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Chapter 1: Problem 55

Rewrite the group of numbers ordered from least to greatest. $$-17,-19,-15,-18,-20,-10$$

Short Answer

Expert verified
-20, -19, -18, -17, -15, -10.

Step by step solution

01

Listing the Numbers

First, write down the list of numbers provided in the exercise: -17, -19, -15, -18, -20, -10.
02

Understanding Negative Numbers

Recognize that when dealing with negative numbers, the further you are from zero, the smaller the number. For example, -20 is less than -19.
03

Ordering the Numbers

Arrange the numbers from the smallest (most negative) to the largest (least negative). The correct order is: -20, -19, -18, -17, -15, -10.
04

Verifying the Order

Double-check the order by ensuring that each number is larger than the previous one (closer to zero): -20 < -19 < -18 < -17 < -15 < -10.

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Key Concepts

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

Ordering Numbers
Ordering numbers, especially negative ones, might seem tricky, but it鈥檚 all about recognizing their positions relative to zero. With positive numbers, we know that a number is larger if it's further to the right on the number line. However, for negative numbers, the opposite is true. The further left a number is, the smaller it is. In practice:
  • The sequence of ordering from least to greatest for these numbers: -20, -19, -18, -17, -15, and -10 follows this principle.
To double-check your work, compare each number to see if the one that follows is closer to zero. The closer a negative number is to zero, the larger it actually is in value. So, understanding this process helps in correctly arranging the numbers.
Number Line
The number line is an essential tool in mathematics for visualizing the order of numbers, especially when dealing with both positives and negatives. It is a straight line with numbers placed at equal intervals or segments along its length. To understand how numbers are ordered, it鈥檚 helpful to draw a number line. Here鈥檚 why:
  • All numbers to the right are greater than those to the left. This comes in handy when ordering numbers, as we visually determine their positions.
  • Negative numbers appear to the left of zero, meaning they are less than positive numbers or zero itself.
Placing numbers such as -20, -19, -18, -17, -15, and -10 on a number line helps students visually grasp the concept of ordering negative numbers through a simple left-to-right scan.
Understanding Negative Numbers
Grasping the concept of negative numbers is fundamental in mathematics. Negative numbers are less than zero and are typically used to represent a deficit or decrease. Think of them as steps backwards rather than forwards. When one first encounters negative numbers, it's often in a practical context, such as temperature changes, bank overdrafts, or altitudes below sea level. Here鈥檚 what to remember:
  • They are expressed with a minus sign (-), indicating their position below zero on the number line.
  • Ordering them requires comprehension that the number furthest from zero is the least (more negative) and closest to zero is the greatest (less negative).
Remembering these points helps in tackling problems that involve the comparison or ordering of negative numbers effectively.

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