Split and multiply

In your book, Maths Mela (Chapter 6, The Dairy Farm), a family makes about 35 kg of kitchen waste in a month. In a year, that is 12 × 35 kg. Nida splits both numbers into tens and ones: 35 is 30 + 5, and 12 is 10 + 2. She draws a grid with 30 and 5 along the top and 10 and 2 down the side, and fills in the four part products: 10 × 30 = 300, 10 × 5 = 50, 2 × 30 = 60 and 2 × 5 = 10. Then she adds them: 300 + 50 + 60 + 10 = 420.

Kanti writes the same four part products in rows, one under another: 10 (2 × 5), 60 (2 × 30), 50 (10 × 5) and 300 (10 × 30), and adds them to get 420. John does it in two rows: 2 × 35 = 60 + 10 = 70, and 10 × 35 = 300 + 50 = 350. Then 70 + 350 = 420. All three ways split the numbers and add the parts, so all three get the same answer: 420 kg of waste in a year.

The family turns its waste into about 150 kg of compost a year. Compost costs ₹24 a kg in the market, so they save ₹24 × 150. Split 150 into 100 + 50 and 24 into 20 + 4: 4 × 150 = 600 and 20 × 150 = 3,000. 600 + 3,000 = 3,600, so the family saves ₹3,600.

The book's next example is 69 × 45. Split 69 into 60 + 9 and 45 into 40 + 5. The grid gives 40 × 60 = 2,400, 5 × 60 = 300, 40 × 9 = 360 and 5 × 9 = 45. Add the two parts under 60: 2,400 + 300 = 2,700. Add the two parts under 9: 360 + 45 = 405. Then 2,700 + 405 = 3,105.