# General discussion of mental maths **URL:** \ **Category:** Mental Calculation, Mathematics, and Puzzles\ **Created:** [August 12, 2013, 10:25pm UTC](https://forum.artofmemory.com/t/general-discussion-of-mental-maths/28679 "2013-08-12T22:25:34Z")\ **Posts on this page:** 1\ **Showing post:** 22
**Author:** ![Kinma](https://forum.artofmemory.com/letter_avatar_proxy/v4/letter/k/a88e4f/32.png) [@Kinma](https://forum.artofmemory.com/u/Kinma)\ **Post date:** [July 10, 2017, 3:29pm UTC](https://forum.artofmemory.com/t/general-discussion-of-mental-maths/28679/22 "2017-07-10T15:29:25Z")
> [@](#): > > 89 x 47 Criss cross using [negative values](https://artofmemory.com/forums/avoiding-the-carry-5494.html): 90 -1 50 -3 \_\_\_\_\_\_\_ X 90X50 = 4500 (-1 X 50) + (-3 X 90) = -50 - 270 = -320 -1 X -3 = 3 \_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_ + 4500 -320 (=4180) -+3 (=4183) Anchor method using 50 as anchor: 1st step. We add 3 to 47 to get 50. Therefore we subtract the same 3 from 89 to get 86. Now multiply them: 50 X 86 = 4300 Now subtract the difference from the base numbers (we changed 47 into 50 and 89 into 86. So difference is 3) and multiply by the distance of the anchor and the biggest number: -3 X (89 - 50) = -3 X 39 = -117 4300 -117 = 4183 Btw this is based on: (a+c)(a+d) = a(a+c+d) + cd > [@](#): > > or when they end with high unit digits such as 87 x 39? Criss cross (using negative values): 90 -3 40 -1 \_\_\_\_\_\_\_\_\_\_ X 3600 -90-120 = -210 (total is 3390) –1X-3 = 3 (total is 3393) Anchor using 40: 40 X 86 = 3200 + 240 = 3440 -1 X (87-40) = -1 X (47) = -47 3440 -47 = 3393 You privately asked me: > [@](#): > > 53 x 74 Anchor method seems quick: 50 X 77 = 3850 3 x 24 = 72 3850 + 72 = 3922 > [@](#): > > 67 x 87 Either do: 70 -3 90 -3 Or anchor: 60X94 + 7X27 > [@](#): > > 67 x 79 Either do: 70 -3 80 -1 Or anchor: 60X86 + 7X19 --- _[View the full topic](https://forum.artofmemory.com/t/general-discussion-of-mental-maths/28679)._