Quotient and Remainder

In mathematics, a quotient is the result of a division. For example, when dividing 10 by 2, the quotient is 5, while 10 is called the dividend, and 2 the divisor. The quotient can also be expressed as the number of times the divisor divides into the dividend.

If a and d are natural numbers, with d non-zero, it can be proven that there exist unique integers q and r,

such that a = qd + r and 0 = r < d.

The number q is called the quotient

while r is called the remainder.

The division algorithm provides a proof of this result and also an algorithm describing how to calculate the remainder. Example for Quotient and Remainder:

Problem for quotient and remainder: 1

Divide 126 by 4.

Solution:

Given that 126 by 4

quotient and remainder

Take the 4 and divide 12.

There are 3 times 4 in 12.

So the quotient is 3.

Next take the 4 and divide 6

There is 1 time 4 in 6

So the quotient is 1.

The remainder will be 6 – 4 = 2.

Answer Quotient is =31

Remainder = 2

Problem for quotient and remainder 2:

Divide 184 by 3

Solution:

Given that 184 divided by 3

quotient and remainder

Take the 3 and divide 18.

There are 6 times 3 in 18.

So the quotient is 6.

Next take the 3 and divide 4

There is 1 time 3 in 4

So the quotient is 1.

The remainder will be 4 – 3 = 1

Answer is Remainder = 1

Quotient = 61 Some other Examples for Quotient and Remainder:

Example problem: 3

Divide the number 71 by 5.

Solution:

Given that 71 by 5

quotient and remainder

Take the 5 and divide 7.

There is 1 time 5 in 7.

So the quotient is 1.

The remainder is 7 – 5 = 2

Take this remainder and keep as 21

Next take the 5 and divide 21

There are 4 time 5 in 21

So the quotient is 4.

The remainder will be 21 - 20 = 1.

Answer is Remainder = 1

Quotient = 14

Example problem: 4

Divide the number 99 by 7.

Solution:

Given that 99 by 7

quotient and remainder

Take the 7 and divide 9.

There is 1 time 7 in 9.

So the quotient is 1.

The remainder is 9 – 7 = 2

Take this remainder and keep as 27

Next take the 7 and divide 29

There are 4 time 7 in 29

So the quotient is 4.

The remainder will be 29 - 28 = 1.

Answer is Quotient = 14

Remainder = 1.

know more Quotient Rule Derivative i found this link interesting Second Derivative Test

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