Problem 44 - Beginning and Intermediate Algebra

Question

Find each sum. $$ [(-8)+(-6)]+14 $$

Step-by-Step Solution

Answer

0.

Step 1: Group the terms inside the parentheses

Firstly, add the numbers within the parentheses: [(-8) + (-6)] + 14.

Step 2: Add the numbers within the parentheses

Combine -8 and -6: -8 + (-6) = -14.

Step 3: Add the result to the remaining number

Now add the result from Step 2 to the remaining number: -14 + 14.

Step 4: Calculate the final sum

Finally, perform the addition: -14 + 14 = 0.

Key Concepts

integer addition

Adding integers is one of the fundamental concepts in math. Integers are whole numbers, and they can be either positive, negative, or zero. For example, -3, 0, and 7 are all integers. Calculating the sum of two integers involves adding their values together.
When working with integers:

• If both integers are positive, their sum is a larger positive number. For example, 5 + 3 = 8.
• If both integers are negative, their sum is a larger negative number. For example, -5 + (-3) = -8.
• If one integer is positive and the other is negative, you effectively subtract the smaller absolute value from the larger absolute value. For example, 5 + (-3) = 2.

These basic rules help us understand how to handle various integer addition scenarios.

negative numbers

Negative numbers are numbers that are less than zero. They are often used to represent loss, debt, or positions to the left of zero on a number line.
In the context of addition:

• When you add two negative numbers, the result is a more negative number. For example, adding -8 and -6, as seen in the exercise, gives -14.
• When adding a negative number to a positive number, you decrease the positive number by the absolute value of the negative number. For instance, adding -4 to 10 results in 6 (10 - 4 = 6).

It's helpful to think of the negative sign as a direction indicator. When you add negative numbers, you're moving further away from zero in the negative direction.

sum calculation

Sum calculation involves finding the total amount by adding numbers together. For integers, follow these simple steps:

1. Identify the numbers to be added. For example, in the exercise, you have -8, -6, and 14.
2. Perform the operations within parentheses first. Combine -8 and -6 to get -14.
3. Add the result to the remaining number. Here, you add -14 and 14.

In our exercise, the computed steps would look like this:

• -8 + (-6) = -14
• -14 + 14 = 0

It’s important to follow the order of operations, especially when dealing with multiple terms. Group and simplify wherever necessary to avoid mistakes.