Problem 47 - Algebra 1: Concepts and Skills

Question

Perform the indicated operation. $$ 2.5-0.5 $$

Step-by-Step Solution

Answer

The result of the operation 2.5 - 0.5 is 2.0.

Step 1: Identify the Numbers to Subtract

The numbers that will be subtracted are 2.5 and 0.5.

Step 2: Perform the Subtraction

Subtract 0.5 from 2.5. When subtracting decimal numbers, align the numbers by their decimal points for clarity and perform the subtraction operation as when subtracting whole numbers. Hence, the result is \(2.5 - 0.5 = 2.0\).

Key Concepts

Subtraction

Subtraction is one of the basic arithmetic operations, and understanding it forms a foundation for more complex calculations. At its core, subtraction is about finding the difference between two numbers. It involves taking one quantity away from another. For example, if you have 5 apples and you eat 2, you are subtracting 2 from 5, leaving you with 3 apples.

When performing subtraction, it’s crucial to align numbers correctly. This ensures that you subtract each digit from the correct place value, such as units, tens, or hundreds. In simpler terms, align the numbers vertically so that digits in the same position are lined up. This method helps prevent mistakes, particularly in problems involving larger numbers or decimals.

Moreover, subtraction isn't limited to just whole numbers. You can subtract fractions, decimals, and even negative numbers. Each of these requires slightly different techniques, but the underlying principle remains the same: finding the difference.

Decimal Numbers

Decimal numbers are numbers that include a decimal point to represent a fraction of a whole number. They are used in many everyday situations, such as measuring weight, height, or calculating money.

It’s important to understand the role of each digit’s place value when working with decimals. Each position to the right of the decimal point represents a fractional part of a whole number: tenths, hundredths, thousandths, and so on.

• The first digit to the right of the decimal is the tenths place.
• The second is the hundredths place.
• Further places continue as thousandths, ten-thousandths, etc.

Understanding place value is critical when performing any arithmetic operations with decimals, such as addition, subtraction, multiplication, and division. Without this understanding, it’s easy to make mistakes like misaligning decimals or misunderstanding the size of a number.

Arithmetic Operations

Arithmetic operations encompass a set of basic mathematical operations that include addition, subtraction, multiplication, and division. These operations are foundational in mathematics and are used in virtually every calculation.

Each arithmetic operation serves a distinct purpose:

• Addition combines quantities together.
• Subtraction finds the difference between quantities by removing the smaller from the larger.
• Multiplication involves repeated addition of the same number.
• Division distributes a number into equal parts.

Understanding how to execute these operations with different types of numbers, such as integers, fractions, and decimals, is crucial for solving a wide range of mathematical problems. For example, combining decimal numbers in subtraction requires aligning the decimal points before subtracting, ensuring each place value is correctly computed as demonstrated in the original problem (e.g., 2.5 - 0.5). This alignment is pivotal in maintaining the accuracy of the result.