NCERT Solutions for Class 5th Maths Chapter 6 Daljeet Kaur arranges the butter packets — Order of Numbers in Multiplication
Book page 72 Updated on2026-09-19
Q1.
Daljeet Kaur runs a milk processing unit. She has arranged the butter packets in the following ways. Find the number of butter packets in each case. What pattern do you notice (or observe)? Discuss in class. (a) 2 × 3 and 3 × 2 (b) 5 × 8 and 8 × 5, then 6 × 13 and 13 × 6, (e) 10 × 5 and 5 × 10 (f) 8 × 20 and 20 × 8 (g) 12 × 9 and 9 × 12
Answer
Both arrangements in every pair hold the same number of packets. Here are all the answers.
Case
First way
Second way
Packets
(a)
2 × 3
3 × 2
6
(b)
5 × 8
8 × 5
40
(c)
6 × 13
13 × 6
78
(e)
10 × 5
5 × 10
50
(f)
8 × 20
20 × 8
160
(g)
12 × 9
9 × 12
108
The pattern: the number of groups and the group size are swapped, but the total never changes.
The same tray of packets, seen two ways. Turning it does not add or remove anything.
Why it happens: Think of the packets laid out in a rectangle. Counting along the rows gives one multiplication. Counting down the columns gives the other. You are counting the very same packets, just in a different direction, so the total must be equal.
Sample answer for the class discussion: We noticed that 6 × 13 and 13 × 6 both give 78. So the order of the two numbers does not matter when we multiply. This is handy — 8 × 20 is easier to work out than 20 × 8 in your head, and you are allowed to choose whichever is easier.
Q2.
What is 9 × 0? 0 × 9? Is this true for the product of any two numbers? Discuss in class.
Answer
9 × 0 = 0 and 0 × 9 = 0. Yes, the order rule is true for every pair of numbers.
Read 9 × 0 as nine groups of nothing. Nine empty trays hold no packets at all. So 9 × 0 = 0.
Read 0 × 9 as no groups of nine. There are no trays, so again there are no packets. So 0 × 9 = 0.
Compare. Both give 0, so 9 × 0 = 0 × 9.
9 × 0 = 0 0 × 9 = 0 So 9 × 0 = 0 × 9 ✓
Why it is true for any two numbers: Any multiplication can be drawn as a rectangle of dots. Swapping the two numbers only turns the rectangle on its side. The dots are the same dots, so the answer is the same answer. Mathematicians call this the order property of multiplication.
Sample answer for the class discussion: We tested it with big numbers too. 25 × 4 = 100 and 4 × 25 = 100. It worked every time. We also noticed it does not work for subtraction: 9 − 4 = 5 but 4 − 9 is not 5. So the order rule belongs to multiplication and addition, not to subtraction and division.