Comparing and Ordering Integers Lesson: Positives, Negatives, and Zero

Integers are everywhere from temperatures and elevations to bank transactions and sports scores. They are numbers that include positives, negatives, and zero. To fully understand how these numbers relate to each other, students must know how to compare and order them properly. This skill is essential in both math problems and real-life decision-making.

What Are Integers?

Integers are whole numbers that can be positive, negative, or zero.

• Positive integers: 1, 2, 3, 10, 25
• Negative integers: –1, –2, –3, –10, –25
• Zero: 0

Key Points:

• Integers do not include fractions or decimals.
• Every positive integer has a negative counterpart.
• Zero is neither positive nor negative but is essential as the central point on the number line.

Integers are often used in real-world scenarios:

• Profit or loss in a business
• Changes in temperature
• Elevation above or below sea level
• Gaining or losing points in a game

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Integers Test: Math Trivia! Quiz

Understanding the Number Line

A number line is a straight line where numbers are placed at equal distances. It is used to show the position of integers.

• Numbers to the right of zero are positive.
• Numbers to the left of zero are negative.

Important Facts:

• The further right you go, the greater the number.
• The further left you go, the smaller the number.
• Zero is the center and helps compare positive and negative values.

Using the number line helps to visualize comparisons like which number is larger or smaller.

Absolute Value: Measuring Distance

The absolute value of an integer is its distance from zero on the number line, regardless of direction.

• It is always a positive number or zero.
• The symbol used is two vertical bars: |x|.

Examples:

• |–7| = 7 → 7 units from zero
• |5| = 5 → 5 units from zero
• |0| = 0 → exactly at zero

Why It Matters:
Absolute value is useful when comparing how far numbers are from zero, especially in real-world problems like changes in temperature or measuring distances.

Comparing Integers

To compare integers means to determine which is greater, smaller, or if they are equal.

Use these symbols:

• > means greater than
• < means less than
• = means equal to

General Rules:

• A positive number is always greater than a negative number.
• Zero is greater than any negative number.
• When comparing two negative numbers, the one with the smaller absolute value is greater.

Examples:

• 4 > –3 → Positive is greater than negative
• –2 > –5 → –2 is closer to zero
• 0 < 1 → Zero is less than any positive number

Tip:
Always use the number line or absolute value to check your comparison.

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Integers Quiz Questions and answers

Ordering Integers

Ordering means arranging integers from least to greatest or greatest to least.

Steps to Order:

1. Identify the sign of each integer (positive or negative).
2. Use a number line to place them visually.
3. Start with the smallest and go up for ascending order.
4. Start with the largest and go down for descending order.

Examples:

• Ascending order: –6, –3, 0, 4
• Descending order: 5, 2, 0, –4

Practice Set:
Given: –2, 3, –5, 1
Ascending: –5, –2, 1, 3

Real-Life Applications of Integers

Integers are not just for math class-they appear in many everyday situations. Understanding how to compare and order them helps make better decisions.

Examples:

• Weather Reports: Temperatures below freezing are negative (e.g., –10°C is colder than –5°C).
• Banking: A negative bank balance shows money owed (e.g., –$50 is worse than –$20).
• Elevation: Depth below sea level is negative, height above is positive.
• Games: Losing points = negative, gaining points = positive.

Absolute Value in Comparisons

Sometimes, you need to compare integers based on their absolute value, not just their face value.

Examples:

• Compare |–6| and |4| → 6 vs. 4 → |–6| > |4|
• Compare –3 and –7 → |–3| = 3, |–7| = 7 → –3 > –7

Even if a number has a higher absolute value, it may be less if it is negative.

Symbol Practice in Comparisons

You often need to place the correct symbol between two values.

Rules Recap:

• Use < when the first number is smaller.
• Use > when the first number is larger.
• Use = when both values are equal.

Symbol Examples:

• –5 < –2
• 0 = |0|
• 6 > –4

Common Mistakes to Avoid

Being aware of these mistakes can help avoid confusion during problem-solving.

Comparing and Ordering at a Glance

By mastering the comparison and ordering of integers using rules, number lines, and real-life context, students can gain a solid foundation in mathematical reasoning. This knowledge prepares them for more advanced math topics and strengthens logical thinking for daily situations involving numerical data.

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Comparing and Ordering Integers Quiz: Test!