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Chapter 4 : Multiplication

4.2 : Multiplication near to the base

4.2.1 Both the numbers are lower than the base. 4.2.1.3 Multiplication using a base of 1000

Example 1: Find 786 X 998

Here base is 1000

Complement of 786 is 214.

7 from 9 is 2 and 8 from 9 is 1 and 6 from 10 is 4 .

Complement of 998 is 002

786 -214 [ BASE 1000]

998 -002

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(786-002) or (998-214) / (214X2)

786 -214 [ BASE 1000]

998 -002

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784 / 428

Answer is 784428

Example. 2: Find 994 X 988.

Here base is 1000

994 -006 [ BASE 1000]

988 -012

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(786-002) or (998-214) / (214X2)

994 -006 [ BASE 1000]

988 -012

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982 / 072

Answer is 982072

Example. 3: Find 750 X 995.

Here base is 1000

750 -250 [ BASE 1000]

995 -005

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(750-005) or (995-250) / (250X005)

750 -250 [ BASE 1000]

995 -005

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745 / 1250

Since the base is 1000, we write down 250 and carry 1 over to the left giving us 745 / 1250 = (745+1) / 250

Answer is 746250

Assignments

Assignments Answers

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Chapter 4 : Multiplication

4.2 : Multiplication near to the base

4.2.2 Both the numbers are higher than the base.

The method and rules : The only difference is the positive deviation. Instead of cross?subtract, we follow cross?add.

Example.1: Find 13X12.

Base is 10

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(13 + 2) or (12 + 3) / (3 X 2)

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15 / 6

Answer is 156

Example.2: Find 18X14.

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22 / 32

Since the base is 10, we write down 2 and carry 3 over to the left giving us 22 / 32 = (22+3) / 2

Answer is 252

Example 3: Find 104 X 102

Here base is 100

104 04 [ BASE 100]

102 02

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(104 + 02) or (102 + 04) / (04 X 02)

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Chapter 4 : Multiplication

4.2 : Multiplication near to the base

4.2.3.1.1 Bar Numbers and application

Look at the following Subtractions

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9 = 10 ?1 = 11

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8 = 10 ?2 = 12

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7 = 10 ?3 = 13

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6 = 10 ?4 = 14

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5 = 10 ?5 = 15

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4 = 10 ?3 = 16

9 is same as 10 - 1 , and this may be written as one ten in the ten?s column and take away 1 in the units column.

8 is same as 10 - 2 , and this may be written as one ten in the ten?s column and take away 2 in the units column.

More examples

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98 = 100 ? 2 = 102

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196 = 200 ? 4 = 204

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32 = 30 ? 2 = 28

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145 = 140 ? 5 = 135

A Viniculum Number OR Bar Number is a take away or minus number.

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28 = 30 ? 2 = 32 because 28 is 2 less than 30.

Thirty viniculum two is 28.

Example 1.

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Bar number of 47 can be found by 47 = 50 ? 3 = 53 One more than 4 is 5 and the complement of 7 is 3.

It is like telling the time when we say ?Five to six? instead of 5:55

To change a number back into its ordinary form, write down the complement of the viniculum number and subtract 1 from the next digit to the left

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To convert Viniculum 53

Complement of 3 is 7 and 5 ? 1 is 4 give us the original number as 47.

Example 2

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To convert 75

Complement of 5 is 5 and 7-1 gives 6

The original number is 65

To change a tens column digit into a Viniculum we use same method. The digit is replaced by its complement and the digit to the left is increased by 1

Example 3

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Convert Viniculum 174