Quotient: Definition & Meaning

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  • 0:05 What is a Quotient?
  • 0:21 Finding the Quotient
  • 2:59 Lesson Summary
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Lesson Transcript
Instructor: Jennifer Beddoe
A quotient is the answer to a division problem. This lesson will give a definition of the word and describe how to find a quotient in different ways. There will also be a quiz for you to check your understanding.

What Is a Quotient?

The word quotient is from the Latin 'quotiens', which means 'how many times'. A quotient is the answer to a division problem. A division problem describes 'how many times' a number will go into another. The first known usage of the word in mathematics is found around 1400-1500 AD in England.

Finding the Quotient

There are at least two different ways to find the quotient of two numbers. You can also find the quotient of an algebra problem.

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Fractions

The quotient of a fraction is the whole number that is obtained when you simplify the fraction. If the simplification of a fraction is not a whole number, the quotient is the decimal form of the fraction.

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The quotient can also be the solution to a division problem involving two fractions.

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Solve the above example using:

A = 2

B = 3

C = 4

D = 7

When you plug in the numbers, you get:

(2/3) / (4/7)

Since division is the opposite of multiplication, you can turn this division problem into a multiplication problem by multiplying the top fraction by the reciprocal of the bottom fraction.

(2/3) x (7/4) = 14/12

This fraction can be reduced to 1 1/6

Therefore, 1 1/6 is the quotient of the division problem (2/3) / (4/7).

Division

You can also find the quotient of an arithmetic division problem.

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24 divided by 4 is 6. This means that 24 can be divided into 6 equal groups, each containing 4 items.

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The answer to a larger division problem is also the quotient. For the above problem, the quotient is 18.

If the division problem does not work out evenly, there will be a remainder. The quotient is still the whole number, but the amount 'left over' is the remainder.

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Algebra

Not all quotients have to be numbers. You can also find the quotient to an algebraic problem involving variables.

You can divide one monomial by another.

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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

So, the answer is 3b.

Or you can divide a polynomial by a monomial.

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