Split a number near 100
Show on a big screenA box holds 96 pencils. A shop buys 12 boxes. Find how many pencils without long multiplication.
Slide the number near 100. The strip is the gap. Find where the split stops helping.
Loading lab…
- The shop buys 12 boxes of 96: 96 × 12.
- 96 is 4 short of 100.
- A full block of 100 × 12 holds 1200.
- The strip of 4 × 12 holds 48. Take it off.
- 1200 − 48 = 1152.
The rule
The shop buys 1152 pencils.
Look for a number just under or just over 100. Write the number as 100 plus or minus a small gap. The gap is how far the number is from 100.
Multiply each part by the other number. Then subtract the gap's part, or add it.
96 × 12 = (100 − 4) × 12. Then 100 × 12 = 1200 and 4 × 12 = 48. So 1200 − 48 = 1152.
107 × 8 = (100 + 7) × 8. Then 100 × 8 = 800 and 7 × 8 = 56. So 800 + 56 = 856.
The gap's part is the gap times the other number. A one-digit gap keeps that part short, like 4 × 12.
With 67, the gap is 33. That gap has two digits, so the split does not help.
| The product | The split | The parts | The value |
|---|---|---|---|
| 96 × 12 | (100 − 4) × 12 | 1200 − 48 | 1152 |
| 107 × 8 | (100 + 7) × 8 | 800 + 56 | 856 |
| 67 × 43 | (100 − 33) × 43 | 4300 − 1419 | 2881 |
Try the lab to finish this lesson.