Problem 22 - Fundamentals of Mathematics

Question

How should the number in the following 6 problems be read? (Write in words.) \(-(-1)\)

Step-by-Step Solution

Answer

The number should be read as "one."

Step 1: Understand the Expression

The expression given is \(-(-1)\). This means we have a double negative, which typically involves negating a number twice.

Step 2: Simplify the Negation

When you negate a negative number, it becomes positive. Hence, \(-(-1)\) simplifies to \(1\).

Step 3: Convert Number to Words

Now that we have simplified the expression to \(1\), we write it in words as "one."

Key Concepts

Double Negative

In mathematics, a double negative occurs when you have two negative signs in an expression. This may seem a bit tricky, but it helps to think of it as an operation that cancels itself out. Imagine you are negating a number, which means taking its opposite.
For example, if you have

• A single negative like \(-1\), it flips the number to its opposite. So, \(-1\) becomes \(1\).
• A double negative such as \(-(-1)\), you are flipping it twice. First, \(-1\) flips to \(1\), and there's nothing left to flip, so it stays as \(1\).

This principle can also be applied in more complex expressions. Remember, two negative signs together end up doing nothing to the number because they cancel each other out. It is like the opposite of an opposite, which brings us right back to where we started.

Negation in Mathematics

Negation is a fundamental concept in mathematics that involves reversing the sign of a number or expression. When we think about negating a number, we are effectively looking for its opposite.
Mathematics uses this concept in various scenarios:

• In arithmetic, negating a positive number yields a negative. For example, the negation of \(5\) is \(-5\).
• Conversely, negating a negative number returns a positive one, like the example of \(-(-2)=2\).

When understanding expressions, particularly ones involving negation, always keep an eye on the signs. Handling negative signs with care can prevent mistakes in calculations and ensure the correct interpretation of the expressions.

Simplifying Expressions

Simplifying expressions is a crucial part of algebra and arithmetic. It involves reducing an expression to its simplest form, which often makes solving equations easier and more manageable. When simplifying, focus on a few key ideas.

• Identify Like Terms: Look for terms that can be combined because they share the same variable or similar elements.
• Apply Mathematical Rules: Use rules such as the distributive property and rules of arithmetic (like negation) to streamline the expression.
• Eliminate Double Negatives: As discussed earlier, two negative signs cancel each other out, which can significantly simplify expressions.

For instance, simplifying \(-(-1)\) boils down to eliminating the double negative, which gives us a straightforward \(1\). Reading numbers in words after simplification also becomes easier, allowing us to articulate them clearly in a sentence.