Integers and the Number Line

What You Will Learn

• Recognise positive integers, negative integers and zero.
• Place integers on a number line.
• Compare and order integers.
• Understand opposite numbers and absolute value.
• Connect integers to everyday situations.

1. What Are Integers?

Integers are whole numbers and their negative opposites, including zero. They do not include fractions or decimals.

• Positive integers: 1, 2, 3, 4, ...
• Negative integers: −1, −2, −3, −4, ...
• Zero: 0, which is neither positive nor negative.

2. Understand the Number Line

On a number line, numbers increase as you move to the right and decrease as you move to the left. Zero is the reference point.

3. Compare Integers

The number farther to the right on a number line is greater. This means every positive integer is greater than zero, and zero is greater than every negative integer.

• 5 > 2 because 5 is to the right of 2.
• −2 > −5 because −2 is to the right of −5.
• −3 < 0 because −3 is to the left of zero.

4. Order Integers

To order integers from least to greatest, start with the number farthest left on the number line.

Move from left to right: −4, −1, 0, 2, 3.

From greatest to least, reverse the order: 3, 2, 0, −1, −4.

5. Opposite Integers

Opposite integers are the same distance from zero but on opposite sides of the number line.

• The opposite of 4 is −4.
• The opposite of −7 is 7.
• The opposite of 0 is 0.

Opposite numbers add to zero. For example, 6 + (−6) = 0.

6. Absolute Value

The absolute value of an integer is its distance from zero. Distance is never negative, so absolute value is always zero or positive.

• |5| = 5
• |−5| = 5
• |0| = 0

7. Integers in Everyday Life

Temperature

A temperature of −3°C is three degrees below zero. A temperature of 4°C is above zero. Therefore, 4°C is warmer than −3°C.

Floors in a building

Ground floor can be represented by 0. A basement level may be −1, while a floor above ground may be +2.

Money changes

A deposit of $15 can be represented by +15. Spending $8 can be represented by −8. The total change is +7.

8. Common Mistakes to Avoid

9. Practice Exercises

Try these before revealing the answers.

1. Is −4 positive, negative or zero?
2. Which is greater: −2 or −6?
3. Order −3, 4, 0 and −1 from least to greatest.
4. What is the opposite of −9?
5. Find |−12|.
6. Which temperature is warmer: −5°C or −1°C?
7. A person deposits $20 and then spends $7. What is the total change in money?

10. Test Your Understanding

Choose one answer for each question, then select Check Answers. Each question is worth one point.

11. Free Printable Worksheet

Print this worksheet or save it as a PDF for extra practice.

12. Lesson Summary

• Integers are positive whole numbers, negative whole numbers and zero.
• Numbers increase to the right on a number line.
• Every positive integer is greater than zero; every negative integer is less than zero.
• Opposite integers are the same distance from zero on opposite sides.
• Absolute value is the non-negative distance from zero.