# Quotient

## Quotient Meaning

When you divide two numbers the result you get is defined as the quotient.

The word quotient is derived from the Latin word 'quotiens', which means 'how many times'. In simple language a quotient is the answer to a division problem. Evenly divisible numbers produce quotients of a round number while others will yield a quotient followed by a remainder.

The first known usage of the word ‘ quotient’ in mathematics is found around 1400-1500 AD in England. In this article let us study quotient meaning and terms related to quotient.

## A Quotient is Represented as

 Dividend ÷ Divisor = Quotient

Example : 60 10 = 6; 6 is the quotient.

### Quotient Representation

Quotient is the number obtained by dividing one number from the other.

The number which does not divide a number entirely gives a number, which is said to be the remainder. The division symbol is denoted by ‘÷’ or ‘/’.

## We can Represent it in the General Form as:

 Dividend = (Quotient x Divisor) + Remainder

Here:

• Dividend: Is the number which is to be divided

• Divisor: Is the number which divides the given dividend

• Remainder: Is the number which is left after the division method. When a number is completely divisible then the remainder is zero, but when a number is not completely divisible, the remainder is not equal to zero.

### Finding the Quotient

A quotient is calculated in two ways one is by fraction and other is by long division method.

By Fraction

The quotient is a number obtained by dividing the dividend by divisor which is a simple division of numerator and denominator.A dividend is a numerator and a divisor is a denominator and the result obtained is the quotient.

Refer the below example:

Here 5 is the dividend, 25 is the divisor and 5 is the quotient.

By Division:

In division operation the number which we divide is called the dividend. The number by which we divide the dividend is the divisor. The result so obtained is called the quotient. The number which is left down is called the remainder.

Refer the below example

Here 3 is the divisor, 17 is the quotient, 2 is the remainder and 5 is the quotient.

Cross Check

You can also cross check if you quotient is correct or not by the general formula

Dividend = quotient x divisor + remainder

Let us consider the above example and cross check the answer.

Consider RHS

= quotient x divisor + remainder

Here quotient = 5

Divisor = 3

Remainder = 2

Put the values

= 5 x 3 + 2

= 15 + 2

= 17

= LHS

Thus Dividend = quotient x divisor + remainder is verified.

### Quotients in Variables

Division in variables is quite similar to fractions.

You can  find the quotient to an algebraic problem involving variables in the similar way as in numbers.

You can divide one monomial by another.

Let us consider an example

24ab / 8a

First, divide the numbers:

24 / 8 = 3

Then, simplify the variables. The a in both the numerator and the denominator will cancel each other out and you are left with the b

### Fun Facts

• When a zero is divided by number the quotient is always zero.

• When the number is divided by zero the quotient is undefined.

### Solved Examples

1. Divide 5679 by 7

Solution:

7 )  5679 ( 811

-     56

----------------

7

- 7

-----------------

9

-7

-----------------

2

-------------------

Dividend = 5679

Divisor = 7

Quotient = 811

Remainder = 2

To Verify:

Dividend = quotient x divisor + remainder

5679 = 811 x 7 + 2

= 5677 + 2

= 5679

LHS = RHS

Thus verified

b. Divide 1876 by 9

Solution:

9 )  1876 ( 208

-     18

----------------

7

- 0

----------------

76

- 72

-------------------

4

--------------------

Dividend = 1876

Divisor = 9

Quotient = 208

Remainder = 4

To Verify:

Dividend = quotient x divisor + remainder

1876 = 208 x 9 + 4

= 1872 + 4

= 1876

LHS = RHS

Thus verified.

### Quiz Time

1. Divide 153 by 3.

2. Divide 243/4.

3. Find the value of 450/12.

4. Find 633 ÷ 9.

1. How to Find the Quotient of two Fractions?

Answer: we know that quotient is a number obtained on dividing two numbers.

In fraction it is represented as x/y = quotient.

So to find the quotient of two fractions, suppose

(a/b)/(x/y) i.e a/b ÷ x/y

Let us first take the reciprocal of the bottom fraction, and multiply it by the first fraction.

= (a/b) x (x/y)

Fractions can be multiplied together by multiplying the numerators with numerators and multiplying the denominators with denominators.

= (ay)/(bx)

For example, 2/4 divided by 5/4 can be re-written as 2/4 multiplied by 4/5. Because the denominator of the dividend and the numerator of the second term are both 4, they cancel out, leaving a final answer of 2 over 5, or 2/5.

2. What is the Rounding up of Quotient Meaning?

Answer : Rounding is a process by which you can write a long number in a shorter form with approximate value.

To round up a quotient identify the places of the number.

Step 1: The tenths decimal place is the digit immediately to the right of the decimal point, such as the 4 in 12.478, so to round it identify the hundredths decimal place.

Step 2: If the hundredths digit is five or above, add one to the tenths decimal place and delete the rest of the numbers from hundredth’s place. This is called rounding up.

Step 3: Write out the new number with the new tenths digit.

For example, in 4.6791, the hundredths digit is 7. So, this means that in the tenths digit, you add 1 to 6, to result in 7 in the tenths digit, giving you 4.7.