Integers & Negative Numbers
Week 6 · Integers & Negative Numbers
Explore the number line, compare integers, find absolute values, and add and subtract negative numbers.
What are Integers?\n**Integers** are whole numbers and their opposites: ..., -3, -2, -1, 0, 1, 2, 3, ...\n\nPositive integers are greater than 0. Negative integers are less than 0. Zero is neither positive nor negative.\n\n## The Number Line\nIntegers are arranged on a number line. Numbers to the **right** are greater; numbers to the **left** are smaller.\n\n**-5 < -2 < 0 < 3 < 7**\n\n## Absolute Value\n**Absolute value** is the distance from zero — always positive!\n\n|-8| = 8 and |6| = 6\n\nThink of it as "how far from zero?" without caring about direction.\n\n## Adding Integers\n- Same signs: add the values, keep the sign. (-3) + (-5) = -8\n- Different signs: subtract the smaller from the larger, take the sign of the larger. (-3) + 7 = 4\n\n## Subtracting Integers\nSubtracting is the same as adding the opposite!\n\n5 - 8 = 5 + (-8) = -3\n-2 - 4 = -2 + (-4) = -6
Worked Examples
Example 1
📝 What is -6 + 9?
✓ Answer: 3
Different signs: subtract smaller from larger (9 - 6 = 3). The larger number (9) is positive, so the answer is positive: 3.
Example 2
📝 What is 3 - 10?
✓ Answer: -7
Rewrite as adding the opposite: 3 + (-10). Different signs: 10 - 3 = 7. The larger value (10) is negative, so the answer is -7.
Common Mistakes to Avoid
- ⚠️Thinking -8 is greater than -2 because 8 looks bigger — on the number line, -8 is further left and smaller
- ⚠️Forgetting that absolute value is always positive — |-5| = 5, not -5
- ⚠️Subtracting a negative and getting confused — remember: subtracting a negative means adding a positive