Problem 12 - Fundamentals of Mathematics

Question

Find the sums. $$ 0+(-6) $$

Step-by-Step Solution

Answer

The sum is -6.

Step 1: Understand the Problem

The task is to find the sum of the numbers 0 and -6. Remember that when you add zero to any number, the value of the original number remains unchanged.

Step 2: Apply the Addition Rule

When adding zero to any number, the result is the number itself. This means that adding 0 to -6 will not change its value.

Step 3: Calculate the Sum

Since the sum of zero and another number leaves the original number unchanged, we write: \[0 + (-6) = -6\]

Key Concepts

Addition Rule

The Addition Rule is all about how numbers are combined in a sum. When adding two integers, consider their signs. If they have the same sign, add their absolute values and keep the sign. If their signs are different, subtract the smaller absolute value from the larger one and take the sign of the number with the larger absolute value. This method helps simplify the addition of negative and positive numbers.

In our example, we add zero to a negative number (-6). The addition rule tells us that regardless of zero's presence, our focus is on the natural process of adding integers. Since our second integer is negative, -6 remains until zero influences it in calculations. Adding zero doesn't influence the rule of combining absolutes, but directly influences the result in a simple way, as discussed in Zero Property.

Zero Property

The Zero Property is a simple rule that often plays a significant role in simplifying math problems. It states that any number added to zero will remain the same. In other words, zero is like a neutral element in addition operations.

Think of zero as a friend who joins you but doesn't change your plans—your destination and speed remain as they were. In the expression \(0 + (-6)\), since we are adding zero, the sum remains \(-6\).

Key points of the Zero Property:

• Zero keeps the original number unchanged.
• It simplifies expressions, especially when dealing with negative numbers.
• This property is crucial for checking calculations.

Negative Numbers

Negative numbers can sometimes be tricky, but with some understanding, they are straightforward to work with. Negative numbers are those less than zero and are represented with a minus (-) sign.

When adding negative numbers, imagine moving to the left on the number line. For example, adding \(-6\) means starting at zero and taking six steps left. Negative numbers affect totals differently than positive numbers, often reducing the sum.

Things to remember about Negative Numbers:

• They are represented with a minus sign.
• When added, they result in a smaller or more negative value.
• They can be combined with positive numbers using the Addition Rule.

Understanding negative numbers helps make sense of calculations involving both positives and negatives, such as in our exercise.