Problem 42 Write the given numbers in order... [FREE SOLUTION]

Chapter 3: Problem 42

Write the given numbers in order from smallest to largest. $$6,-9,-12,8$$

Short Answer

Expert verified

The numbers arranged from smallest to largest are: -12, -9, 6, 8. Negative numbers are always smaller than positive numbers.

Step by step solution

Identify Positive and Negative Numbers

In the list of numbers $6, -9, -12, 8$, there are two positive numbers $6, 8$ and two negative numbers $-9, -12$

Arrange Negative Numbers

When arranging negative numbers, the number with the biggest absolute value is the smallest. So, among $-9, -12$, $-12$ is smaller.

Arrange Positive Numbers

For positive numbers, the number with the smallest absolute value is the smaller. So, among $6, 8$, $6$ is smaller.

Merge Arranged Lists

The all numbers ordered from smallest to largest are: negative numbers $-12, -9$, followed by positive numbers $6, 8$.

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Key Concepts

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

Positive and Negative Numbers

Numbers can be positive or negative. Understanding this is crucial when ordering any list of numbers.
Positive numbers are greater than zero. They appear to the right of zero on a number line. For instance, in the numbers given, both 6 and 8 are positive. They increase as they move rightward.
Negative numbers, on the other hand, are less than zero. They appear to the left of zero on a number line. In our exercise, -9 and -12 are negative, meaning they decrease as you move left.
Thus on a number line, any positive number will always be larger than any negative number. Remembering this is key when you are tasked with sorting a mixture of positive and negative values.

Absolute Value

The absolute value of a number tells you how far it is from zero on a number line, regardless of direction. This is why a positive or negative sign doesn't matter when comparing absolute values.
For instance, the absolute value of both 6 and -6 is 6. Both numbers are the same distance from zero, but in opposite directions.
When ordering numbers, we often consider their absolute values, especially with negatives.

Negative numbers are smaller the larger their absolute value.
Positive numbers simply increase as their values increase.

So for our exercise, -12, with a larger absolute value than -9, is deemed smaller on the number line.

Number Line Concepts

A number line is a visual representation of numbers along a straight line. It is an excellent tool for understanding the relative size of numbers, whether they are positive or negative.
Numbers increase as you move to the right and decrease as you move to the left. Zero is the central point separating positive from negative numbers.

All numbers to the left of zero are negative.
All numbers to the right of zero are positive.

In terms of ordering, the process involves placing the furthest left numbers first up to the farthest right. This logic dictates that when working with negatives, you look at the absolute values to determine the initial order, then merge with the positive numbers as we did with the list: -12, -9, 6, 8.

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91影视

Write the given numbers in order from smallest to largest. $$6,-9,-12,8$$

Short Answer

Step by step solution

Identify Positive and Negative Numbers

Arrange Negative Numbers

Arrange Positive Numbers

Merge Arranged Lists

Key Concepts

Positive and Negative Numbers

Absolute Value

Number Line Concepts

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