Problem 30 - Fundamentals of Mathematics

Question

For the following 18 problems, perform each subtraction. Use a calcula tor to cherk each result. $$ 0-(-7) $$

Step-by-Step Solution

Answer

The result of the subtraction \(0 - (-7)\) is \(7\).

Step 1: Understand the Problem

The exercise is asking you to subtract \(-7\) from \(0\). In mathematical terms, we have: \(0 - (-7)\).

Step 2: Simplify the Expression

When you subtract a negative number, it's the same as adding its positive counterpart. So, \(0 - (-7) = 0 + 7\).

Step 3: Perform the Addition

Now, simply add \(0\) and \(7\):\[0 + 7 = 7\]

Step 4: Validate Using a Calculator

Confirm the result by using a calculator. Enter \(0\), then add \(7\), which should give you \(7\).

Key Concepts

Understanding Negative Numbers

Negative numbers might seem tricky, but they are just as simple as positive numbers once you understand their role. A negative number represents a value less than zero. It's like a step below zero on a number line. For instance,

• -1 is one step below 0.
• -2 is two steps below 0.

Negative numbers are often used in real-world scenarios like measuring depths below sea level or temperatures below freezing.

When dealing with subtraction, remember the rule: subtracting a negative number means you're actually adding its positive counterpart. This is because subtracting a negative is the same as canceling out the loss, essentially increasing the value.

The Magic of Addition

Addition is one of the most basic arithmetic operations. It involves combining values to get a sum. It gets even more interesting when negative numbers are involved!

When you "add" a negative, you're effectively subtracting. Conversely, when you "subtract" a negative, you're actually adding. For example:

• If you're dealing with the problem \(0 - (-7)\), you turn it into \(0 + 7\). The subtraction of a negative \(-7\) turns into the addition of a positive \(7\).

Working with positive and negative integers in addition is easy once you grasp these fundamental rules. It allows for seamless calculations in many mathematical and practical applications.

Using a Calculator Effectively

Calculators are excellent tools for verifying your math calculations. They are especially helpful when you're learning new concepts like working with negative numbers.

In practice:

• Enter the numbers and operations exactly as you have written them. For \(0 - (-7)\), you'll type 0, then "+" (not "+/-") to add 7.

Remember, a calculator can quickly show you the answer, but understanding how it arrives at that answer is crucial. Use it as a guide, especially to confirm results while you're learning the logic behind arithmetic operations.