Problem 67 - Algebra 1

Question

Find the sum. $$-10+(-1)$$

Step-by-Step Solution

Answer

The sum of -10 and -1 is -11.

Step 1: Identify the numbers

Identify the numbers that have to be added and their sign. Here, the numbers are -10 and -1.

Step 2: Apply the arithmetic rule for adding two negatives

The general rule says, negative m + negative n will be negative m-n. So, negative 10 + negative 1 will be negative 10 - 1.

Step 3: Perform the subtraction operation

Subtract 1 from 10 to obtain the result. Thus, -10 - 1 = -11.

Key Concepts

Understanding Negative Numbers

Negative numbers are numbers less than zero. They have a minus sign (-) in front of them, such as -10 or -1. These numbers are common in various contexts, such as indicating temperature below zero or a debt in finance. Negative numbers can initially be confusing because they work differently than the positive numbers most people are familiar with.
When you add negative numbers, it actually means you are moving further left on the number line, making the number more negative. Therefore, when two negative numbers are added, the result is more negative than either of the starting numbers. Understanding this basic concept is crucial when working with integer addition involving negatives.

Mastering Arithmetic Rules

Arithmetic rules provide the foundation for solving math problems accurately. When adding integers, especially negative numbers, it's important to remember some key rules:

• Adding two positive numbers gives a positive number.
• Adding two negative numbers gives a negative number.
• If you add a positive number and a negative number, subtract the smaller absolute value from the larger absolute value, and keep the sign of the larger number.

In our problem \(-10 + (-1)\)\, we are using the rule for adding two negative numbers. According to the rule, when you add two negative numbers, you add their absolute values and then attach the negative sign to the result.

Subtraction Operation in Integer Addition

Subtraction involves finding the difference between numbers. However, in the context of adding negative numbers, subtraction takes on an unusual but simple role. Instead of the typical positive addition we do with positive numbers, adding negatives mimics subtraction as it pushes the result further into negative territory.
In the problem \(-10 + (-1)\)\, this addition transforms into a subtraction scenario because we are essentially adding more negative value. Therefore, adding -1 to -10 results in \(-10 - 1 = -11\). This shows how negative addition impacts results similarly to subtraction. Embracing this concept helps in handling math problems involving negative integers more smoothly.