Problem 23 - Fundamentals of Mathematics

Question

How should the number in the following 6 problems be read? (Write in words.) \(-(-5)\)

Step-by-Step Solution

Answer

Five.

Step 1: Understand the Expression

The given expression is \(-(-5)\). This means we are taking the negative of negative five.

Step 2: Simplify the Expression

Taking the negative of a negative number changes it to a positive number. Therefore, the expression \(-(-5)\) becomes 5.

Step 3: Convert to Words

Now that we have simplified the expression to the number 5, we need to write it in words. The number 5 in words is 'five'.

Key Concepts

Negative Numbers

Negative numbers are numbers less than zero. They are usually indicated with a minus sign in front of them. These numbers are common in many areas of mathematics and are used to represent values below a defined reference point, such as debts in accounting or temperatures below freezing.
When dealing with negative numbers, it’s crucial to understand that:

• They represent a position to the left of zero on a number line.
• When a negative and a positive number are added, you are essentially subtracting the lesser number from the greater one.
• Multiplying two negative numbers results in a positive number.

For example, in the expression \(-(-5)\), the negative of a negative number turns it into a positive number, leading to a final result of 5. This concept is fundamental when simplifying expressions.

Number Words

Expressing numbers in word form is an essential skill. It helps improve mathematical literacy and can be particularly useful in situations where written documents are concerned where numerals might be misread, like checks or formal writing.
To convert numbers into words:

• Identify the numerical value.
• Write the identified number using its corresponding word representation.

For instance, the number 5 is written as 'five'. This exercise of converting can help enhance understanding of numeric values and ensure accuracy when communicating numbers.

Simplifying Expressions

Simplifying expressions is the process of reducing complexities within an expression to make it easier to understand or solve. This often involves removing unnecessary elements or combining like terms to create a simpler equivalent.
Key steps to simplify expressions with negative numbers include:

• Resolve any double negatives, which result in a positive.
• Combine any like terms, if present.
• Order the expression in terms of operations, such as completing within parentheses first, then exponents, followed by multiplication and division, and finally addition and subtraction (following PEMDAS/BODMAS rules).

For example, simplifying \(-(-5)\) involves recognizing the double negative, which simplifies down to the positive 5. This process not only clears up expressions but aids in further solving equations.