Sunday Maths - Quickly Multiplying Teens

In a similar vein to last week's post on simplifying squares, this one uses some basic algebra to make it easier to multiply numbers between 10-20:

(10 + x)(10 + y) = 100 + 10x + 10y + xy = 10(x + y + 10) + xy

Like the simplified squares equation, this converts a single calculation that's too hard to do in your head with multiple small calculations that are easy to do mentally. For example:

14 × 15 = (10 + 4)(10 + 5)
14 × 15 = 10(4 + 5 + 10) + 4×5
14 × 15 = 10(19) + 4×5
14 × 15 = 190 + 20
14 × 15 = 210

13 × 17 = 10(3 + 7 + 10) + 3×7
13 × 17 = 200 + 21
13 × 17 = 221

19 × 18 = 10(9 + 8 + 10) + 9×8
19 × 18 = 270 + 72
19 × 18 = 342

As shown in the working of the examples, I find it easier to go left-to-right on the calculation and do 10+x+y part before working out xy and adding to the former. If I do the xy first I often forget it while doing the first term.

A simpler version can be used for teens × units:

(10+x) × y = 10y + xy

13 × 7 = 70 + 21 = 91

Updated 2019-11-11: Added a second example and reformatted the formula to emphasize the left-to-right process.