One tray, counted two ways
A tray has 6 rows and 13 columns of laddoos. Count them in two easy parts.
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Step 1 of 6
- The tray: 6 rows × 13 columns.
- The whole tray: 6 × 13 = 78.
- Draw a line after column 10.
- Left block: 6 × 10 = 60.
- Right block: 6 × 3 = 18.
- Add the blocks: 60 + 18 = 78.
The rule
The tray holds 78 laddoos. The two parts hold 60 and 18.
Drawing that line moves no laddoo. So both counts must agree.
A rule that holds for all numbers is called a property.
6 × (10 + 3) = 6 × 10 + 6 × 3. Both sides are 78: 6 × 13 = 78, and 60 + 18 = 78. This is the distributive property. A number times a sum is that number times each part, added.
It works with subtraction too. 98 is 100 − 2. So 98 × 15 = (100 − 2) × 15. That is 100 × 15 − 2 × 15 = 1500 − 30 = 1470.
| Line after column | Left block | Right block | Both |
|---|---|---|---|
| 10 | 60 | 18 | 78 |
| 7 | 42 | 36 | 78 |
| 1 | 6 | 72 | 78 |
Watch out!
Give every block its own 6. Writing 6 × 10 + 3 gives 63, not 78.