Problem 11 - Fundamentals of Mathematics

Question

Find the sums. $$ 15+(-18) $$

Step-by-Step Solution

Answer

The sum is -3.

Step 1: Understand the Operation

The problem requires you to find the sum of a positive number and a negative number. Addition of numbers with opposite signs involves finding the difference between their absolute values.

Step 2: Identify the Absolute Values

Find the absolute values of the numbers 15 and -18. The absolute value of 15 is 15, and the absolute value of -18 is 18.

Step 3: Subtract the Smaller Absolute Value from the Larger Absolute Value

Subtract the smaller absolute value (15) from the larger absolute value (18): \[ 18 - 15 = 3 \]

Step 4: Determine the Sign of the Result

Since -18 has the larger absolute value and is negative, the result of the addition is also negative. Therefore, the final result is -3.

Key Concepts

Understanding Absolute Value

Absolute value refers to the magnitude of a number, regardless of its sign. It tells us how far a number is from zero on the number line.

For example:

• The absolute value of 15 is 15, because it is 15 units away from zero.
• Conversely, the absolute value of -18 is 18, as it is also 18 units away from zero, disregarding the direction.

This concept is crucial in integer addition, particularly when dealing with numbers of opposite signs. Understanding absolute value helps us calculate the difference without getting tangled in signs.

In operations like this exercise, you find the absolute values first, compare them, and then perform the necessary computations.

Utilizing the Number Line in Math

The number line is a visual tool that helps us understand how numbers work together. It's a straight line where numbers are placed at equal intervals. Zero is typically in the center, with positive numbers to the right and negative numbers to the left.

When adding integers, especially those of opposite signs, the number line can illustrate the journey from one number to another.

• Start at the first number (15 in this case).
• Since we're adding a negative (-18), move 18 units to the left, signifying the subtraction process.

This method gives a clear visual representation of why the sum is negative when the negative number has a larger absolute value.

Comprehending Negative Numbers

Negative numbers are less than zero and typically symbolize a deficit or decrease in value. They exist on the left side of the number line.

Addition involving negative numbers may seem tricky at first, but understanding their placement relative to positive numbers helps.

• Adding a negative number is like subtracting its absolute value from the other number.
• For instance, 15 + (-18) can be visualized as starting at 15 and moving 18 units left.

The result is -3, revealing that the negative influence in the sum outweighs the positive input. This insight is essential when working with real-world scenarios, such as calculating debt (negative) and savings (positive). Recognizing the effect of negative numbers aids in better comprehension of integer operations.