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?

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.

Answer 4

When it comes to decimals and fractions, the concept of multiplication as repeated addition might not be as intuitive. However, there are alternative ways to understand and visualize these types of multiplication.

For the equation 0.3 x 3, you can think of it as "adding 0.3, three times." One way to approach this is by using a place value model. Write out 0.3 three times vertically, aligning the decimal points. Then, add up the numbers vertically:

0.3
+ 0.3
+ 0.3
------
0.9

Here, you're essentially adding the tenths column three times, resulting in 0.9.

Now, let's consider (2/3) x 3. This can be thought of as "adding 2/3, three times." To visualize this, you can use a fraction bar or a diagram.

Using a fraction bar, divide it into thirds and shade two of them:

2/3 + 2/3 + 2/3

Alternatively, you can use a diagram by drawing a rectangle and dividing it into three equal parts, shading two of them. Then, repeat this process three times and count the shaded parts:

+---+---+---+
|███|███| |
+---+---+---+
|███|███| |
+---+---+---+
| | | |
+---+---+---+

In both cases, you can see that the sum is equal to 2.

These visualizations provide a different perspective on multiplication, specifically for decimals and fractions. By understanding that multiplication can be interpreted in various ways, you can better grasp these concepts beyond the idea of repeated addition.