Problem 72 - Algebra 1

Question

Find the difference. $$ 17-6 $$

Step-by-Step Solution

Answer

The difference between 17 and 6 is 11.

Step 1: Identify the subtraction operation

The given exercise is a simple subtraction problem where the larger number (17) is subtracted from the smaller number (6). The subtraction operation is symbolized by the '-' sign.

Step 2: Execute the subtraction operation

Subtracting 6 from 17 can be executed directly as it doesn't involve any carrying over numbers or other complex operations. The operation is then performed as follows: \(17 - 6 = 11\)

Key Concepts

Basic Arithmetic

Basic arithmetic is the foundation of all mathematics and includes operations such as addition, subtraction, multiplication, and division. These operations are the building blocks for more complex mathematical concepts. Subtraction, specifically, is one of the crucial components of basic arithmetic used to determine the difference between numbers.
Understanding the principles of arithmetic is essential for everyday life, as it allows us to calculate expenses, understand distances, and perform a myriad of other practical tasks. When approaching subtraction, one typically starts with larger numbers and 'takes away' a smaller quantity to find the remainder, or difference.

Performing Subtraction

Performing subtraction involves finding the difference between two numbers. When subtracting two numbers, it's important to start with the larger number, referred to as the minuend, and subtract the smaller number, called the subtrahend. The result of this operation is known as the difference.

In the exercise \( 17 - 6 \), the number 17 is the minuend, and 6 is the subtrahend. The steps to solve this problem are straightforward: simply take the subtrahend away from the minuend. The key to successful subtraction is to ensure accurate counting back or removal, which in this case, leads to a difference of 11.
Performing subtraction is a skill that improves with practice. Using number lines, counters, or drawing models can help visualize the process, making the concept clearer and aiding in achieving the correct answer.

Arithmetic Operations

Arithmetic operations form the basis of most mathematical calculations. These operations include addition, subtraction, multiplication, and division. Each operation has rules and properties that dictate how numbers interact with one another. Subtraction, for example, is not commutative, which means that changing the order of the numbers alters the result.

In the context of arithmetic operations, being familiar with terms like minuend, subtrahend, and difference is valuable. Moreover, understanding that subtraction can be seen as the inverse operation of addition is crucial. For instance, if we have \( 17 - 6 = 11 \), we know that \( 11 + 6 = 17 \), illustrating the close relationship between these two operations. To master arithmetic operations, consistency and practice are key, as these skills are not only academic but practical and necessary for daily activities.