Question

Find the sum. $$-2+(-3)$$

Short answer

The sum of -2 and -3 is -5.

Step-by-step solution

Understand the problem

The problem is to find the sum of two negative numbers, specifically -2 and -3. The sum can be calculated by using the rule: when adding negative numbers, simply add the numbers then apply a negative sign.

Perform the addition

Ignoring their signs, add 2 and 3 together which equals 5.

Apply the negative sign

Finally, apply the negative sign to the result from the previous step. The sum becomes -5 or \(-5\).

Key concepts

Negative Integers

Understanding negative integers is crucial for grasping basic arithmetic and algebra. A negative integer is simply a whole number that is less than zero, represented by a minus (-) sign. In arithmetic, negative numbers are used to denote the opposite of positive numbers.

For instance, if you think of a number line, zero is in the middle, positive integers move to the right, and negative integers extend to the left. When you're adding negative numbers, such as (-2) and (-3), imagine you're moving left on the number line each time. So, starting from zero, you move two steps to the left, and then another three steps further left.

Negative numbers come in handy in a variety of real-world scenarios, like accounting for debts or measuring temperatures below freezing. It's important to be comfortable with negative integers because they form the basis for many algebraic concepts.

Basic Algebra

Basic algebra serves as the foundation for advancing in mathematics. It involves using letters and symbols to represent numbers in equations and formulas, making it easier to solve problems. When dealing with negative numbers in algebra, understanding the rules of arithmetic operations allows you to simplify and solve equations confidently.

Consider an algebraic expression like (-x) + (-y). Although the values for (x) and (y) are not known, the rule for adding negative numbers still applies: combine their absolute values, then assign a negative sign to the result. This concept is fundamental when you progress to more complex algebraic expressions and equations.

Algebra is not just about finding unknowns but also about articulating relationships between quantities and predicting outcomes, which is essential in fields like engineering, science, and economics.

Arithmetic Operations

Arithmetic operations are the building blocks of math. They include addition, subtraction, multiplication, and division. When performing these operations with negative numbers, there are specific rules to follow.

In the context of adding negative integers, remember the simple rule: adding negative numbers means combining their magnitudes (the numbers without their signs) and then affixing a negative sign to the sum. Think of it as accumulating debt; if you owe 2 dollars and borrow 3 more, you then owe a total of 5 dollars ((-2) + (-3) = (-5)).

Ensuring you understand these operations allows you to effortlessly carry out more complex mathematical tasks. Arithmetic with negative numbers is just one such operation that opens the door to understanding algebra and beyond.