What are 2 ways that you can multiply 18 x 34?

Answer 1

There are many ways and these depend on your fluency with number and their inter-relations.

For example, since I know that 17^2 = 289 so I would do

18*34 = (17+1)*(2*17) = 2*17^2 + 2*17 = 2*289 + 2*17 = 2*(289+17) = 2*306 = 612. Of course, I would not go through all those steps but they are shown there so that you may be able to follow.

An alternative would be to multiply 18 by 4 and 30 and then to sum the answers:

18*4 = 72, 18*30 = 540 and so the answer is 72+540 = 612.

This is equivalent to 18*34 = 18*(30 + 4)

Yet another method, attributed to Euclid is to halve the smaller number and double the other, ignoring halves, and keep going until the smaller number reaches 1.

18 ... 34

9 ... 68

4 ... 136

2 ... 272

1 ... 544

Then add together the larger numbers for which the left hand number is odd. Thus 68 + 544 = 612.