Take away
To subtract more than you have, introduce zero pairs (a + and a − together change nothing) so there is enough to remove.
Why it works
Break a note into coins to make change.
Integers · Subtract integers · 5.1
Subtract with counters.
Subtraction is taking away counters. If you don’t have enough to remove, add zero pairs (they’re free) until you do, then remove. 5 − 8 needs more negatives.
See it work.
Zero pairs
A +1 and a −1 cancel.
5 − 8 = 5 + (-8)
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Watch the method
Subtract with counters
5 − 8: add zero pairs, remove 8 positives, 3 negatives remain → −3.
1
Add the opposite
Subtracting is adding the opposite: change − to + and flip the sign of 8.
2
Different signs — subtract
Subtract the smaller size from the larger: 8 − 5.
3
Take the bigger sign
8 is the larger size and it is negative, so the answer is negative.
Practice until it feels automatic.
Your turn
Work it out.
Type a whole number — negatives allowed, e.g. -7.
streak 0
best 0
… =
The idea underneath.
From easy to tricky.
Subtract -8 - 3
1
Add the opposite
Subtracting is adding the opposite: change − to + and flip the sign of 3. -8 - 3 = -8 + (-3)
2
Same sign — add the sizes
Both are negative, so add their sizes: 8 + 3. 8 + 3 = 11
3
Keep the sign
Both negative → the answer is negative. -8 + (-3) = -11
Subtract -8 - 2
1
Add the opposite
Subtracting is adding the opposite: change − to + and flip the sign of 2. -8 - 2 = -8 + (-2)
2
Same sign — add the sizes
Both are negative, so add their sizes: 8 + 2. 8 + 2 = 10
3
Keep the sign
Both negative → the answer is negative. -8 + (-2) = -10
Subtract 6 - 2
1
Add the opposite
Subtracting is adding the opposite: change − to + and flip the sign of 2. 6 - 2 = 6 + (-2)
2
Different signs — subtract
Subtract the smaller size from the larger: 6 − 2. 6 - 2 = 4
3
Take the bigger sign
6 is the larger size and it is positive, so the answer is positive. 6 + (-2) = 4
Where students slip.
Trap
Saying 5 − 8 can’t be done.
Fix
Add zero pairs — the answer is −3.
Trap
Removing the wrong counters.
Fix
Remove what the second number says.
Test yourself.
The Test
12 problems across three tiers. Auto-graded on submit. Hints and a full walkthrough on every question. Your work is saved on this device — sign in to keep it across devices.
0/12Answered
How to answerType just the value. Formatting won't trip you up — we ignore spaces, capital letters, commas, and subscript style, so
t₁ = 5, d = 3 and t1=5,d=3 both count. For a list of numbers, separate them with commas (e.g. 3, 10, 17).Core
Core (4)
C1
Subtract -8 - 3
Need a hint?
- Add zero pairs until you can remove.
- Count what is left.
C2
Subtract 6 - 7
Need a hint?
- Add zero pairs until you can remove.
- Count what is left.
C3
Subtract -10 - 3
Need a hint?
- Add zero pairs until you can remove.
- Count what is left.
C4
Subtract -12 - 5
Need a hint?
- Add zero pairs until you can remove.
- Count what is left.
Apply
Apply (4)
A1
Subtract -8 - 2
Need a hint?
- Add zero pairs until you can remove.
- Count what is left.
A2
Subtract 3 - 6
Need a hint?
- Add zero pairs until you can remove.
- Count what is left.
A3
Subtract 11 - 11
Need a hint?
- Add zero pairs until you can remove.
- Count what is left.
A4
Subtract 1 - 6
Need a hint?
- Add zero pairs until you can remove.
- Count what is left.
Extension
Extension (4)
E1
Subtract 6 - 2
Need a hint?
- Add zero pairs until you can remove.
- Count what is left.
E2
Subtract -11 - 7
Need a hint?
- Add zero pairs until you can remove.
- Count what is left.
E3
Subtract -12 - 2
Need a hint?
- Add zero pairs until you can remove.
- Count what is left.
E4
Subtract 10 - 4
Need a hint?
- Add zero pairs until you can remove.
- Count what is left.