Math Delights

from www.woodlands-junior.kent.sch.uk/maths/timestable/tricks.html#11,
Secrets of Mental Math by Arthur Benjamin, and Math for Smarty Pants by Marilyn Burns
adapted by Nancy Blachman, MathDelights.org

Some people, like Arthur Benjamin for example, are incredibly fast at doing calculation in their heads. Learn the following shortcut for multiplying a two-digit number by 11 and you are on your way to becoming a calculating wiz.

The eleven times table (up to 9 x 11) is easy to learn., e.g., 4 x 11 = 44, 7 x 11 = 77.

Here are two easy way of multiplying 11 by a two-digit numbers (whose digits sum up to 9 or less):

Consider, for example: What is 34 x 11 ?

Method 1: Add the first and second digits ... 3 + 4 = 7;
....Insert the total between the the first and second digits .... 374
The answer is 374.

Method 2: Multiply the number by 10 and then add the number itself.
34 x (10 + 1) = 34 x 10 + 34 x 1 = 340 + 34 = 374 (300 + 40 + 30 + 4)

Try using one or both of these methods:

42 x 11 =

35 x 11 =

17 x 11 =

63 x 11 =

When the sum of the two digits is greater than 9 in Method 1, increase the left-hand number by 1 (to carry).

For example: What is 79 x 11 ?

Method 1: Add the two digits ... 7 + 9 = 16
....Add 1 to 7 to get 8
Place the 6 between the 8 and 9
The answer is 869.

Method 2: Multiply the number by 10 and then add the number itself.
79 x (10 + 1) = 79 x 10 + 79 x 1 = 790 + 79 = 869 (700 + 90 + 70 + 9)

Use method 1 or method 2 to find the following products:

39 x 11 =

67 x 11 =

58 x 11 =

76 x 11 =

94 x 11 =

Devise an easy way to multiply 11 by a three-digit or larger number, for example, 345 x 11 = ? or 657 x 11 = ?

Use this shortcut to impress your friends by quickly computing the sum of a list of 10 numbers from a Fibonacci sequence.