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Chapter 1: Problem 68

Find the absolute value. $$|7-11|$$

Short Answer

Expert verified
The absolute value of |7-11| is 4.

Step by step solution

01

Perform the Subtraction

First, subtract 11 from 7 to get: \(7-11 = -4\)
02

Determine the Absolute Value

Take the absolute value of the resulting number \(|-4|\). The absolute value of any number is always non-negative. Therefore, the absolute value of -4 is 4.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Understanding Subtraction
Subtraction is one of the basic arithmetic operations involving finding the difference between two numbers. It works by taking one number away from another. For example, when we say "7 minus 11," we're asking how much 7 would change if we took away 11 from it. Let's break down this process:
  • Identify the two numbers involved. Here, they are 7 and 11.
  • Subtract the second number (11) from the first number (7).
  • The result of this operation can be a positive number, zero, or even a negative number.
In this case, subtracting 11 from 7 results in \( 7-11 = -4 \). This operation yields a negative number because 11 is greater than 7.
Exploring Negative Numbers
Negative numbers are a fascinating part of our number system. They are opposite to positive numbers and are located to the left of zero on a number line. Negative numbers have a "minus" sign (-) in front of them. Here are some essential points about negative numbers:
  • Negative numbers represent values less than zero.
  • They are used to denote loss, decrease, or below zero measurements such as temperatures below freezing.
  • In arithmetic, subtracting a larger number from a smaller one results in a negative number.
When we subtracted 11 from 7, the result, \( -4 \), was negative because we tried to take away more than what we started with.
Using the Number Line
The number line is a straightforward visual tool that helps to illustrate numbers, their relationships, and operations like subtraction. It's a horizontal line with integers placed at intervals along it:
  • Zero is typically in the center.
  • Positive numbers lie to the right of zero.
  • Negative numbers lie to the left of zero.
Let's imagine our example of subtracting 11 from 7 on the number line. Start at the point marked 7, and move 11 units to the left. After moving left 11 spaces, you'll land on -4. The position -4 is our result. The number line makes it easy to visualize why subtracting a bigger number from a smaller one results in a negative outcome.

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