What Is a Quotient?

The quotient is the result you get when you divide one number by another. In 12 ÷ 3 = 4, the quotient is 4.

The parts of a division problem:

• Dividend — the number being divided (12).
• Divisor — the number you're dividing by (3).
• Quotient — the answer (4).

So: dividend ÷ divisor = quotient. The word comes from the Latin quotiens, meaning "how many times" — which is literally what division asks.

Examples:

• 20 ÷ 5 = 4 → the quotient is 4
• 100 ÷ 10 = 10 → the quotient is 10
• 45 ÷ 9 = 5 → the quotient is 5
• 7 ÷ 2 = 3.5 → the quotient is 3.5

Quotients with remainders: Division doesn't always come out evenly. With 17 ÷ 5:

• 5 goes into 17 three times (5 × 3 = 15), with 2 left over.
• The quotient is 3, and the remainder is 2. It's written as 3 R2.
• As a decimal, the quotient is 3.4; as a mixed number, 3⅖.

In everyday maths the whole-number part is called the quotient and the leftover is the remainder. In a decimal answer, the entire result (3.4) is the quotient.

Where the quotient sits in long division: in the traditional layout, the quotient is written on top, above the division bar — the dividend goes inside, and the divisor outside.

How it compares to the other operation results: these four terms are commonly confused, and questions often use them interchangeably:

So when a question says "find the quotient of 36 and 6", it's asking you to divide: 36 ÷ 6 = 6.

Reading word problems: "the quotient of a and b" always means a ÷ b, in that order — the first number named is the dividend. Order matters, since 36 ÷ 6 and 6 ÷ 36 give very different answers.

A quick way to check your answer: multiply the quotient by the divisor and you should get the dividend back. For 45 ÷ 9 = 5, check that 5 × 9 = 45. With a remainder, it's (quotient × divisor) + remainder = dividend: (3 × 5) + 2 = 17. ✓

Two special cases worth knowing:

• Dividing any number by 1 gives that same number as the quotient.
• Dividing by zero is undefined — there is no quotient.

In algebra, the same word applies to expressions: the quotient of x² and x is x. Fractions are also quotients — ¾ is simply another way of writing 3 ÷ 4.