Ordering Integers
Learn how to arrange integers from least to greatest and greatest to least.
Definition
- Ascending order (least to greatest): Start with the smallest and go up
- Descending order (greatest to least): Start with the largest and go down
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Worked Examples
Order these integers from least to greatest: , , , ,
Find the most negative number
Compare and : since is further left on the number line → is the smallest
Find the next negative number
is the only other negative number → comes second
Place zero
Zero is between negative and positive numbers → comes third
Order the positive numbers
Compare and : since → , then
Answer:
Common Mistakes
Ordering , , as (thinking larger digit means larger number)
Why it's wrong: With negative numbers, the larger the digit, the smaller the value. is further from zero in the negative direction.
Correct: Ascending order: (furthest left to furthest right on the number line)
Forgetting where to place zero
Why it's wrong: Zero is the boundary between positive and negative numbers.
Correct: Zero always comes after all negative numbers and before all positive numbers in ascending order.
Confusing ascending and descending
Why it's wrong: The terms can be mixed up, especially when nervous.
Correct: Ascending = going UP (like climbing stairs): smallest to largest. Descending = going DOWN: largest to smallest.
Interactive Visual
Click on the number line to find the target number. Test your skills!
Interactive Sandbox
Expression Calculator
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History
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Practice Problems
16 problemsWhich list shows the integers in ascending order (least to greatest)?
Why It Matters
- Weather forecasting: Ranking temperatures from coldest to warmest days
- Sports standings: Ordering golf scores (where negative is better!)
- Elevations: Ranking locations from lowest to highest altitude
- Finance: Sorting account balances or comparing debts
Real World Applications
Weather and Climate
Meteorologists order temperatures to find the coldest and warmest days of the week or to track temperature trends.
Example:
Weekly lows: Mon , Tue , Wed , Thu , Fri . Ordered coldest to warmest:
A weather report shows these temperatures for five mountain peaks: Peak A: , Peak B: , Peak C: , Peak D: , Peak E:
Order the peaks from coldest to warmest.
Step 1: Write the mathematical expression
Write the temperatures from smallest to largest:
Golf Scores
In golf, scores below par are negative (good!) and above par are positive. Ordering scores shows the rankings.
Example:
Player scores: Ali , Ben , Cara , Dan , Eve . Best to worst:
Five golfers finished with these scores: Player A: , Player B: , Player C: , Player D: , Player E:
Order the players from best (lowest) to worst (highest) score.
Step 1: Write the mathematical expression
Write the scores in ascending order:
Key Takeaways
- 1Ascending order means arranging from least to greatest (smallest first)
- 2Descending order means arranging from greatest to least (largest first)
- 3Use the number line: left to right is ascending, right to left is descending
- 4Negative numbers with larger digits are SMALLER (further from zero)
- 5Zero always falls between negative and positive numbers
Frequently Asked Questions
Glossary
- Ascending order
- Arranging numbers from smallest to largest (least to greatest)
- Descending order
- Arranging numbers from largest to smallest (greatest to least)
- Integer
- A whole number that can be positive, negative, or zero
- Number line
- A line showing numbers in order, with negatives on the left and positives on the right