Exploring Multiplication

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• #31178

Multiplication is a wonderful way to explore mathematics as well as develop mental powers of agility, memory, flexibility and creativity.

Here are seven methods covered in the course:

1. Base method  e.g. 87×97, Lesson 14,15 (and 31×33 using Proportionately)
2.         Average  e.g. 41×39, Lesson 17 (and 82×39 using Proportionately)
3.         By One More  e.g. 74×76, Lesson 17 (and 47×86 using Proportionately)
4.         Doubling & Halving  e.g. 35×46, Lesson 7
5.         Eleven  e.g. 43×11 (and 52×22 using Proportionately), Lesson 12
6.         Addition & subtraction  e.g. 34×19, Lesson 2
7.         General method (vertically and crosswise)  e.g. 23×31, Lesson 13

(Lesson 32 shows another multiplication method)

You can use addition and subtraction with the other methods too. For example, for 23×42 you could think of this as 22×42 + 42, so that you can use the 11 method to find 22×42 and add 42 to it.

Try these:

62 x 58 =                     42 x 43 =                      11 x 56 =
65 x 85 =                     41 x 38 =                      38 x 39 =
71 x 79 =                     72 x 45 =                      87 x 11 =
31 x 21 =                     78 x 36 =                      21 x 53 =

Can you give a pair of numbers whose product cannot be found by any of the first 6 methods above?
Can you find a pair of numbers whose product can be found using all of the methods above?

• #31663

Pair of the numbers whose product can be found using all the methods is 11

I am able to found the product of each pair of No. using the Base method.  65 X 85 – for this number except for the Base method and Vertical and cross-wise method we can’t find the product with other methods.

• #31664

Pair of the numbers whose product can be found using all the methods is 11 X 56

• #31677

Thanks Anupama. Can you explain how 11 x 56 can be done by all the the 6 methods.

For 65 x 85 you can double them both and find 13×17 using By One More, put two zeros on and halve twice.

• #31733

For 11 X 56

Base method –  11    + 1

14   +4    (56/4)

——————

15        4            =    154 * 4 = 616

Average  =    (11*4) 44  X 56 = 6 Avg = 2500 (50*50) – 6* 6 = 2464/4 = 616

By one more = (11*2) 22  X (56/2)  28   = 616

Double and Halving =  (56/2 )  28 * 11 = 308 * 2  = 616

Eleven  =  56 * 11 = 5   11    6    = 616

Addition & Subtraction = 56 * 10 = 560 + 56  =  616

• #31796

Thanks Anupama, this is impressive.

These special methods give us a huge range of possibilities, and inspire creativity in the classroom.

• #31734

Thank you for explaining. I am still not thinking much. Need to practice on that.

These practices helping me to think about all the possibilities and making me more interested to explore. Thank you Ken.