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How to Use This Book

1 Clever Calculations Basic Concepts

Basic Concepts Multiplying Numbers Made Up of One Number Creative math begins right here!
At the beginning of each lesson, Basic
We can find the following rules when we multiply numbers made up of only Concepts presents various examples and
8’s and 9’s. figures to help you grasp the main idea of
the day’s lesson. Work on example
8 9 72 the product of 8 and 9 problems based on the basic concepts.
88888 99999 8888711112 Read the Class Notes that will guide you
through the problems step by step.
(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 ,

Type 1-1 Number Pyramids Types

Find the pattern in the number pyramid below and write the correct This is where the main type of questions for
numbers for and . each topic is introduced. Follow the steps to
find the solution to each problem.
9 99 108
9 99 999 1107
9 99 999 9999 99999 111105

9 99 999 99999999
9 99 999 999999999

1 Find the patterns for the digits in the ones place, the tens place, and the
rest of the higher place values.

2 Write the correct numbers for and according to the pattern.
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