Table of Contents
Quotient Meaning
- Mathematically, a quotient is the result of dividing one number by another. For example, the quotient of 4 divided by 2 is 2. This means that 2 is the number that is left over when 4 is divided by 2. The quotient can also be thought of as the result of multiplying the dividend (4) by the reciprocal of the divisor (2).
- In everyday language, a quotient can be thought of as a ratio. For example, if there are ten students in a classroom and twenty desks, the quotient would be two. This means that for every two students, there is one desk.
Quotient Representation
A quotient representation of a number is a way of representing that number as the result of dividing it by another number. The number that is being divided is called the dividend, and the number that is doing the dividing is called the divisor. The quotient representation is the result of dividing the dividend by the divisor, and it is written as a fraction.
Finding the Quotient
- To find the quotient, divide the numerator by the denominator.
- In this example, we divide 9 by 3 to get 3.
Quotients in Variables
A quotient is a number that is divided by another number. The result of this division is called the quotient. In algebra, a quotient can be represented by a variable. For example, if x represents the quotient, then x = 7 ÷ 3 would equal 2.
Solved Examples
-
Find the quotient and remainder. And verify your answer.
-
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.
