Problem 11 - Fundamentals of Mathematics

Question

Perform the indicated subtractions. $$ 0-16 $$

Step-by-Step Solution

Answer

The result of the subtraction is -16.

Step 1: Understand Subtraction from Zero

When you subtract a positive number from zero, it means you're moving to the left on the number line that amount, resulting in a negative value. So, subtracting a positive number from zero will yield its negative counterpart.

Step 2: Apply Subtraction

For the expression given, calculate: \[0 - 16\]According to the principle explained in step 1, subtracting 16 from zero results in \(-16\).

Step 3: Conclusion

The subtraction operation results in a negative value. Therefore, placing the solution in standard form, we find that:\[0 - 16 = -16\].

Key Concepts

Subtraction

Subtraction is a fundamental arithmetic operation. It involves removing a certain quantity from another. In simple terms, it tells you how much is left after taking something away.

When you subtract one number from another, you're finding the difference between them. Subtraction has several properties that make it unique:

• It is not commutative. This means that changing the order of the numbers will change the result. For example, \(8 - 5 eq 5 - 8\).
• Subtracting zero from a number leaves the number unchanged. So, \(n - 0 = n\).

In the exercise, we saw the subtraction \(0 - 16\). Importantly, subtracting a positive number from zero results in a negative number. This happens because it's like moving 16 steps to the left on the number line, ending up at \(-16\).

Number Line

A number line is a visual representation of numbers in a straight line. It's a handy tool for understanding addition and subtraction, especially with negative numbers.

Numbers on the line are usually equally spaced, with zero in the middle. Positive numbers are placed to the right of zero, while negative numbers are to the left. Using the number line to subtract involves:

• Starting at the first number (0 in our example).
• Moving to the left for each unit of the number being subtracted (16 here).

So for \(0 - 16\), start at 0 and move 16 steps to the left. You'll land on \(-16\). This helps visualize why subtracting a larger number from a smaller number gives a negative result.

Integers

Integers are whole numbers that can be positive, negative, or zero. They do not include fractions or decimals but are fundamental in math and various real-life scenarios.

Understanding integers is crucial for performing arithmetic operations like subtraction.

• Positive integers are numbers greater than zero (e.g., 1, 2, 3...).
• Negative integers are numbers less than zero (e.g., -1, -2, -3...).
• Zero is an integer that is neither positive nor negative.

When subtracting integers, especially when involving negative results, it's helpful to think of money. Imagine \(0\) as having no money and "subtracting" means owing someone. So, if you owe 16 (or \(0 - 16\)), you'd end up with \(-16\), showing debt. This intuitive approach aids understanding how integers work with subtraction.