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Patterns in multiplication
Observe the pattern in the following multiplications.

1. In each multiplication, the last two 2. The products are the multiples of

digits of the product is 25 and the 105.
remaining digits 15 × 15 = 225 35 × 3 × 1 = 105
can be obtained 25 × 25 = 625 35 × 3 × 2 = 210

by multiplying
the tens digit of 35 × 35 = 1225 35 × 3 × 3 = 315
a factor with its ____ × ____ = _____ ____ × ____ × ____ = _____
successor.

Fill in the blanks by observing the pattern:

3. 1 × 1 = 1 4. 9 × 1 = 9
11 × 11 = 121 9 × 11 = 99

111 × 111 = 12321 9 × 111 = 999

____ × ____ = ______ ____ × ____ = _____

Patterns in Division

We can see many patterns in division. Look at the following pattern and try to fill in

the blanks.

1. 6 ÷ 2 = 3 2. 10 ÷ 5 = 2

60 ÷ 2 = 30 100 ÷ 5 = 20

600 ÷ 2 = 300 1000 ÷ 5 = 200
____ ÷ ____ = _____ ____ ÷ ____ = _____

____ ÷ ____ = _____ ____ ÷ ____ = _____

3. 111 ÷ 3 = 37 4.
1
222 ÷ 6 = 37 (9 – 1) ÷ 8 = 12
(98 – 2) ÷ 8 =
333 ÷ 9 = 37
____ ÷ ____ = ____ (987 – 3) ÷ 8 = _____
(9876 – 4) ÷ 8 = _____
____ ÷ ____ = ____

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Symmetry and Patterns