Splitting a number on purpose
Show on a big screenSeven packets of biscuits cost ₹23 each. What is the total?
- 23 × 7, one block.
- Cut at the round number: 20 and 3.
- 20 × 7 = 140.
- 3 × 7 = 21.
- 140 + 21 = 161.
Splitting a number on purpose
The total is ₹161. Splitting 23 as 20 + 3 makes the sum easy.
Each number in a product is a factor. A round number ends in 0, like 20 or 100.
Rule: any factor may be split into a sum or a difference. Cut at a round number. One piece then needs almost no working.
| Product | Cut as | Two pieces | Total |
|---|---|---|---|
| 23 × 7 | (20 + 3) × 7 | 140 and 21 | 161 |
| 12 × 15 | 12 × (10 + 5) | 120 and 60 | 180 |
| 6 × 104 | 6 × (100 + 4) | 600 and 24 | 624 |
| 6 × 98 | 6 × (100 − 2) | 600 and 12 | 588 |
A poor cut still works. Cut 23 as 11 + 12. Then 11 × 7 = 77 and 12 × 7 = 84. Together, 77 + 84 = 161. The pieces are only harder.
The same idea gives a quick way to multiply by 11. 4265 × 11 = 4265 × (10 + 1) = 42,650 + 4,265 = 46,915.
Watch out!
Split 3 × (4 × 5) into 3 × 4 and 3 × 5. Multiplying those gives 12 × 15 = 180. The bracket holds a product, 4 × 5 = 20. The real answer is 3 × 20 = 60. Only a sum or difference may be split.
Drag the gap to a round number. Add the two parts.
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Try the lab to finish this lesson.