Negative numbers, integer operations, number line
Middle School Bridge • 6-8
Temperature drops below zero. A submarine descends 200 feet beneath sea level. Your bank account shows a negative balance. Negative numbers are not just a math concept -- they describe real situations where values go below a reference point. In this lesson, you will learn to work confidently with negative numbers and master the rules for integer operations.
Integers are the set of whole numbers and their opposites: ..., -3, -2, -1, 0, 1, 2, 3, ...
On a number line, positive numbers extend to the right and negative numbers extend to the left. Zero is neither positive nor negative. The further left a number sits, the smaller it is: -5 < -2 < 0 < 3 < 7.
| Situation | Rule | Example |
|---|---|---|
| Same signs | Add the absolute values, keep the sign | (-4) + (-3) = -7 |
| Different signs | Subtract the smaller absolute value from the larger; keep the sign of the larger | (-8) + 5 = -3 |
Compute (-6) + 9.
To subtract an integer, add its opposite. This converts every subtraction problem into an addition problem.
Compute 3 - (-7).
The sign rules are the same for both multiplication and division:
Same signs: positive result
(-4) × (-5) = +20
(-12) ÷ (-3) = +4
Different signs: negative result
6 × (-3) = -18
(-20) ÷ 5 = -4
Compute (-3) × 4 + (-2) × (-5).
The expression -32 is NOT the same as (-3)2. Without parentheses, the exponent applies only to 3: -32 = -(3 × 3) = -9. With parentheses: (-3)2 = (-3) × (-3) = 9. Always pay attention to parentheses.
1. Compute (-8) + (-5).
Same signs: add absolute values and keep the negative sign. 8 + 5 = 13, so the answer is -13.
2. Compute (-4) - (-9).
Rewrite: (-4) + 9 = 5.
3. Compute (-7) × 6.
Different signs: negative. 7 × 6 = 42, so the answer is -42.
4. Compute (-36) ÷ (-4).
Same signs: positive. 36 ÷ 4 = 9.
5. The temperature at dawn was -6 degrees C. By noon it had risen 14 degrees. What was the noon temperature?
-6 + 14 = 8 degrees C.
Integers include all positive and negative whole numbers and zero. When adding integers with the same sign, add and keep the sign; with different signs, subtract and keep the sign of the larger absolute value. To subtract, add the opposite. For multiplication and division, same signs give a positive result and different signs give a negative result.