Problem 52 - Algebra for College Students

Question

Simplify each of the numerical expressions. $$18+17-9-2+14-11$$

Step-by-Step Solution

Answer

The simplified expression is 27.

Step 1: Group the Numbers

Identify the types of operations involved in the expression. The expression consists of addition and subtraction: \[ 18 + 17 - 9 - 2 + 14 - 11 \]

Step 2: Simplify Additions

First, perform the additions: \[ 18 + 17 + 14 = 49 \] Add 18, 17, and 14 together.

Step 3: Simplify Subtractions

Now, perform the subtractions: \[ 49 - 9 - 2 - 11 \] You can simplify this step-by-step as follows: - \(49 - 9 = 40\)- \(40 - 2 = 38\)- \(38 - 11 = 27\)

Step 4: Write the Simplified Answer

The simplified answer is the result of the previous steps, which is 27.

Key Concepts

Addition and Subtraction

Addition and subtraction are fundamental operations in mathematics. They help to determine the total or the difference between numbers. In our numerical expression, we deal with both operations.
The rules are simple:

• When adding, combine numbers to create a sum.
• When subtracting, remove the value of one number from another.

Dealing with these operations also involves understanding the order. In any expression, perform the operations from left to right. This is crucial in obtaining the correct answer when you have a mix of both.
This is precisely what we practiced in the original exercise, where we first added the numbers before moving to subtraction. Always aim to simplify expressions by addressing one operation at a time to avoid errors.

Step-by-Step Solutions

Taking each step carefully is important when simplifying numerical expressions. It is a common approach in mathematics where complex problems are broken down into manageable steps.
Here's how you can tackle a step-by-step solution:

• Identify and group similar operations (addition or subtraction, in this case).
• Focus on completing one type of operation before moving onto the next.
• Maintain an accurate sequence of solutions to ensure that the final answer is correct.

In our example, we first summed up all the numbers marked for addition, then proceeded to tackle the subtractions. This approach reduces confusion and mistakes. Finishing one operation category before the next is like checking tasks off a list: methodical and effective.

Basic Arithmetic Operations

Before diving deeper into mathematics, one must master basic arithmetic operations. These include addition, subtraction, multiplication, and division.
In our exercise, focus is placed on addition and subtraction:

• Addition combines values to find a sum.
• Subtraction eliminates values from one another to find a difference.

This operation foundation not only helps solve school problems but also assists in real-world applications like budgeting or measuring. Practicing arithmetic with step-by-step precision lays the groundwork for tackling more complex mathematical concepts in the future.
Thus, mastering simplification of expressions using these operations as shown ensures both accuracy and efficiency. Always focus on one aspect of arithmetic, and with practice, speed and comprehension will inevitably follow.