Many products can be easily obtained by applying doubling and halving together or one after another.

Example 7.1: 7 x 16 = 7 x ( 8 x 2) = (7 x 8) x 2 = 56 x 2 = 112

• Halve 16 to get 8
• Multiply 7 by 8 to get 56
• Double 56 to get 112

Example 7.2:  22 x 47 =(11 x 2 ) x 47 = 11 x (2x 47) = 11 x 94 = 1034

• Halve 22 to get 11
• Double 47 to get 94
• Multiply 94 by11to get 1034

 Example 7.3: 18 x 14=  (9 x 2) x (7 x 2) = (9 x 7) x (2 x 2) = (63 x 2) x 2 = 126 x 2 = 252

• Divide both 18 and 14 by two  to get 9 and 7,
• Multiply 9 by 7to get 63.
• Double 63 to get 126.
• Double 126 to get 252.

Multiplicands ending in 5 or .5 can be doubled for easier computation.

Example 7.4: 16 x 35 = (8 x 2) x 35 = 8 x (2 x 35) = 8 x 70 = 560

• Halve 16 to get 8
• Double 35 to get 70
• Multiply 8 by 70 to get 560

Example 7.5: 484 x 2.5 =(242×2) x (2.5) = (242) x (2×2.5)= (121 x 2) x 5 = 121 x10 = 1210

• Halve 484 to get 242
• Double 2.5 to get 5
• Halve 242 to get 121
• Double 5 to get 10
• Multiply 121 by 10 to get 1,210

Exercise 7: Compute the following using halving and doubling

1.       16 x 4 =
2.       18 x 3 =
3.       36 x 22 =
4.       62 x 22 =
5.       160 x 3.5 =
6.       1.5 x 24 =
7.       55% of 1800
8.       125 x 48 =
9.       1.75 x 32 =
10.       55 x 64 =

Answers to all exercises are found in the answer key.

Discover the 25 Math Short Cuts ( 25 MSC )!