Page 11 - NUMINO Challenge_C1

1 Clever Calculations

Basic Concepts Multiplying Numbers Made Up of One Number

We can find the following rules when we multiply numbers made up of only
8’s and 9’s.

8 9 72 the product of 8 and 9

88888 99999 8888711112

(8 1) 9 81 the product of a number greater than 8 by 1 and 9

Example The following multiplication is made of only 7’s and 9’s. Find the
pattern and calculate 77777777 99999999.

79 63
77 99 7623
777 999 776223
7777 9999 77762223

Class Notes

Since the product of 7 and 9 is , write the two numbers and .

77777777 99999999

According to the rule, the two numbers and that make up ,

which is the product of 9 and a number
greater than 7 by 1, appear in the answer

times.
Therefore, the product of the two numbers is
.

Try It Again Look at the equations below. Find the pattern and calculate
9999999 9999999.

99 81
99 99 9801
999 999 998001
9999 9999 99980001

8 NUMINO Challenge C1