Problem 50 - Beginning and Intermediate Algebra

Question

Find each sum. $$ [-5+(-9)]+[16+(-2)] $$

Step-by-Step Solution

Answer

0

Step 1: Simplify the First Brackets

First, calculate the sum inside the first set of brackets: n1 + n2 = -5 + (-9). Combine the numbers: -5 + (-9) = -14.

Step 2: Simplify the Second Brackets

Next, calculate the sum inside the second set of brackets: n3 + n4 = 16 + (-2). Combine the numbers: 16 + (-2) = 14.

Step 3: Combine the Results

Now, add the results of the two simplified brackets: Sum = -14 + 14. Combine the numbers: -14 + 14 = 0.

Key Concepts

integer operations

Integer operations are the fundamental arithmetic actions we perform using whole numbers, which include positive numbers, negative numbers, and zero.

Addition, subtraction, multiplication, and division are the main operations you will work with.

**Positive and Negative Numbers:**
When adding integers, remember:

• A positive number plus another positive number gives a larger positive number.
• A negative number plus another negative number gives a larger negative number.
• A positive number plus a negative number depends on their absolute values (size without considering the sign). If the positive number is larger, the result is positive; if the negative number is larger, the result is negative.

In our exercise, we see this in action: [-5 + (-9)] and [16 + (-2)]. With the rules in mind:

• -5 + (-9) combines two negatives making a larger negative: -14.
• 16 + (-2) adjusts the positive 16 by subtracting 2, leading to 14.

Understanding these basics will make integer operations less intimidating!

combining like terms

Combining like terms is essential in simplifying expressions. Like terms are terms that have the same variables raised to the same power.

When you combine like terms, you add or subtract them as if they were simple numbers.
Here’s how it looks in our exercise:

• First we deal with the sums inside the brackets: [-5 + (-9)] and [16 + (-2)].
• After these are simplified to -14 and 14 respectively, we combine these two results: -14 + 14.

Combining -14 and 14 gives 0. Essentially, the positive and negative numbers cancel each other out. This shows the power of combining like terms to simplify expressions!

simplifying expressions

Simplifying expressions means making them easier to understand or work with, often by combining like terms and performing basic operations.

Through simplification, mathematical expressions become more manageable, whether for solving equations or understanding the problem.

Our example demonstrates simplification well:

• First, simplify the sums within the brackets: [-5 + (-9)] = -14 and [16 + (-2)] = 14.
• Next, combine these simplified results: -14 + 14.
• Finally, note how -14 adds to 14, resulting in a final simplified result of 0.

The main idea is to break down the expression step by step, simplifying as you go, to reach a clear and concise final answer.