Question

if we consider multiplication as repeated addition then it is simple to visualise 3x4=12 as 4 being added three times which is basically repeated addition , a general definition of multiplication.But it is difficult for me to understand or visualize questions like 0.3x3 and (2/3)x3 .Can anyone please tell me how do i add 3 0.3 times and 3 (2/3) times? it seems quite impossible to add 3 0.3 times. it is something that i couldn't understand by considering that multiplication is repeated addition.Is there something else that i need i need to understand about multiplication?

Answer 1

how about thinking of .3 in terms of money
$ .3 would be 30 cents
and 3(30 cents) = 90 cents = $ .90 = $.9
so 3(.3) = .3 + .3 + .3 = .9

or simply, add with decimals lined up
.3
.3
.3
----
.9

For (2/3)(3)
= 2/3 + 2/3 + 2/3
= 6/3
= 2

using a piece of paper, draw 3 circles, and divide each of them into thirds.
Cut each of the circle into thirds, take two pieces from each of the 3 circles.
You now have 6 pieces, each equal to 1/3 of a circle, or 2/3 from each circle.

Now piece those 6 pieces together, and you can see that you have 2 whole circles.

Answer 2

or think of 4/7 times 8 as
4 added eight times, then broken into seven parts?

This real issue is when irrational numbers are involved, trying to visuallize that as repeated addition, such is in
2 PI. At least it was difficult for me when I was a tadpole. By now, I have forgotten my worries on it.

Answer 3

Bob, now that I am an old bull-frog I am still trying to fathom how
e^(πi) = -1
maybe my imaginary powers are not what they used to be.