Make zero pairs
Pair each + with a − to cancel. The counters that remain — all the same colour — are the answer.
Why it works
A dollar earned cancels a dollar owed.
Integers · Add integers · 4.1
Zero pairs.
A +1 and a −1 combine to make 0 — a zero pair. To add integers, make as many zero pairs as you can; whatever is left is the answer.
See it work.
Zero pairs
A +1 and a −1 cancel.
5 + -8
+
+
+
+
+
−
−
−
−
−
−
−
−
Watch the method
Zero pairs
5 + (−8): five zero pairs cancel, leaving 3 negatives → −3.
1
Different signs — subtract
Subtract the smaller size from the larger: 8 − 5.
2
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.
Add 6 + -2
1
Different signs — subtract
Subtract the smaller size from the larger: 6 − 2. 6 - 2 = 4
2
Take the bigger sign
6 is the larger size and it is positive, so the answer is positive. 6 + (-2) = 4
Add -4 + 7
1
Different signs — subtract
Subtract the smaller size from the larger: 7 − 4. 7 - 4 = 3
2
Take the bigger sign
7 is the larger size and it is positive, so the answer is positive. -4 + 7 = 3
Add -11 + 1
1
Different signs — subtract
Subtract the smaller size from the larger: 11 − 1. 11 - 1 = 10
2
Take the bigger sign
11 is the larger size and it is negative, so the answer is negative. -11 + 1 = -10
Where students slip.
Trap
Adding the sizes regardless of sign.
Fix
Opposite signs cancel — subtract, don’t add.
Trap
Forgetting the leftover’s sign.
Fix
The colour that remains gives the sign.
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
Add 6 + -2
Need a hint?
- Pair every + with a −.
- Count what is left, with its sign.
C2
Add 12 + -12
Need a hint?
- Pair every + with a −.
- Count what is left, with its sign.
C3
Add 6 + -3
Need a hint?
- Pair every + with a −.
- Count what is left, with its sign.
C4
Add 6 + -10
Need a hint?
- Pair every + with a −.
- Count what is left, with its sign.
Apply
Apply (4)
A1
Add -4 + 7
Need a hint?
- Pair every + with a −.
- Count what is left, with its sign.
A2
Add 10 + -9
Need a hint?
- Pair every + with a −.
- Count what is left, with its sign.
A3
Add 6 + -9
Need a hint?
- Pair every + with a −.
- Count what is left, with its sign.
A4
Add 2 + -10
Need a hint?
- Pair every + with a −.
- Count what is left, with its sign.
Extension
Extension (4)
E1
Add -11 + 1
Need a hint?
- Pair every + with a −.
- Count what is left, with its sign.
E2
Add 4 + -4
Need a hint?
- Pair every + with a −.
- Count what is left, with its sign.
E3
Add -9 + 12
Need a hint?
- Pair every + with a −.
- Count what is left, with its sign.
E4
Add -12 + 12
Need a hint?
- Pair every + with a −.
- Count what is left, with its sign.