Problem 50 - Beginning and Intermediate Algebra

Question

Find each sum or product. $$ 1846+1293+(-46)+(-93) $$

Step-by-Step Solution

Answer

3000

Step 1: Identify and Group Numbers

First, identify the numbers to be added: 1846, 1293, -46, and -93. It is easier to group positive numbers together and negative numbers together.

Step 2: Add Positive Numbers

Add the positive numbers first: 1846 + 1293.Calculate: 1846 + 1293 = 3139.

Step 3: Add Negative Numbers

Next, add the negative numbers: -46 + -93.Calculate: -46 + -93 = -139.

Step 4: Combine Sums

Now, combine the sum of positive numbers and the sum of negative numbers: 3139 + (-139).Calculate: 3139 - 139 = 3000.

Key Concepts

Addition of Integers

When adding integers, it's important to manage both positive and negative numbers correctly. The key process involves combining positive numbers first and then adding any negative numbers separately. This method helps to clarify the overall result. For example, in the problem, the integers are 1846, 1293, -46, and -93. We first add the positive integers (1846 + 1293) to get 3139. Then, we handle negative integers separately and sum them (-46 + -93) to get -139. Finally, we combine the results: 3139 + (-139). It illustrates how we can simplify complex additions by breaking them down systematically.

Grouping of Numbers

Grouping numbers effectively can simplify calculations. Separate positive and negative numbers to streamline the process. This strategy involves:

• Identifying all positive and negative numbers.
• Adding positive numbers first.
• Adding negative numbers together.

In our exercise, the positive numbers (1846 and 1293) are grouped and added first to get 3139. Then, the negative numbers (-46 and -93) are grouped and summed to get -139. This approach allows us to clearly see the effect of positive and negative contributions to the final result, making complex calculations easier to handle.

Negative Numbers

Dealing with negative numbers can be tricky, but understanding their properties helps. When we add negatives, it's like subtracting their absolute values from the total. For instance:

• Negative plus negative results in a larger negative number: \( -46 + -93 = -139 \).
• A positive number plus a negative number results in a smaller number: \( 3139 + (-139) = 3000 \).

In the given exercise, we add negative integers separately (-46 and -93) to get -139. When combining this with the previously summed positive integers (3139), we effectively subtract 139 from 3139. This simplified example shows how we integrate negative quantities into our overall sum, leading to 3000 as the final result.