Problem 28 - Fundamentals of Mathematics

Question

Find the sums in the following 27 problems. If possible, use a calculator to check each result. $$ 8+(-15) $$

Step-by-Step Solution

Answer

The sum of \(8 + (-15)\) is \(-7\).

Step 1: Understanding the Addition of Negative Numbers

To solve the problem \(8 + (-15)\), we need to understand that adding a negative number is the same as subtracting its positive counterpart. So, \(8 + (-15)\) is equivalent to \(8 - 15\).

Step 2: Subtracting the Numbers

Now perform the subtraction: \(8 - 15\). Since 15 is greater than 8, this will result in a negative number. Start from 8 and count backwards 15 units to get the result. This gives us \(-7\).

Step 3: Verifying with a Calculator

To verify the result using a calculator, input \(8\), then add \(-15\). The calculator should confirm the result \(-7\).

Key Concepts

Understanding Negative Numbers

Negative numbers are, as the name suggests, numbers that are less than zero. They are represented with a minus sign (e.g., -3, -5, or -15). Negative numbers are used to describe quantities that are below a specific threshold, such as temperatures below zero or owing money.

When negative numbers are involved in addition or subtraction, they can initially be confusing. Adding a negative number is essentially the same as subtracting a positive number. For instance, adding (-15) to 8 is the same as subtracting 15 from 8. This concept applies to any operation involving negative numbers.

Understanding how negative numbers interact with positive numbers is crucial in math, as it helps us solve many everyday problems.

The Process of Subtraction

Subtraction is one of the basic operations in arithmetic. It involves taking one number away from another. When performing subtraction with negative numbers, the key is to remember that subtracting a negative number is like adding its positive counterpart.

For example, when we look at the problem: 8 - 15, we start with the number 8 and then move backwards on a number line by 15 units. Because 15 is greater than 8, you'll end up past zero, landing at -7.

Here’s a simple way to think of this:

• Start at 8.
• Subtract 15 by moving backwards 15 steps.
• End at -7.

Visualizing the number line can help make subtraction with negative numbers more tangible.

Using Calculators for Verification

Calculators are helpful tools for checking mathematical calculations. They can be particularly handy when working with negative numbers and complex arithmetic. To verify problems like adding negative numbers, a calculator can quickly confirm your results.

To check the calculation of 8 + (-15) using a calculator:

• Enter the first number: 8.
• Press the addition key (+).
• Enter the negative number by pressing the negative sign before 15 (-15).

The displayed result should be -7. Using calculators not only provides accuracy but also builds confidence in your math skills.