- #1

AndersHermansson

- 61

- 0

Multiplication is defined as repeated addition.

3x5 = 5+5+5

How do we define 10/2?

3x5 = 5+5+5

How do we define 10/2?

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- Thread starter AndersHermansson
- Start date

- #1

AndersHermansson

- 61

- 0

Multiplication is defined as repeated addition.

3x5 = 5+5+5

How do we define 10/2?

3x5 = 5+5+5

How do we define 10/2?

- #2

Pocketwatch

- 40

- 0

Repeated subtraction?Originally posted by AndersHermansson

Multiplication is defined as repeated addition.

3x5 = 5+5+5

How do we define 10/2?

10-2-2-2-2-2=0 5 equal parts.

10/3

10-3-3-3=1 3.3333333333333 parts. 3 and 1/3

- #3

HallsofIvy

Science Advisor

Homework Helper

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- #4

Q: How many times can you subtract 5 from 21

and what do you have left?

A: I can subtract 5 from 21 as many times as I like,

and I always have 16 left.

- #5

Dissident Dan

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- #6

hypnagogue

Staff Emeritus

Science Advisor

Gold Member

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Originally posted by Dissident Dan

What about something like 1/3? How many times do you have to subtract 3 from 1 to get 0? The answer is "1/3 of 3" times, but the answer here using the above formulation doesn't get us any closer to a meaningful answer than the initial question. It's circular.

- #7

a=b(q)+r

for some integers q and 0<= r< b. Here q and r are uniquely deteremine. 28/5 is the same thing as 28=5(5)+3 If you want to get fancy schmancy. Take the integers Z and since Z is an integral domain define the field of rationals Q as all the numbers(quotients) that satisfy the following equation for x

xm=n

all solution are n/m where m and n are integers, here you have the field of quotients or Q

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