NCERT Solutions for Class 5th Maths Chapter 6 The Dairy Farm
Updated on 2026-09-19
About this chapter
Order does not change a product. Daljeet Kaur puts 6 groups of 13 butter packets on a tray. Turn the tray sideways and it becomes 13 groups of 6. The packets did not move, so the total is the same: 6 × 13 = 13 × 6 = 78. This is true for every pair of numbers. Multiplying by 10, 100 and 1,000. Multiply by 10 and every digit shifts one place to the left, so a zero appears at the end: 45 × 10 = 450. Multiply by 100 and the digits shift two places: 8 × 100 = 800. Multiply by 1,000 and they shift three: 5 × 1,000 = 5,000. That is why 30 × 20 is easy — think 3 × 10 × 2 × 10 = 6 × 100 = 600. Doubling and halving. A block of butter packets 3 rows deep and 18 across can be cut in half and the two pieces stacked. Now it is 6 rows deep and 9 across. Nothing was added or thrown away, so 3 × 18 = 6 × 9
- Daljeet Kaur arranges the butter packets
- Filling the place value tables
- Five children find 18 × 5
- Cutting a block of butter packets in half
- Jump to a friendly number, then adjust
- Word problems: use the strategies flexibly
- Nida's, Kanti's and John's ways of multiplying
- Filling the grid and the column methods
- Solve like Nida, like Kanti, like John; then word problems
- Mili's father's method: multiplying with place values
Quick revision
| Word | What it means | Where it appears | Example |
|---|---|---|---|
| Product | The answer you get when you multiply | Page 72 onwards | The product of 6 and 13 is 78 |
| Multiplicand | The number being multiplied | Doubling and Halving, page 76 | In 14 × 3, the multiplicand is 14 |
| Multiplier | The number you multiply by | Doubling and Halving, page 76 | In 14 × 3, the multiplier is 3 |
| Number of groups | How many equal groups there are | Order of Numbers in Multiplication, page 72 | 6 groups of 13 packets |
| Group size | How many things are in one group | Order of Numbers in Multiplication, page 72 | Group size 13 |
| Place value | What a digit is worth because of where it sits | Pages 73, 81, 82 | In 268, the 6 is worth 6 tens = 60 |
| Doubling and halving | Double one number and halve the other; the product does not change | Doubling and Halving, page 75 | 3 × 18 = 6 × 9 = 54 |
| Nearest multiple | A friendly number close by, like 20 or 100, that is easy to multiply | Nearest Multiple, page 76 | 4 × 19 = 4 × 20 − 4 = 76 |
| Estimate | A quick answer that is close, not exact | Page 88 | 248 × 49 is about 12,500 |
| Multiple | A number you reach by counting in steps of another number | Page 71 | 18, 27, 36 are multiples of 9 |
| Carrying | Moving a ten, hundred or thousand from one column to the next | Dairy Cooperative, pages 81–83 | The 30 in 32 goes to the tens column |
| Number pair | Two numbers that sit next to each other in a row or a column | Page 90 | 11 and 14 in the grid |
Exercises
- Shape puzzles, butter milk pouches, Which number am I?, Make your own numbers — Let Us Think Page 70–71
- Daljeet Kaur arranges the butter packets — Order of Numbers in Multiplication Page 72
- Filling the place value tables — Patterns in Multiplication by 10s and 100s Page 72–74
- Five children find 18 × 5 — Many Ways to Multiply Page 74
- Cutting a block of butter packets in half — Doubling and Halving Page 75–76
- Jump to a friendly number, then adjust — Nearest Multiple Page 76
- Word problems: use the strategies flexibly — Let Us Solve Page 77
- Nida's, Kanti's and John's ways of multiplying — Waste and Composting Page 77–78
- Filling the grid and the column methods — Let Us Multiply Page 79
- Solve like Nida, like Kanti, like John; then word problems — Let Us Do Page 79–80
- Mili's father's method: multiplying with place values — Dairy Cooperative Page 81–83
- Practise Nida's, John's and Mili's father's methods — Let Us Solve Page 83–84
- Are these children's solutions correct? — Check, Check! Page 85
- Same answers without calculating, easy ways, and using a known product — Let Us Do Page 86–87
- Coloured box puzzles and estimating products — Let Us Think Page 87–88
- Three ministers, three choices of gold — The King's Reward Page 88–89
- How the product changes, and number-pair grids — Multiplication Patterns Page 89–90
- The last set of word problems — Let Us Solve Page 91