Problem 20 - Elementary Algebra

Question

Simplify the following problems. $$ 16-18+5 $$

Step-by-Step Solution

Answer

Question: Simplify the given arithmetic expression: 16 - 18 + 5 Answer: 3

Step 1: Identify the order of operations

According to the order of operations, we will perform all additions and subtractions from left to right.

Step 2: Simplify the expression from left to right

Now, we will perform the arithmetic operations from left to right: $$ 16 - 18 + 5 $$ Initially, we will do the subtraction operation (16 - 18): $$ -2 + 5 $$ Now, we proceed with the addition operation (-2 + 5): $$ 3 $$ Finally, we have simplified the expression: $$ 16 - 18 + 5 = 3 $$

Key Concepts

Order of Operations

When solving mathematical expressions, it's crucial to follow a specific sequence known as the order of operations. This ensures that everyone interprets and solves the problems in the same way. For arithmetic operations, we use the acronym PEMDAS as a reminder of the order:

• Parentheses - solve expressions inside parentheses first.
• Exponents - calculate all exponential terms next.
• M/Dultiplication and Division - solve from left to right.
• A/Sddition and Subtraction - perform these last, again from left to right.

In our original exercise, only addition and subtraction are involved, which are ranked equally. Therefore, we handle them sequentially from left to right. This makes following the order of operations crucial for avoiding mistakes.

Arithmetic Operations

Arithmetic operations are basic calculations that form the foundation of mathematics. These include addition, subtraction, multiplication, and division. In the original exercise, we dealt purely with addition and subtraction.

• Subtraction involves taking away a number from another, which can result in a negative number, as seen when subtracting 18 from 16.
• Addition is combining numbers together, making it possible to offset negatives. In the solution, adding 5 to -2 results in a positive outcome of 3.

The key lies in understanding how these operations interact. Arithmetic calculations need to be carried out accurately by following mathematical conventions, including handling negative numbers correctly. This ensures clear reasoning and correct results.

Simplifying Expressions

Simplifying expressions means breaking down complex math expressions into their simplest form. This involves systematically working through arithmetic operations while adhering to the order of operations rules. In our example:

• Start with the initial expression: \(16 - 18 + 5\).
• Solve sequentially from left to right: first, \(16 - 18\), resulting in \(-2\).
• Continue by solving \(-2 + 5\), yielding the final simplified expression: \(3\).

Simplifying expressions makes them easier to understand and relate to real-world problems. The result is a clear, concise answer derived from well-applied mathematical principles. This methodical approach ensures that even complex expressions are made manageable and comprehensible.