Problem 51 - Algebra for College Students

Question

Simplify each of the numerical expressions. $$16+9-4-2+8-1$$

Step-by-Step Solution

Answer

The simplified expression is 26.

Step 1: Identify the Expression

The given numerical expression is \(16 + 9 - 4 - 2 + 8 - 1\). Our task is to simplify this expression by adding and subtracting the numbers sequentially.

Step 2: Add the First Two Numbers

Start by adding the first two numbers in the expression. Calculate \(16 + 9\) which equals 25.

Step 3: Subtract the Next Number

From the result obtained in Step 2, subtract the next number: \(25 - 4 = 21\).

Step 4: Subtract the Following Number

Continue by subtracting the next number: \(21 - 2 = 19\).

Step 5: Add the Subsequent Number

Next, add the following number to the current result: \(19 + 8 = 27\).

Step 6: Subtract the Final Number

Finally, subtract the last number to complete the simplification: \(27 - 1 = 26\).

Key Concepts

Understanding Addition

Addition is one of the fundamental operations in arithmetic that combines two or more numbers to yield a single number, called the sum. In the expression from the exercise, addition involves calculating the sum of numbers in a sequence. Here's a simple breakdown:

• Look for numbers that are to be added in a sequence, starting from the left.
• Add the numbers to get an intermediate result. If there are more numbers, continue adding to the result.

For example, in the sequence given, we begin by adding the first two numbers: \(16 + 9\) resulting in \(25\). This step sets the foundation for the rest of the operations, as we build on this initial sum.

Mastering Subtraction

Subtraction is another primary arithmetic operation that involves taking away a number from another, resulting in the difference. In the context of a sequential expression like the given, subtraction occurs right after addition or directly follows another subtraction:

• Identify the number to be subtracted from the current result or sum.
• Calculate the difference and proceed to the next operation in sequence.

Following the given expression, after achieving the sum of the first two numbers, \(25 - 4\) is computed, equaling \(21\). Subsequent subtraction steps involve continuously updating the result, as shown by \(21 - 2 = 19\), ensuring the process is orderly and straightforward.

Step-by-Step Solutions Made Easy

Breaking down a mathematical expression into step-by-step solutions is crucial for understanding how operations work in a sequence. It simplifies complex expressions by tackling each part one at a time, using a consistent methodology:

• Begin with the initial operation and proceed methodically through to the final solution.
• Check each operation as you proceed, ensuring all steps are correctly calculated.
• Use each result as a stepping stone for the next calculation.

This approach empowers learners to manage and simplify expressions without feeling overwhelmed. By the end of the given exercise, starting from the addition of \(16 + 9\) to final subtraction, all operations are interdependent, making the progression crucial for finding the final solution of \(26\). Thus, step-by-step allows learners to gain confidence and skills essential for handling more complex expressions in the future.