Adding & Subtracting Negative Numbers — Math Worksheet for 12-Year-Olds (Pre-Algebra)

Instructions

Welcome, adventurer! You are on a Mountain Expedition where you'll practice adding and subtracting negative numbers. Think of it this way:

• Positive numbers (+) mean you are climbing UP the mountain.
• Negative numbers (-) mean you are descending DOWN the mountain.

1. Read the instructions for each section carefully.
2. Use the number line in the first section to help you visualize your movements.
3. Work through the problems, which get more challenging as you climb higher.
4. Check your work with the Answer Key at the end.

Section 1: Base Camp Training

Use this number line to track your position. For 3 + (-5), you would start at 3 and move 5 units to the left (down).

<--|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|--> -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10

Calculate your final position after each move.

1. Start at 4, then move down 7.
   4 + (-7) =

2. Start at -2, then climb up 8.
   -2 + 8 =

3. Start at 5, then move down 5.
   5 - 5 =

4. Start at -8, then move down 2.
   -8 + (-2) =

5. Start at 3, then climb up 7.
   3 + 7 =

6. Start at 6, then move down 10. 6 - 10 =

Section 2: The Ascent - Combining Moves

Remember these two key rules for climbing:

• Adding a negative is the same as subtracting. 10 + (-4) is the same as 10 - 4.
• Subtracting a negative is the same as adding. 8 - (-3) is the same as 8 + 3. It's like cancelling a plan to go down, so you go up instead!

Solve the following problems.

1. -5 + (-11) =

2. 14 + (-20) =

3. 9 - (-5) =

4. -12 - (-8) =

5. 7 - 15 =

6. -3 - (-3) =

Section 3: Summit Weather - Real-World Problems

Apply your skills to solve these real-world scenarios from the mountain peak.

1. Temperature Drop: At sunrise, the temperature was -4°C. By noon, it had warmed up by 12°C. But by nightfall, the temperature plummeted by 15°C from its noon high. What was the temperature at nightfall?

   Answer:

2. Elevation Change: A climber starts at an elevation of 300 meters. She climbs down 80 meters to retrieve some gear, then climbs up 150 meters from there. What is her final elevation?

   Answer:

3. Supply Count: Your team starts with 25 ration packs. On Day 1, you use 7. On Day 2, a supply helicopter drops off 10 more packs. On Day 3, a hungry yeti steals 12 packs. How many ration packs do you have left?

   Answer:

Section 4: The Challenge Peak (Optional)

These problems involve multiple steps. Take your time and track each move carefully.

1. 15 + (-20) - (-5) =

2. -9 - 4 + (-7) =

3. Find the missing number in the sequence:
   11 + _____ = -5

4. A research submarine is exploring a deep-sea trench. It starts at a depth of -450 meters. It then rises 125 meters to scan a coral reef, and then dives another 200 meters. What is the submarine's final depth?

   Answer:

Answer Key

Section 1: Base Camp Training

1. 4 + (-7) = -3
2. -2 + 8 = 6
3. 5 - 5 = 0
4. -8 + (-2) = -10
5. 3 + 7 = 10
6. 6 - 10 = -4

Section 2: The Ascent - Combining Moves

1. -5 + (-11) = -16
2. 14 + (-20) = -6
3. 9 - (-5) = 14
4. -12 - (-8) = -4
5. 7 - 15 = -8
6. -3 - (-3) = 0

Section 3: Summit Weather - Real-World Problems

1. Noon temp: -4 + 12 = 8°C. Nightfall temp: 8 - 15 = -7°C. The temperature at nightfall was -7°C.
2. 300 - 80 + 150 = 220 + 150 = 370. Her final elevation is 370 meters.
3. 25 - 7 + 10 - 12 = 18 + 10 - 12 = 28 - 12 = 16. You have 16 packs left.

Section 4: The Challenge Peak (Optional)

1. 15 + (-20) - (-5) = -5 - (-5) = -5 + 5 = 0
2. -9 - 4 + (-7) = -13 + (-7) = -20
3. The missing number is -16 (11 + (-16) = -5).
4. -450 + 125 - 200 = -325 - 200 = -525. The final depth is -525 meters.