Problem 39 - Algebra 1

Question

Find the opposite of the number. $$-2.01$$

Step-by-Step Solution

Answer

The opposite of -2.01 is 2.01

Step 1: Understand the Concept of Opposite

The opposite (or additive inverse) of a number \(a\) is \(-a\). When you add a number and its opposite, the result is 0: \(a + (-a) = 0\).

Step 2: Find the Opposite

The given number is \(-2.01\). To find its opposite, we change its sign.

Step 3: State the Result

The opposite of -2.01 is 2.01

Key Concepts

Negative Numbers

Negative numbers are values less than zero. They are often used to represent loss or reduction, such as temperatures below freezing or depths below sea level.
To visualize negative numbers, think of a number line with zero in the middle. Numbers to the left of zero are negative. As you move further left, the numbers decrease. For example, -1, -2, and -3 are all negative numbers. Negative numbers have unique arithmetic rules:

• Adding a negative number is the same as subtracting its positive counterpart.
• Subtracting a negative number is like adding its positive counterpart.
• Multiplying or dividing two negative numbers results in a positive number.
• Multiplying or dividing a negative number by a positive number results in a negative number.

Negative numbers are important in everything from day-to-day budgeting to advanced mathematical calculations.

Positive Numbers

Positive numbers are all numbers greater than zero. They are what we typically think of as the counting numbers: 1, 2, 3, and so on.
On a number line, these numbers appear to the right of zero. The further right you move, the larger the positive number. Some simple properties of positive numbers include:

• Adding two positive numbers always results in a positive number.
• Subtracting a smaller positive number from a larger one still gives a positive number.
• Multiplying or dividing two positive numbers yields a positive result.

In everyday life, positive numbers are used to denote quantities like age, height, or bank account balances unless there's debt involved. They form the foundational building blocks of mathematics.

Sign Change

The concept of sign change is crucial for understanding opposite numbers. It's like flipping the position of a number on the number line.
If you have a positive number, applying a sign change makes it negative. Similarly, changing the sign of a negative number makes it positive. This is because switching the sign swaps a number's direction relative to zero.To change a sign:

• Start with the original number, say \(x\).
• If \(x\) is positive, its opposite is \(-x\).
• If \(x\) is negative, its opposite is \(-(-x) = x\), since the double negative cancels out.

Thus, the opposite of -2.01 is 2.01, as demonstrated in the original solution. This technique can be used in various mathematical scenarios to find opposites or solve equations.