Remainder when the dividend is less than the divisor

[SHASHWAT PRATAP SING]

I am Sorry it's a silly question but its been bothering me, So I needed to ask...
In the process of division, when there is a condition like- 4/5
when the divisor is greater then the dividend.
why is the Remainder 4 ? as when the divisor is greater then the dividend then the division goes in decimals, and the final remainder comes
outto be 0, then why do we do like this.

 

[Hill]

Because a remainder is what left after subtracting a divisor from a dividend as many times as possible.

 

[fresh_42]

It is because we have the equation ##4= 0\cdot 5 + 4.## It is the general form of the Euclidean algorithm that considers ##a= q\cdot b +r .## It is what happens if we divide ##a=4## by ##b=5## with a remainder ##r.##

The basic idea is to do everything with addition and multiplication only since the integers do not allow a division. In order to divide, we need to use the rational or real numbers. Then we can write ##\dfrac{4}{5}=0.8## without remainders. But over the integers, we have ##4= 0\cdot 5 + 4.##

Long story short: it depends on which number field you use.

 

[PeroK]

If the remainder upon division of 4 by 5 is not 4, then what is the alternative?

 

[FactChecker]

Some things make no sense as a fraction and you would want to know how much is left over.
If my will divided 5 cars between 2 children, I would give each child 2 cars and have one left over. I would not give each child 2.5 cars. (Which half of a car would each get?)

 

[PeroK]

Some things make no sense as a fraction and you would want to know how much is left over.
If my will divided 5 cars between 2 children, I would give each child 2 cars and have one left over. I would not give each child 2.5 cars. (Which half of a car would each get?)

You might have to be specific in your will as to which child gets which cars.

 

[pasmith]

Some things make no sense as a fraction and you would want to know how much is left over.
If my will divided 5 cars between 2 children, I would give each child 2 cars and have one left over. I would not give each child 2.5 cars. (Which half of a car would each get?)

It is possible for two or more people to co-own a car in equal (or unequal) shares. (Although it may be that only one of them can be the registered keeper.)

 

[FactChecker]

It is possible for two or more people to co-own a car in equal (or unequal) shares. (Although it may be that only one of them can be the registered keeper.)

Sure. But they may not want to share it or sell it.

 

[FactChecker]

You might have to be specific in your will as to which child gets which cars.

Yes, but the point is that it might not be easy to divide them equally.

 

[fresh_42]

Yes, but the point is that it might not be easy to divide them equally.

No problem. Give me the Bentley and the others the rest of your cars.

 

[SHASHWAT PRATAP SING]

Thanks for helping me guys, my doubt is resolved.