Problem 43 - Elementary Algebra

Question

For the following exercises, perform the indicated operations. $$ 0-15 $$

Step-by-Step Solution

Answer

Answer: -15

Step 1: Subtract 15 from 0

To perform 0-15, just subtract 15 from 0: $$ 0-15 = -15 $$ The answer is -15.

Step 2: Identify the algebraic structure

Determine the type of algebraic problem.

Step 3: Apply algebraic techniques

Use factoring, expanding, or systematic methods.

Step 4: Simplify and solve

Simplify expressions and solve for unknowns.

Step 5: State the result

Write the final answer.

Key Concepts

Negative Numbers

Negative numbers are numbers less than zero, often used to represent a loss, decrease, or a position on a number line below zero. For example, when looking at a thermometer, temperatures below zero degrees Celsius are negative. In mathematics, negative numbers are crucial for operations such as subtraction when a larger number is subtracted from a smaller number.

They are indicated by a minus sign (-) before the number. An easy way to think of negative numbers is as owing something or as positions below a starting point of zero. When you have 0 and you subtract a positive number like 15, you move to the left on the number line, which is usually indicated by a negative result, in this case -15.

Negative numbers are not just for special applications; they appear naturally when performing various operations, especially subtraction and solving equations.

Basic Arithmetic Operations

Arithmetic operations are the backbone of mathematics and include addition, subtraction, multiplication, and division. Each of these operations has its own rules and applications, helping us to calculate and solve mathematical problems.

• Addition: Combines two numbers together to get a sum.
• Subtraction: Removes one number from another to find the difference, like in 0 - 15.
• Multiplication: Involves combining equal groups, seen as repeated addition.
• Division: Splitting a number into equal parts or groups.

In the example 0 - 15, subtraction is the arithmetic operation used. This operation tells us how much less or more one number is compared to another. When dealing with 0 - 15, we're basically finding out how far below zero 15 is on the number line, resulting in the answer -15.

A firm grasp of basic arithmetic operations is crucial for progressing in math, as they are foundational tools for more complex mathematical ideas.

Integer Operations

Understanding how to operate with integers, whole numbers that include positive numbers, negative numbers, and zero, is essential. Integer operations follow specific rules depending on whether they are addition, subtraction, multiplication, or division. With integers, subtraction is particularly interesting when it involves negative outcomes.

The operation 0 - 15 uses integers, where 0 is an integer and 15 is a positive integer. When a positive integer like 15 is subtracted from zero, the result is negative, which is mathematically expressed as -15. This reflects the rule that subtracting a larger integer from a smaller one produces a negative result.

Understanding these operations helps in dealing with everyday problems involving gains and losses, altitude, temperature scales, and much more. Mastery of integer operations also sets the stage for algebra and other advanced mathematical studies.