Question

Find the sum. $$-1+6$$

Short answer

The sum of \(-1 + 6\) is 5.

Step-by-step solution

Identify the Numbers

In the given expression \(-1+6\), we have two numbers: -1 and 6.

Applying Addition of Negative Numbers

Adding a negative number is the same as subtracting its absolute value. In other words, \(-1 + 6\) is the same as \(6 - 1\).

Calculate the Result

Perform the operation \(6 - 1\) to get the result.

Key concepts

Basic Arithmetic

At its core, basic arithmetic encompasses the fundamental operations used for calculating numbers, which includes addition, subtraction, multiplication, and division. Mastery of these is critical for higher mathematical learning. When we deal with numbers, it's essential to understand the nature of these numbers—whether they're positive or negative—because that influences how these operations work.

For example, when adding numbers like in the exercise \( -1 + 6 \), it's straightforward when both numbers are positive. But when we encounter a mix of positive and negative numbers, we need to approach the problem with a solid understanding of basic arithmetic rules, such as how to combine these numbers. This understanding builds the foundation for accurately solving more complex problems.

Addition and Subtraction

Addition and subtraction are opposite operations that work hand in hand. In the realm of mathematics, these operations allow us to combine values (addition) or find the difference between values (subtraction).

When engaging with exercises like \( -1 + 6 \), it's important to recognize that addition of negative numbers introduces the concept of direction. Positive numbers can be thought of as moving to the right on a number line, while negative numbers move to the left. Thus, when we add a negative number, we're essentially moving left from our starting point, which effectively subtracts the number's value from our total.

Negative Number Operations

Working with negative numbers can at first seem counterintuitive, but there are clear rules to help. The operation of adding a negative number—such as \( -1 \)—to a positive number—like \( 6 \) in our exercise—is akin to subtracting the absolute value of the negative number from the positive number. The absolute value is the distance a number is from zero, disregarding whether it is positive or negative.

So, when we see \( -1 + 6 \), what we're actually doing is taking the starting number, 6, and moving one unit to the left on the number line, ending up with 5. This is a fundamental concept in working with negative numbers and builds the basis for more advanced mathematics such as algebra.

Integer Arithmetic

Integers are whole numbers that can be positive, negative, or zero, and arithmetic with integers follows specific rules that take into account the positive or negative sign of the numbers involved. In the context of our exercise, \( -1 + 6 \), we're engaging with integer arithmetic by combining a negative integer with a positive integer.

In integer arithmetic, the sign of the number dictates the direction and magnitude of the operation. This explains why adding a negative number results in subtraction—because integers include both directions along the number line. Understanding integer arithmetic is essential for solving equations and problems across various areas of mathematics and science.