number. Remember, addition of a negative number is essentially subtraction. So instead of adding -5, you will subtract 5.

Step 2: Perform Addition/Subtraction

Start by having the positive number: 3. Now, instead of adding -5, subtract 5 from 3. Which will give you \(3 - 5\).

Step 3: Calculate the Result

When you subtract 5 from 3, it gives you -2. This is because you're taking away more than you have, resulting in a negative number.

Key Concepts

Addition and Subtraction

When dealing with addition and subtraction of numbers, especially negative numbers, it's important to recognize that adding a negative number is similar to subtraction. This concept may sound confusing, but let's break it down.

Imagine a simple addition problem: adding a negative number to a positive number. For example, in the problem \(3 + (-5)\), what we're really doing is taking away 5 from 3. When you hear the term "add negative," think of it as "subtract."

• "Add a negative number" means to subtract that number.
• "Subtract a positive number" can also mean you're adding a negative.

This makes the math more intuitive and helps transition mental actions into concise mathematical operations.

Integers

Integers are a set of numbers that include all whole numbers, their negative counterparts, and zero. They do not include fractions or decimals, making them easy to use in basic arithmetic operations like addition and subtraction.

• Positive integers are numbers greater than zero: 1, 2, 3, etc.
• Negative integers are numbers less than zero: -1, -2, -3, etc.
• Zero is a neutral integer, neither positive nor negative.

In the problem \(3 + (-5)\), 3 is a positive integer and -5 is a negative integer. Performing arithmetic operations with integers involves understanding how these positive and negative values interact, always keeping in mind the direction (or sign) of the operation you are performing.

Mathematical Operations

Mathematical operations are the processes we use to solve problems with numbers, such as addition, subtraction, multiplication, and division. Here, our focus is on addition and subtraction, especially when negative numbers are involved.

In the expression \(3 + (-5)\), we're using the addition operation, but because of the negative sign, it's equivalent to subtracting:\(3 - 5\). This interaction between negative and positive numbers requires understanding the rules of arithmetic operations:

• Adding a positive moves you forward on the number line.
• Adding a negative (or subtracting a positive) moves you backward.
• Subtracting a negative is like adding a positive, as the negatives cancel each other out.

By applying these rules consistently, you can confidently tackle equations involving both positive and negative integers.