Problem 8
Question
Perform the indicated subtraction. $$2-15$$
Step-by-Step Solution
Verified Answer
The result of \(2 - 15\) is -13.
1Step 1: Identify the Numbers to Subtract
The numbers given are 2 and 15.
2Step 2: Perform the Subtraction
Subtract 15 from 2. Write the subtraction as \(2 - 15 = -13\) Since 2 is less than 15, the result is a negative number.
Key Concepts
Negative NumbersArithmetic OperationsBasic Algebra
Negative Numbers
Negative numbers are a fundamental concept in mathematics representing values less than zero. They're indicated by a minus sign (-) before the number. In the context of everyday situations, negative numbers can represent debt, temperatures below freezing, or depths below sea level.
In arithmetic, when you perform operations with negative numbers, it's crucial to understand the rules that govern them to obtain the correct result. For instance, subtracting a larger positive number from a smaller positive number, like in the exercise \(2 - 15\), results in a negative number. This is because we are essentially moving 15 units to the left from 2 on the number line, landing at \-13. This concept can initially be confusing, but visualising a number line can be immensely helpful in understanding negative numbers.
In arithmetic, when you perform operations with negative numbers, it's crucial to understand the rules that govern them to obtain the correct result. For instance, subtracting a larger positive number from a smaller positive number, like in the exercise \(2 - 15\), results in a negative number. This is because we are essentially moving 15 units to the left from 2 on the number line, landing at \-13. This concept can initially be confusing, but visualising a number line can be immensely helpful in understanding negative numbers.
Arithmetic Operations
Arithmetic operations are basic mathematical operations that include addition, subtraction, multiplication, and division. These operations are essential in everyday calculations and form the foundation of more complex mathematical concepts.
When subtracting two numbers, as in the given exercise (\(2-15\)), you are finding the difference between them. If the number being subtracted is larger than the number it is being subtracted from, the result is a negative number. Subtraction can be seen as taking away or moving backward on the number line. Understanding how these operations work with both positive and negative numbers is crucial for students as it is frequently applied not just in math but in real-life contexts as well.
When subtracting two numbers, as in the given exercise (\(2-15\)), you are finding the difference between them. If the number being subtracted is larger than the number it is being subtracted from, the result is a negative number. Subtraction can be seen as taking away or moving backward on the number line. Understanding how these operations work with both positive and negative numbers is crucial for students as it is frequently applied not just in math but in real-life contexts as well.
Basic Algebra
Basic algebra is the branch of mathematics that uses letters and symbols to represent numbers and quantities in formulas and equations. It allows for generalizing arithmetic operations and solving a wide range of problems.
When we solve an equation like the subtraction exercise in question, \(2 - 15 = -13\), we are performing an arithmetic operation within an algebraic framework. By applying the rules of arithmetic operations to a simple algebraic equation, it can be correctly solved, leading to a negative value as the answer. Algebra provides the tools to analyze and solve more complex problems by abstracting these basic operations. It's important to get comfortable with this abstraction early on, as it's foundational for all math that follows.
When we solve an equation like the subtraction exercise in question, \(2 - 15 = -13\), we are performing an arithmetic operation within an algebraic framework. By applying the rules of arithmetic operations to a simple algebraic equation, it can be correctly solved, leading to a negative value as the answer. Algebra provides the tools to analyze and solve more complex problems by abstracting these basic operations. It's important to get comfortable with this abstraction early on, as it's foundational for all math that follows.
Other exercises in this chapter
Problem 8
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Evaluate each expression for \(x=4\). $$\frac{36}{x}$$
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