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**by**11**to 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**7**to 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

- 16 x 4 =
- 18 x 3 =
- 36 x 22 =
- 62 x 22 =
- 160 x 3.5 =
- 1.5 x 24 =
- 55% of 1800
- 125 x 48 =
- 1.75 x 32 =
- 55 x 64 =

Answers to all exercises are found in the answer key.

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