Problem 49 - Beginning and Intermediate Algebra

Question

Find each sum or product. $$ 843+627+(-43)+(-27) $$

Step-by-Step Solution

Answer

1400

Step 1: Identify positive and negative numbers

List out the positive numbers: 843 and 627. Then list out the negative numbers: -43 and -27.

Step 2: Add positive numbers

Calculate the sum of the positive numbers: 843 + 627. This equals to: 1470.

Step 3: Add negative numbers

Now, calculate the sum of the negative numbers: -43 + (-27). This equals to: -70.

Step 4: Combine the results

Finally, add the sum of the positive numbers to the sum of the negative numbers: 1470 + (-70). This results in: 1400.

Key Concepts

Addition of Integers

When adding integers, the process is simple: you combine the values based on their signs. Let's break it down.

• If both integers are positive, simply add them.
• If both integers are negative, add their absolute values and then apply a negative sign to the result.
• If one integer is positive and the other is negative, subtract the smaller absolute value from the larger absolute value, and apply the sign of the larger absolute value's integer to the result.

To illustrate, when you have the problem 843 + 627 + (-43) + (-27), we first group the positive numbers together (843, 627) and the negative numbers together (-43, -27) for easier calculation.

Positive and Negative Numbers

Understanding positive and negative numbers is crucial. Positive numbers are numbers greater than zero, and negative numbers are less than zero. Here's more detail on how to handle them:

• Positive Numbers: These numbers are straightforward; for example, 843 and 627 are positive.
• Negative Numbers: These have a minus sign in front of them, like -43 and -27. When added, the negative sign must be considered during calculation.

The negative numbers' addition follows the rule of adding their absolute values and applying a negative sign, as we've done in Step 3 with -43 + (-27) to get -70.

Combining Sums

After grouping and calculating separately, combining sums brings everything together. This step shows the final addition of positive and negative sums. Let's revise how it's done.

• Find the sum of positive numbers: 843 + 627 = 1470.
• Find the sum of negative numbers: -43 + (-27) = -70.
• Combine these sums: add the positive result to the negative result. Here, it is 1470 + (-70).

When adding these, think of moving along a number line. Starting at 1470 and moving 70 units to the left (since -70 is negative), you reach 1400. Thus, the final result is 1400.