Multiplication Lives

MultiplicationLives

•Cuneiform tablet found in West Asia about 2700 BC

•The table helps people figure out the area of a region by multiplying width by length.

•The first column is the width, the second is the length, and the third column is the area.

•It uses a system for writing down large numbers in base 60 (the way our clocks work today).

Let’s analyze what’s happening.

Simplest type problem:

2 x 3= 6

4 x 5= 20

What about a problem like this?

13 x 4The intersection of 13 lines 4 lines.

10 lines

10 points

4

12+

= 52

Sample Problem: 12 x 234

12 x 234102

101

101

100

100

(1 x 3)102

(1 x 2)103

(2 x 2)102

(1 x 4)101

(2 x 3)101

(2 x 4)100

2 710 8

2808

a b c x d e f

a

c

d

e

f

104

102

103

101

102

100

b

102

101

102

100

100

101

103

102

101

a2 b

1 c

0 x d

2 e

1 f

0

101 100102103104

a2d

2a

2e

1+b

1d

2a

2f0+b

1e

1+c

0d

2b

1f0+c

0e

1c

0f0

a b cd e fx

101 100102103104

a2d

2a

2e

1+b

1d

2a

2f0+b

1e

1+c

0d

2b

1f0+c

0e

1c

0f0

fcfbfaeceb

dceadbda+

cfbfafcebe

cdaebdad

a.bc x de.f

a

c

d

e

f

b

10?

10?

10?

10?

10?

10?

a.bc x de.f

a

c

d

e

f

b

101

100

100

10-1

10-2

10-1

Decimal Multiplication

€

2.1× 3.27 = 21×1

10

⎛

⎝ ⎜

⎞

⎠ ⎟× 327 ×

1

100

⎛

⎝ ⎜

⎞

⎠ ⎟

€

= 21× 327( ) ×1

10×

1

100

⎛

⎝ ⎜

⎞

⎠ ⎟

€

= 6867( ) ×1

1000

⎛

⎝ ⎜

⎞

⎠ ⎟

€

=6.867