Question

Complete the sentence. The absolute value of \(-7\) is ____________

Short answer

Answer: The absolute value of -7 is 7.

Step-by-step solution

Identify the number

The given number is -7.

Find the absolute value

To find the absolute value of -7, we remove the negative sign. The absolute value of \(-7\) is \(7\). So, the complete sentence is: The absolute value of \(-7\) is 7.

Key concepts

Integers

Integers are a fundamental part of mathematics. They include whole numbers and their negative counterparts. Unlike decimal or fractional numbers, integers are complete values without fractional or decimal parts. The set of integers is represented as \(\mathbb{Z}\) and includes:

• Positive integers like 1, 2, 3, ...
• Negative integers such as -1, -2, -3, ...
• Zero, which is neutral and neither positive nor negative

Integers are often used in everyday life to count, order, and perform basic calculations. One of their key properties is they can represent quantities that can increase or decrease, making them incredibly versatile in addition and subtraction operations. Understanding integers is crucial because they serve as the building blocks for more advanced math topics.

Negative Numbers

Negative numbers are integers that are less than zero. They usually have a minus sign (-) before them. In the context of real-world use, negative numbers can represent losses, debts, or temperatures below zero. The concept of negative numbers can initially be confusing, as they appear to represent 'less than nothing,' when in fact, they are quite useful in many scenarios. For instance:

• In finance, a negative number can denote a debt or loss.
• In thermometers, they are used to show temperatures below the freezing point.
• In sports, they might be used to represent yard losses in American football.

The absolute value of a negative number is always positive. For example, the absolute value of -7 is 7. This concept highlights that the absolute value function disregards the negative sign and focuses purely on the distance from zero on a number line.

Mathematical Operations

Mathematical operations are processes that involve numbers to perform calculations. The main operations are addition, subtraction, multiplication, and division. When working with integers, these operations follow specific rules:

• Addition and Subtraction: Adding a positive number moves you to the right on the number line, while adding a negative number moves you left. Subtracting is the opposite of adding.
• Multiplication: Multiplying two positive or two negative numbers gives a positive result, while multiplying a positive number by a negative one results in a negative product.
• Division: Similar to multiplication, dividing two negatives or two positives results in a positive quotient. Dividing a positive by a negative (or vice versa) gives a negative quotient.

These operations are essential for solving equations and understanding larger mathematical concepts. Grasping how they work with different kinds of numbers, like integers and negative numbers, broadens arithmetic competence.