# multiplying

#### Ryan$##### Full Member Hi guys, I'm really confused and it would be much appreciated if you help me to how I can visualize it. lets assume I have 3*4=12, why if I multiplying grater numbers from 3,4 I will get equal amount greater than 12 .. in other words if I multiply 4*4=16 so once I increase one of the operand which was 3 to 4 I got equal value 16 which is greater than 12 (3*4) .. so why once increasing the multiplicand operands(two operands) I get greater value?! is the multiplying function that's increasing once we increase the input?! how can I visualize it?! #### topsquark ##### Full Member There's actually a link on this site that you might find to be helpful. It's here. Look down the left side of the page until you get to the section that says "Understand Multiplication." I looked over it.. It's a good tutorial. -Dan #### HallsofIvy ##### Elite Member 4(4)= 4(3+ 1)= 4(3)+ 4(1). Since 4(1) is positive the result is larger than 4(3). • topsquark #### lev888 ##### Full Member is the multiplying function that's increasing once we increase the input?! how can I visualize it?! Easy - visualize a room with rows of chairs. 3 rows, 4 chairs in each row. How many chairs? 3*4 = 12. Let's add a row. How many chairs do we have now? 4*4 = 16. As we add rows or increase the number of chairs in each row the total number of chairs increases. #### Otis ##### Senior Member It's easy to view multiplication of Natural numbers as repeated addition. If we increase the number of repeats (or we increase the actual number being added repeatedly), then the result must increase. That's common sense. For example, look at 3×2, 4×2, 5×2, etc: 2 + 2 + 2 = 6 2 + 2 + 2 + 2 = 8 2 + 2 + 2 + 2 + 2 = 10 #### Subhotosh Khan ##### Super Moderator Staff member Don't get too carried away with that visualization. It does not work very well for irrational numbers (√2 * π) or imaginary numbers (i * i). • topsquark #### Otis ##### Senior Member Don't get too carried away with that visualization. It does not work very well for irrational numbers (√2 * π) ... Indeed. I wouldn't want to push Ryan$ toward a mind warp. $$\;$$

• topsquark

##### Full Member
Why 5 liters? 5 is unitless.

Liters multiplied by a number gives you liters. E.g. Ivan drank 3 liters of vodka yesterday. Today he drank 5 times as much. 3 liters * 5 = 15 liters.
but if 5 is unitless, so how we are multiplying with liters? I mean we must have a balanced units for doing math manipulation ..

#### JeffM

##### Elite Member
... we must have a balanced units for doing math manipulation ..
False.

• topsquark

#### lev888

##### Full Member
but if 5 is unitless, so how we are multiplying with liters? I mean we must have a balanced units for doing math manipulation ..
Can you clarify what balance you are talking about?
The only balance we need is the same units on both sides of "=". E.g. "something, something miles" = 5 hours would be wrong.

#### pka

##### Elite Member
if I have 3 liters of water, and I multiply 3 liters by 5, which means 3 *5 = 15 , am I have now 15 liters of water?! what's confusing me, I know I'm having number 15, but what its type/unit? because the number 5 doesn't have any unit, so how we are dealing with it over equations?!
if it was 3 liters of water * 5 of liters water, then yeah it would be 15 liters of water ! maybe I complex it more because I'm not that good at math, please anyone a senseable analogy to me which elaborate the concept behind multiplying something by a constant number?! which can understand from it the answer.

##### Full Member
Hi guys, if I have multiplying something of any type unit by a constant number, would we have the same type of the same something?

I mean, lets assume I have 5cm and if I multiply it by 5, do I get 25cm?! if so, then why it's allowed to multiply something unitless with units?! 5 * 5 [cm] is allowed?! don't make a sense for me, so please it would be much appreciated if you give me analogy that multiplying by constant wouldn't change the type of the amount ....

#### topsquark

##### Full Member
The unit isn't so much a number as it is a "classification" of sorts. So if you are multiplying a quantity (a number with a unit attached) by a number (unitless) then the unit does not change. So we have 5 (unitless) times 5 cm (a quantity)= (5 times 5) cm, or 25 cm.

-Dan

#### Dr.Peterson

##### Elite Member
Suppose I have 5 sticks, each 5 centimeters long, and put them in a row. What is the total length? 5 times 5 cm. And what is that? 25 cm.

Obviously the result should have the same unit, because it is still a length. All we are doing it repeating the same length 5 times.

(We could also have described this situation as 5 sticks times 5 cm/stick. That is just a different way to think of the same thing.)

If it doesn't make sense to you, please be specific. What contradiction do you see arising from this?

• topsquark