Multiplication patterns

In your book, Maths Mela (Chapter 6, The Dairy Farm), there are four multiplication patterns to complete. Look carefully at how each answer grows, and you can find the next one without long multiplication.

Pattern 1: 1 × 1 = 1, 11 × 11 = 121, 111 × 111 = 12,321. The digits climb up and come back down: 1 2 1, then 1 2 3 2 1. So 1111 × 1111 = 1234321, which we write as 12,34,321.

Pattern 2: multiplying by 11. 11 × 12 = 132, 11 × 34 = 374, 11 × 56 = 616. For 11 × 34, the first digit is 3, the last digit is 4, and the middle digit is 3 + 4 = 7: 374. So 11 × 54 = 594, because 5 + 4 = 9 goes in the middle. If the middle sum is 10 or more, carry the 1 to the hundreds: 11 × 82 has 8 + 2 = 10 in the middle, so it is 800 + 100 + 2 = 902.

Pattern 3: numbers ending in 5, multiplied by themselves. 15 × 15 = 225: multiply the tens digit 1 by the next number, 2, to get 2, then write 25. 25 × 25 = 625 (2 × 3 = 6, then 25), and 35 × 35 = 1,225 (3 × 4 = 12, then 25). So 45 × 45 = 2,025 (4 × 5 = 20, then 25), and 55 × 55 = 3,025 (5 × 6 = 30, then 25).

Pattern 4: 1 × 9 + 1 = 10, 12 × 9 + 2 = 110, 123 × 9 + 3 = 1,110. Each time one more 1 appears before the 0. So 1,234 × 9 + 4 = 11,110. Check: 1,234 × 9 = 11,106, and 11,106 + 4 = 11,110.