Problem 28 - Fundamentals of Mathematics

Question

Write each expression in words. $$ -2-(-6) $$

Step-by-Step Solution

Answer

Negative two minus negative six.

Step 1: Identify the Numbers and Operations

In the expression \(-2 - (-6)\), we have two key numbers: \(-2\) and \(-6\). The operations involved are subtraction and taking the negative of a number.

Step 2: Break Down the Expression

The expression consists of three parts: the negative sign in front of 2, which we read as 'negative two'; the subtraction sign, which we read as 'minus'; and the negative in front of 6, read as 'negative six'.

Step 3: Convert Mathematical Symbols to Words

Translate each part of the expression into words: \(-2\) as 'negative two,' the minus sign as 'minus,' and \(-6\) as 'negative six.' So, the expression \(-2-(-6)\) can be read as 'negative two minus negative six.'

Key Concepts

Understanding Negative Numbers

Negative numbers are quite fascinating because they represent values less than zero. Imagine you are below sea level or owe money – these are real-world representations of negative numbers. In mathematics, we use the symbol \(-\) before a number to indicate that it is negative. For instance, \(-2\) means "negative two."
Negative numbers can be tricky, especially when combined in expressions with other negative numbers or operations.

• They are often used in temperature scales, like Celsius, to show temperatures below freezing.
• You might also encounter negative numbers when dealing with elevations, such as a valley below sea level.

Let's not forget that negative numbers extend the number line to the left of zero and help us handle situations where debt or loss is involved.

Understanding Subtraction of Negative Numbers

The subtraction operation can become more complex when dealing with negative numbers, but there's a simple way to understand it.
When you see subtraction of a negative number, it can be transformed into addition. This is because subtracting a negative is equivalent to adding a positive. Hence, the expression \(-2 - (-6)\) changes to \(-2 + 6\).
Think of it as two negatives cancelling each other out, turning into a positive.

• Subtracting \(-6\) is the same as adding \(6\).
• Computing \(-2 + 6\) is simpler to visualize and results in positive \(4\).

This concept removes the confusion and shows that subtraction involving negative numbers can often become an addition problem.

Applying Mathematical Operations

Mathematical operations like addition, subtraction, multiplication, and division form the foundation of mathematics. Each operation has rules, especially when incorporating negative numbers. By understanding these rules, we can solve complex problems easily.
When faced with operations involving negative numbers:

• Remember that combining a negative sign with a subtraction turns it into an addition problem.
• In multiplication and division, two negatives make a positive. For example, \((-2) \times (-3) = 6\).

By practicing these mathematical operations, they become intuitive and easy to carry out. Approach these operations with curiosity and confidence. Practice, after all, makes perfect!