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Chapter 3: Problem 114

Write the given numbers in order from smallest to largest. $$-|2|,-(-8), 6,|1|,-7$$

Short Answer

Expert verified
The numbers in order from smallest to largest are: -7, -2, 1, 6, 8.

Step by step solution

01

Interpret the values

First, interpret the value of each given numeric expression. The absolute value of a number is always non-negative, therefore -|2| will be -2. The expression -(-8) is a double negation, making it positive, so it becomes 8. The absolute value of 1, |1| is 1. The other numbers do not contain absolute values or negations, so no changes are needed for those.
02

Determine Numeric Values

Now, determine the numeric value of each, which are: -2, 8, 6, 1, and -7 respectively.
03

Sort in Ascending Order

Finally, arrange these numbers in order from the smallest to the largest. The smallest number will be the most negative, -7, and the largest number will be the most positive, 8.

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Key Concepts

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

Absolute Value
Absolute value is a concept that helps us understand the magnitude of a number, ignoring its sign. Simply put, the absolute value of a number is its distance from zero on a number line, regardless of direction. For example, the absolute value of 2 is 2, and the absolute value of -3 is also 3. This is denoted by placing the number inside vertical bars, like this: \(|x|\).
In our exercise, \(|2|\) equals 2, and then it is negated to become -2, since it is preceded by a negative sign. Similarly, \(|1|\) equals 1. Understanding absolute value is crucial because it ensures we always consider the non-negative distance to zero, which helps when ordering numbers.
Negative Numbers
Negative numbers are numbers less than zero. They represent quantities with a direction opposite to positive numbers. For instance, in temperatures, \(-7掳\) is colder than \(-2掳\). On the number line, negative numbers are found to the left of zero.
In mathematical expressions, a negative sign indicates a number that has been subtracted from zero. For example, -2 in our exercise refers to two units less than zero. Understanding negative numbers is crucial for problems involving ordering, as they indicate values less than positive numbers.
Number Line
A number line is a simple yet powerful visual tool for understanding and comparing numbers. It consists of a straight line with numbers placed at equal intervals, where each point corresponds to a number. Zero is usually at the center, with negative numbers extending to the left and positive numbers to the right.
The number line helps you visualize relationships between numbers, especially when dealing with positive and negative values. For example, in the exercise, placing -7, -2, 1, 6, and 8 on a number line allows you to easily see their order from left (smallest) to right (largest). This visualization simplifies the process of arranging numbers in order.
Ascending Order
Ordering numbers is about arranging them based on their value. When we say 'ascending order,' we mean listing numbers from the smallest to the largest. This involves placing the most negative or smallest value first and the most positive or largest value last.
Let's consider our exercise numbers: -7, -2, 1, 6, and 8. By re-arranging these numbers from the most negative to the most positive, we get an ordered list of: \(-7, -2, 1, 6, 8\). Understanding how to arrange numbers in ascending order is essential for many math problems, including those involving data analysis and interpretation.

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Most popular questions from this chapter

Subtract. $$(-9)-(-3)$$

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