This lesson will teach you what quotient means in math and how to find the quotient in division.
The quotient is the answer to any division problem. The word comes from a Latin word, quotiens, which means “how many times,” as in, “how many times does go into ? The number of times goes into is the quotient or the result of a division problem.
In a division problem, the number being divided into pieces is the dividend. The number by which the dividend is divided is called the divisor. And the answer to the division problem is the quotient.
Here are the parts for the simple division problem, ten divided by two:
When using short or long division, the dividend goes under the division bracket, ⟌, the divisor goes to the left of the bracket, and the quotient goes on top of the bracket aligned by place value with the dividend.
The division symbol, , is called an obelus. It is used in division number sentences. The obelus follows the dividend and precedes the divisor.
Setting up a division problem is a key first step to dividing correctly. First, decide which number is to be divided. That is the dividend. Place it under the division bracket.
The dividend is divided by some other number; that is the divisor, and it goes to the left of the bracket. Perform the division. Your answer is the quotient. Any remainder is placed to the right of the quotient.
Finding the two given parts (dividend and divisor) is often challenging in a word problem, but in a number sentence, these parts stand out. Here is an example sentence:
In this case, our answer would be the whole number . So, the number is one example of a quotient. We will go over more complicated examples of quotients later in the lesson.
When you compute the quotient in division, you may end up with a remainder. The result of division is called the quotient. The number left over is called the remainder. The remainder is part of the result.
Here is a quotient example with a remainder:
goes into four () times, which is . That leaves us with remaining.
Fractions are already division problems. The fraction bar separating numerator and denominator is signaling division:
A more complicated search for a quotient can occur when you are dividing two fractions:
Such a problem can also appear in this form:
Recall the process for dividing fractions; invert the second fraction and multiply:
The quotient for is .
Quotients appear in algebraic expressions, too. You can divide one monomial by another:
The variable in the numerator and denominator cancel out (think: ). And the numbers divide readily, leaving you with as the quotient.
You can also divide a polynomial by a monomial:
You have the polynomial being divided by a monomial, .
First, separate the two terms in the numerator and divide each by the denominator.
This gives you 3x for the first term () and 4 for the second term ():
in the quotient
One polynomial can be divided by another polynomial to get a quotient, too:
Partial quotient is a division method (also called chunking) that uses repeated subtraction to solve simple division problems. The partial quotients method is used when dividing a large number by a small number.
Instead of trying to figure out how many times goes into , you can turn it into a simpler multiplication problem and multiply by an easy multiple like , which gives you . The number 10 becomes your partial quotient, and you subtract from the divided, .
You repeat this step reducing the dividend by chunks until it is reduced as much as it can be by . At the end, you add up your partial quotients, and the result is your quotient.
After working your way through this lesson and video, you have learned:
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