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Chapter 1: Problem 88

List in order from least to greatest. $$13,-12,5,-17$$

Short Answer

Expert verified
-17, -12, 5, 13

Step by step solution

01

- Identify all numbers

List the given numbers: 13, -12, 5, -17.
02

- Identify negative and positive numbers

Negative numbers: -12 and -17. Positive numbers: 13 and 5.
03

- Order negative numbers

Negative numbers in ascending order: -17, -12.
04

- Order positive numbers

Positive numbers in ascending order: 5, 13.
05

- Combine ordered lists

Combine the ordered negative and positive numbers to get the final list: -17, -12, 5, 13.

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Key Concepts

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

Negative Numbers
Negative numbers are numbers less than zero. They are represented with a minus sign (-) in front of them.
When you see a negative number, it means it is to the left of zero on the number line. This makes them smaller than any positive number.
In our example, -12 and -17 are negative numbers.
To order negative numbers, the one with the greater absolute value is smaller because it is further left on the number line.
So, -17 is smaller than -12. To summarize:
  • Negative numbers have a minus sign (-).
  • They are less than zero.
  • Further left on the number line means a smaller value.
Positive Numbers
Positive numbers are numbers greater than zero and are typically written without any sign in front of them.
These numbers are to the right of zero on the number line and are larger than any negative numbers.
In our example, 13 and 5 are positive numbers.
When ordering positive numbers, the usual understanding is that the larger the number, the further right it is on the number line.
So, the number 5 comes before 13. To summarize:
  • Positive numbers have no sign or a plus sign (+).
  • They are greater than zero.
  • Further right on the number line means a greater value.
Ascending Order
Ascending order means arranging numbers from the smallest to the largest.
When dealing with both negative and positive numbers, start with the smallest negative number and work your way up to the largest positive number.
First, you list your negative numbers in ascending order, followed by your positive numbers in ascending order.
In our exercise, combining -17, -12 (negatives) with 5, 13 (positives) in ascending order would give us -17, -12, 5, 13. To summarize:
  • Ascending order means 'smallest to largest'.
  • Negative numbers come before positive numbers.
  • Order each group (negatives and positives) separately before combining them.

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