Problem 29 - Algebra 1

Question

Find the sum. $$-11.6+6.4+(-3.0)$$

Step-by-Step Solution

Answer

The sum of \(-11.6+6.4+(-3.0)\) is \(-8.2\)

Step 1: Addition of positive and negative numbers

Firstly, separate the positive and negative numbers. We have \(-11.6\) and \(-3.0\) as negative numbers, and \(6.4\) as positive number.

Step 2: Add negative numbers together

When we add the negative numbers, \(-11.6 + -3.0\) we get \(-14.6\)

Step 3: Add result from Step 2 to the positive number

Afterwards, we add the sum of the negative numbers from step 2 to the positive number, \(-14.6 + 6.4\). The answer is \(-8.2\).

Key Concepts

Addition of Negative Numbers

Working with negative numbers can seem challenging at first, but it becomes simple once you understand the rules. When we add two negative numbers, we are finding the total value of their negative contributions. For example, in the exercise \(-11.6 + (-3.0)\), we combine the negatives by adding their absolute values: \(11.6 + 3.0 = 14.6\), then we apply the negative sign to the result, giving us \(-14.6\).

• The key is to ignore the negative signs temporarily while adding the numbers.
• Then, reapply the negative sign to the final sum.

Thinking of negative numbers as money owed can help in visualizing this process. Adding debts together results in a larger total debt.

Combining Positive and Negative Numbers

Combining positive and negative numbers is a fundamental concept in operations with real numbers. It involves either increasing or decreasing a quantity depending on the signs of the numbers involved. In the solution, we combined -14.6 (the sum of two negative numbers) with 6.4, a positive number.

• The rule to remember is:
  • When the signs are different, subtract the smaller absolute value from the larger absolute value.
  • The result takes the sign of the number with the larger absolute value.

Applying this to our example, we have \(-14.6 + 6.4\). The absolute values 14.6 and 6.4 are compared, subtracted, and because 14.6 is larger, we keep the negative sign. This results in \(-8.2\).
Visualizing this process can highlight the importance of not just the numbers themselves, but the signs they carry.

Number Line Interpretation

A number line is a powerful tool for visualizing operations involving real numbers. It allows us to see where numbers fall relative to each other and how they combine. Consider the exercise again: \(-11.6 + 6.4 + (-3.0)\).

• Start at zero, move left for negative numbers, and right for positive numbers.
• For \(-11.6\), move 11.6 units to the left.
• Then for \(6.4\), move 6.4 units back to the right.
• Finally, move 3 units to the left for \(-3.0\).

The endpoint on the number line illustrates the sum, which in this case, is \(-8.2\). This visual approach can help clarify the effect of each step in the operation, making more abstract concepts tangible and easier to grasp.