Problem 32 - Fundamentals of Mathematics

Question

Find the sums in the following 27 problems. If possible, use a calculator to check each result. $$ 0+(-4) $$

Step-by-Step Solution

Answer

The sum is -4.

Step 1: Identify the Expression

The expression given is \( 0 + (-4) \). This involves adding zero to a negative number.

Step 2: Evaluate the Addition

Since adding zero to any number does not change the value of the number, \( 0 + (-4) \) simplifies to \(-4\).

Step 3: Verify with a Calculator

Use a calculator to enter the expression \( 0 + (-4) \). The result should be \(-4\), confirming our manual calculation is correct.

Key Concepts

Mathematical Expression Evaluation

When evaluating mathematical expressions, the operation signs and the numbers involved play a crucial role. In the problem we've tackled, we encounter an expression that involves adding a number to zero. Evaluating such an expression is about understanding the inherent properties of zero.

Zero is unique in mathematics because it acts as the identity element for addition. This means whenever you add zero to any number, the result is always that number itself. Therefore, expressions involving zero can be quickly evaluated without extensive computation, simplifying your work and saving time.

Integer Addition

Adding integers is a fundamental skill in arithmetic that involves both positive and negative numbers. In the exercise example, we have to add a negative integer, \((-4)\), to zero.

When dealing with integers:

• Positive integers are greater than zero.
• Negative integers are less than zero.

Adding zero to any integer does not change the value of the integer, which is why the solution to our exercise is simply \((-4)\). This is because there is no change in position on the number line.

Calculator Verification

Using a calculator to verify solutions is a good practice, especially as a means to reinforce learning and build confidence. After manually solving an expression like \(0 + (-4)\), using a calculator provides a quick way to check accuracy.

Here’s how to verify:

• Input the expression faithfully as it appears, ensuring the use of negative signs when needed.
• Observe the result displayed.

If the result matches your manual calculation, as it should in this case by displaying \(-4\), you can be confident that your understanding and computation are correct. This method not only serves as a check but also further reinforces the connection between computational devices and manual arithmetic processes.