Adding and Subtracting Negative Numbers
Add and subtract with negative integers, reading each move as a direction on the number line, and settle what subtracting a negative does.
What a learner can do afterwards
- Work out sums like -7 + 3 and 4 - 9 without a calculator and say which way the answer lies from zero
- Explain why subtracting a negative moves the same way as adding a positive, using a context such as debt or temperature
- Order a mixed list of positive and negative numbers and find the distance between two of them
1 · Read
Negative numbers count things below zero: debt, basement floors, frost. Adding a positive moves right on the number line, adding a negative moves left. For -7 + 3, start at -7 and step 3 places right to land on -4.
Subtracting flips direction, and subtracting a negative flips twice. That is why 5 - (-3) equals 5 + 3, which is 8. Owing a debt and having it cancelled feels like gaining money. The gap from -4 to 6 is 6 minus -4, which is 10.
Same signs combine: keep the sign and add the sizes, so -2 + (-5) is -7. Different signs compete: keep the sign of the bigger size and subtract. Before computing, guess the sign. That one-second check catches most slips. To order mixed numbers, put every negative below every positive, then sort and pick the middle.
Walk the line: plus faces right, minus faces left, and taking away a debt moves you right.
2 · Watch
Take it off screen
Where it sits
This opens up
Where this leads
Jobs that lean on this skill. Follow one to see everything it is built on.
8 questions wait behind this lesson, each with its answer explained. Every answer feeds the sky: stars light as they are learned, and dim when it is time to come back.