Lesson 13 of 19
Zero pairs
Show on a big screenYou hold 5 rupees and must pay 9. Borrow 4, then pay. You owe 4.
A token is a small counter. A positive token is +1. A negative token is −1. The total is positives minus negatives.
Zero pair — one positive token and one negative token. Together they make 0, so adding one changes no total.
Step 1 of 5
- A bag holds 5 positive tokens.
- Take away 9? Only 5 are there.
- Add 4 zero pairs. The total is still 5.
- Now take away 9 positive tokens.
- 4 negative tokens are left. 5 − 9 = −4.
Rule: A is one positive and one negative token. To take away tokens you lack, add zero pairs first.
| Written | Bag at the start | Zero pairs to add | Left in the bag |
|---|---|---|---|
| 5 − 9 | 5 positive | 4 | 4 negative, so −4 |
| 2 − (−3) | 2 positive | 3 | 5 positive, so 5 |
| (−2) − 4 | 2 negative | 4 | 6 negative, so −6 |
| (−8) − (−3) | 8 negative | 0 | 5 negative, so −5 |
The last row needs no pairs. The bag has 8 negatives, so 3 can come out.
Add 9 negative tokens to the 5 positives instead. Five pairs cancel. Four negatives stay. So 5 − 9 and 5 + (−9) both give −4.
Tap the cards in order. The bag shows each step.
Loading lab…
Try the lab to finish this lesson.