Problem 31 - Fundamentals of Mathematics

Question

Write each expression in words. $$ 0-(-11) $$

Step-by-Step Solution

Answer

Zero plus eleven.

Step 1: Recognize Negative Sign

The expression starts with a zero, followed by a subtraction symbol, and then a negative eleven. In words, this translates to zero minus a negative eleven.

Step 2: Translate the Mathematical Symbols to Words

In mathematical terms, subtracting a negative is equivalent to adding the positive. Thus, 'zero minus negative eleven' translates to 'zero plus eleven'.

Key Concepts

Negative Numbers

Understanding negative numbers is essential in arithmetic. Negative numbers are numbers less than zero and are often used to represent opposite values or losses. For example:

• In temperatures, below zero indicates cold weather.
• In finances, negative values indicate debt or loss.

Negative numbers are represented with a 'minus' sign in front of them. Understanding their proper use is key in performing accurate arithmetic operations. Often, they are integral when working with mathematical expressions or equations. In the problem we are solving, the expression holds a negative number, \( -11 \).It's crucial to see this not as a simple eleven, but as "negative eleven." This helps to visualize the operation needed.

Subtraction

Subtraction might seem straightforward, but when it involves negative numbers, it provides unique challenges. Let's break down the rules. A negative number indicates an inverse operation, impacting how subtraction works with them.When you see an expression like "subtracting a negative number," it may cause confusion. Take the example:\( 0 - (-11) \). The phrase "zero minus negative eleven" might be deceptive. However, mathematically, subtracting a negative equates to adding its positive equivalent. Essentially,

• Subtracting \((-11)\) from zero is the same as adding 11 to zero.

Thus, \(0 - (-11) = 0 + 11\). Understanding this subtlety clarifies operations involving negative values.

Mathematical Expressions

Interpreting mathematical expressions involves converting symbolic representations into words or numbers. A mathematical expression like \(0 - (-11)\) can initially appear complex. However, by breaking it down:

• Recognize each component: a zero, a subtraction sign, and then a negative eleven.
• Translate to words: zero minus negative eleven.
• Simplify using arithmetic rules: subtracting a negative is equivalent to addition.

Therefore, \(0 - (-11)\) becomes \(0 + 11\). This reflects how we can simplify expressions through understanding mathematical language. Mastery of this skill aids students in both simple and complex problem solving. It highlights how transformation from one form to another, numbers to words, can demystify mathematics.