Equal groups

In your book, Maths Mela (Chapter 6, The Dairy Farm), a dairy packs buttermilk pouches in equal groups. In the first arrangement there are 30 groups with 2 pouches in each: 30 × 2 = 60 pouches. In the next one the pouches are in groups of 3, and there are 20 groups: 20 × 3 = 60. The same 60 pouches can also be packed as 6 groups of 10 (6 × 10 = 60) or 5 groups of 12 (5 × 12 = 60).

So one total can be shared into equal groups in many ways. The first number tells how many groups there are, and the second tells how many are in each group. 15 × 4 and 10 × 6 also make 60. But 7 × 9 does not: 7 × 9 = 63.

Daljeet Kaur runs a milk processing unit. She sets out her butter packets in 2 rows of 3, and then in 3 rows of 2. Both ways there are 6 packets: 2 × 3 = 3 × 2 = 6. In the same way, 8 × 5 = 5 × 8 = 40, and 6 groups of 13 hold the same as 13 groups of 6: 6 × 13 = 13 × 6 = 78. Changing the order of the numbers does not change the product.

What about 9 × 0? That is 9 groups with nothing in each group, so there is nothing at all: 9 × 0 = 0. And 0 × 9 means no groups of 9, which is also 0. Any number multiplied by 0 gives 0.