Multiplication and Division by Numerical Trituration

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Multiplication and Division by Numerical Trituration

Image: AI Google

I - Multiplication by Numerical Trituration

First Example

157 x 3 =

a = 100 x 3 = 300

b = 50 x 3 = 150

c = 7 x 3 = 21

157 x 3 = a + b + c

157 x 3 = 300 + 150 + 21 = 471

Second Example

45 x 23 =

a = 40 x 20 = 800

b = 40 x 3 = 120

c = 5 x 20 = 100

d = 5 x 3 = 15

45 x 23 = a + b + c + d

45 x 23 = 1035

Third Example

38.9 x 7

a = 30 x 7 = 210

b = 8 x 7 = 56

c = 0.9 x 7 = 6.3

38.9 x 7 = a + b + c

38.9 x 7 = 210 + 56 + 6.3

38.9 x 7 = 272.3

II - Division by Numerical Trituration

First Example

471 : 3 =

a = 400 : 3 = 100 remainder 171

b = 171 : 3 = 50 remainder 21

c = 21 : 3 = 7 remainder zero

471 : 3 = a + b + c

471 : 3 = 100 + 50 + 7

471 : 3 = 157

Second Example

471 : 30 =

a = 400 : 30 = 10 remainder 100

b = 100 : 30 = 3 remainder 10

c = 10 : 30 = 1/3 remainder zero

d = 70 : 30 = 2 remainder 10

e = 10 : 30 = 1/3 remainder zero

f = 1 : 30 = 1/30 remainder zero

471 : 30 = a + b + c + d + e + f

471 : 30 = [10 + 3 + 2] + [1/3 + 1/3 + 1/30]

471 : 30 = 15 + [10/30 + 10/30 + 1/30]

471 : 30 = 15 + [21/30]

471 : 30 = 15 + 0.7

471 : 30 = 15.7

Third Example

272.3 : 7

First Step: multiply by ten

2723 : 70

a = 2000 : 70 = 20 remainder 600

b = 600 : 70 = 8 remainder 40

c = 40 : 70 = 4/7 remainder zero

d = 700 : 70 = 10 remainder zero

e = 20 : 70 = 2/7 remainder zero

f = 3 : 70 = 3/70 remainder zero

2723 : 70 = a + b + c + d + e + f

2723 : 70 = [20 + 8 + 10] + [4/7 + 2/7 + 3/70]

2723 : 70 = 38 + [40/70 + 20/70 + 3/70]

2723 : 70 = 38 + 63/70

2723 : 70 = 38.9