Decimal Calculations 4
Long Multiplication

You are probably familiar with long multiplication. For example, you can find 35 × 19 in the following way:

35
×19
350
+315
665

But there are many other ways of doing this sum.
For example,

(1) Napier's Method

Write the two numbers on the horizontal top and vertical side.

Multiply each digit together to give the two digit entries in the cell (write3×1=3 as 03).

Now add up along the diagonals; carry digits in the usual way – this gives 0665, i.e. 665 as expected!

(2) Russian Multiplication

35   ×   19
1738
876
4152
2304
1608
665(again!)

Write down the multiplication

Divide left hand side by 2, ignoring remainder, and multiply right hand side (RHS) by 2

Continue in this way until 1 is reached on left hand side (LHS)

Cross out terms on RHS if there is an even number on LHS

Add up the remaining numbers on RHS

(3) Box Method

300
270
50
45
665
305
1010 × 30 = 30010 × 5 = 50
99 × 30 = 2709 × 5 = 45
⎫
⎪
⎬
⎪
⎭

Worked Examples

Exercises

Find, by any method:

(a)
3 × 42
(b)
8 × 35
(c)
6 × 22
(d)
9 × 43
(e)
12 × 62
(f)
15 × 32
(g)
84 × 22
(h)
19 × 48
(i)
62 × 18
(j)
43 × 62
(k)
172 × 42
(l)
461 × 78
(m)
184 × 192
(n)
392 × 412
(o)
494 × 72

Use Russian multiplication to find:

(a)
42 × 37
(b)
62 × 81
(c)
14 × 93
(d)
27 × 43
(e)
82 × 29
(f)
38 × 46
(g)
57 × 37
(h)
29 × 49
(i)
33 × 28

Use the box method or Napier's method to find:

(a)
12 × 15
(b)
32 × 21
(c)
89 × 42
(d)
45 × 57
(e)
62 × 91
(f)
112 × 428