Problem 205 - Prealgebra

Question

In the following exercises, simplify. $$ 2,015-1,993 $$

Step-by-Step Solution

Answer

22

Step 1: Identify the numbers

The two numbers involved in the subtraction are 2015 and 1993.

Step 2: Set up the subtraction

Write the equation as: 2015 - 1993

Step 3: Perform the subtraction

Subtract 1993 from 2015: 2015 - 1993 = 22

Step 4: Write the simplified answer

The simplified answer to the subtraction problem is 22.

Key Concepts

Subtraction

Subtraction is one of the four basic arithmetic operations and is essentially the process of taking one quantity away from another. Consider the exercise given, where we're asked to find the difference between 2,015 and 1,993. To solve this:

• First, identify the numbers involved: 2,015 (minuend) and 1,993 (subtrahend).
• Set up the equation as: 2015 - 1993.
• Perform the subtraction by borrowing if necessary and subtracting each digit starting from the rightmost digit to the left.
• The answer is 22.

Subtraction simplifies determining how much less one value is compared to another. The key lesson is to align the numbers properly and subtract digit-by-digit.

Arithmetic

Arithmetic is the branch of mathematics that deals with numbers and basic operations like addition, subtraction, multiplication, and division. In our example, we specifically deal with subtraction, an operation that helps in finding the difference.

In general, arithmetic operations follow specific rules and depending on the complexity of the values, might involve carrying over or borrowing. Here's a general approach to arithmetic using subtraction, modeled from our example:

• Write the numbers in a vertical format aligning units, tens, hundreds, etc.
• If the value in a place value of the minuend is less than the corresponding value of the subtrahend, borrow from the next higher place value.
• Subtract each digit accordingly to get the final result.

Mastering basic arithmetic is crucial as it forms the foundation for solving more complex mathematical problems.

Simplification

Simplification in mathematics refers to the process of reducing expressions or equations to their simplest form. When we simplify, we make problems easier to handle, which helps in better understanding and quicker problem-solving.

For subtraction, simplification means performing the specific operation to find the single value that represents the difference between numbers. As seen in our example:

• We start with two numbers, 2015 and 1993.
• Subtraction yields 22 as the simplified result.

The goal is to reduce the original expression to its simplest, most understandable form. This step is essential in problem-solving as it helps in analyzing and interpreting the core mathematical idea without unnecessary complexity.