Problem 20 - Elementary Algebra

Question

For the following exercises, perform the indicated operations. $$ 2-15 $$

Step-by-Step Solution

Answer

Answer: -13

Step 1: Identify the numbers and operation

In this exercise, the two numbers are 2 and 15, and the operation is subtraction symbolized by the minus sign (-).

Step 2: Subtract 15 from 2

To subtract 15 from 2, subtract each digit of 15 from the corresponding digit in 2 starting from the rightmost digit. Since 2 is smaller than 15, we will have to borrow from the left digit. However, since there is no digit on the left side of 2, the result will be a negative number.

Step 3: Write the final answer

Since the subtraction results in a negative number, we write the difference as follows: $$ 2-15 = -13 $$ The final answer is -13.

Key Concepts

Negative numbers

Understanding negative numbers is crucial as they are widely used in various forms of mathematics, especially when dealing with operations like subtraction. Negative numbers are numbers less than zero, and they are typically shown with a minus sign (-) in front of them. In our everyday life, they can be used to represent things like temperatures below freezing or declines in bank account balances. For instance, if you owe someone $13 and have no money, it can be represented as -13. With negative numbers, there are specific rules for operations:

• When subtracting a positive number from a smaller positive number, the result is negative.
• Adding a negative number is equivalent to subtracting a positive number.

This explanation helps explain why the result of the operation in the exercise is -13.

Operations in arithmetic

Arithmetic operations are the basic building blocks of mathematics and include addition, subtraction, multiplication, and division. Subtraction is one of these fundamental operations and involves finding the difference between two numbers or values. In the exercise given, we see a subtraction statement: 2 - 15. This operation means you are removing more value (15) from a smaller value (2), which results in a negative outcome.
Basic rules of subtraction entail:

• Always move from left to right when performing operations.
• If the number you are trying to subtract is larger than the starting number, the result becomes a negative number.

The ability to manipulate and understand these operations forms the foundation for dealing with more complex mathematical problems, like those found in elementary algebra.

Elementary algebra

Elementary algebra prepares students to handle variables and unknowns in equations. It extends beyond simple arithmetic to include operations with variables and finding solutions to equations. In our exercise, while you are not directly using variables, the principle behind handling negative results and performing basic operations forms the basis of what you'll encounter in algebra.
In algebra, you'll often need to:

• Solve for unknown values.
• Manipulate equations that include both numbers and variables.

Understanding subtraction, even as simple as 2 - 15, aids in grasping how to balance equations where you might subtract terms to isolate a variable. This foundational understanding is what makes elementary algebra an essential extension of arithmetic.