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Quotient is an answer to a division issue in simple terms. Evenly divisible integers create round quotients, whereas others produce a quotient followed by a remainder. When we divide one number by another, the result is a quotient. When we divide 6 by 3, for example, we obtain 2, which is the quotient. An integer or a decimal value can be used as the quotient. We have an integer as a quotient for accurate divisions like 10/5=2, and a decimal as a quotient for divisions like 12/5=2.4. Although a quotient might be greater than the divisor, it is always less than the dividend.
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Key Terms: Reminder, Quotient, Dividend, Divisor, Decimal, Division, Multiplication, Fraction
Quotient in Division
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When we divide a number, we receive a quotient as the result. The division is a mathematical symbol that represents a way of evenly dividing things into groups. For example, 15 balls must be evenly distributed into three groups. As a result, when we split these balls into three equal groups, the division statement is 15/3=5. The quotient, in this case, is 5. This means that each group will have five balls.
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Continuity and Differentiability Detailed Video Explanation:
How to Find Quotient?
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After the division operation is done, the quotient is obtained. This indicates that when a dividend is divided by a divisor, the result is the quotient. The division is one of the four basic mathematical operations, with addition, subtraction, and multiplication being the other three.
The outcome of the division procedure is the quotient. The quotient is the result of entirely dividing a number. When we divide a number, the number does not always get split fully, and we end up with a remainder. Even in this situation, though, a quotient remains as the solution, and the remainder is mentioned separately.
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Methods to find the Quotient
A quotient can be calculated in two ways: fractionally or using the long division method.
By Fraction Method
The quotient is the result of dividing the dividend by the divisor, which is a simple division of the numerator and denominator. The result achieved is the quotient, with a dividend as the numerator and a divisor as the denominator.
45÷9=5
Here 9 is the dividend, 45 is the divisor and 5 is the quotient.
By Division Method
The dividend is the number that we divide in a division operation. The divisor is the number by which we divide the dividend. The quotient is the result obtained in this manner. The remainder is the number that is left behind.
17÷3=5.66
Here 3 is the dividend, 17 is the divisor and 5 is the quotient, and 2 as a reminder
Verification of the Division Result
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We can simply check whether the result we got via long division is valid or not. Because division is the inverse of multiplication, let's see how we may use this information to validate our solution. Dividend=(Divisor Quotient)+Remainder is the formula we utilize. This means we should obtain the dividend if we multiply the divisor by the quotient and add the remainder. If the numbers meet this equation, the solution is right; if they don't, we'll need to double-check our division.
435 is the dividend, 4 is the divisor, 108 is the quotient, and 3 is the remainder. We get 435=(4 ×108)+3 by substituting the value in the formula. This establishes the correctness of the response. Let's look at another scenario. We have a leftover of 0 when we divide 6/2=3. Let's use the formula 6=(2 ×3)+0 to replace these numbers in the formula. This indicates that the response is correct.
Terms Related to Quotient
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Apart from the quotient, additional words are employed in the process of division when we divide a number. Let's look at an example to assist us to comprehend. There's a chocolate bar with 12 pieces, for example. Is it possible to split the bar evenly between two friends? Yes, after the chocolate bar is divided evenly between two pals, each will receive six pieces of chocolate.
Did you notice that there isn't a single piece of chocolate left unattended? As a result, there is no leftovers. For this example, we may express the division statement as 12/2=6. Each of the numbers in the division can be given a unique name here. When we divide a number, we are left with a reminder if we do not divide it completely.
| Terms | Description | Values |
|---|---|---|
| Dividend | The total pieces that are to be shared. | 12 |
| Divisor | The number of equal groups that are to be made. | 2 |
| Quotient | The number of pieces in each group. | 6 |
| Remainder | The remaining piece is not part of any group. | 0 |
Things to Remember
- The quotient is always zero when a zero is divided by a number.
- The quotient is undefined when an integer is divided by zero.
- Dividend÷Divisor=Quotient
- Dividend=(Quotient x Divisor)+Remainder
- The quotient may be greater or lesser than the divisor, but it is never greater than the dividend.
Also read: Root 2 is an irrational number
Sample Questions
Ques. $4000 is distributed among 25 workers for the work completed by them at a construction site. Calculate the amount given to each worker. (3 Marks)
Ans. $4000 is the total money to be distributed. The total number of employees is 25. The amount supplied to each worker must be calculated. To do so, divide 4000 by 25 and obtain the quotient using the long division method.
= 4000/25
=160
Each worker will get $160
Ques. $5,876 is distributed equally among 26 men. How much money will each person get? (3 Marks)
Ans. Money received by 26 men=5876 So, money received by one man=5876÷26
= 226
Each man will get $226.
Ques. If 9975 kg of wheat is packed in 95 bags, how much wheat will each bag contain? (3 Marks)
Ans. Since 95 bags contain wheat 9975 kg
Therefore, 1 bag contains wheat (9975÷95) kg
= 105 kg
Each bag contains wheat=105 kg
Ques. 89 people have been invited to a banquet. The caterer is arranging tables. Each table can seat 12 people. How many tables are needed? (3 Marks)
Ans. To answer this question, we need to divide 89 by 12
89÷12
Quotient - 7
Remainder - 5
If the caterer arranges 7 tables, then 5 people will have no place to sit.
So he needs to arrange 7+1=8 tables.
Ques. How many hours are there in 1200 minutes? (3 Marks)
Ans. We know that there are 60 minutes in 1 hour. Divide the number of minutes by the number of minutes in 1 hour. We get, divide 1200 by 601200÷60=20
So there are 20 hours in 1200 minutes.
Ques. A bus can hold 108 passengers. If there are 12 rows of seats on the bus, how many seats are in each row? (3 Marks)
Ans. Total number of passengers=108
There are 12 rows of seats on the bus.
To find how many seats are there in each row, divide the total number of passengers by the number of rows of seats on the bus.
We get, divide 108 by 12
108÷12=9
Therefore, there are 9 seats in each row.
Ques. Tom had 63 apples. He divides all apples evenly among 9 friends. How many apples did Tom give to each of his friends? (4 Marks)
Ans. Total number of apples=63
There are 9 friends sitting on the bus.
To find how many apples Tom gave to each of his friends, divide the total number of apples by the number of friends.
We get, divide 63 by 9
63÷9=7
Therefore, Tom gives 7 apples to each of his friends.
Ques. Mark baked 195 cookies and divided them equally into 13 packs. How many cookies did Mark put in each packet? (3 Marks)
Ans. Total number of cookies=195
There are 13 packs.
To find how many cookies Mark put in each packet, divide the total number of cookies by the number of packs.
We get, divide 195 by 13
195÷13=15
Therefore, Mark put 15 cookies in each pack.
Ques. Nancy needs 5 lemons to make a glass of orange juice. If Nancy has 250 oranges, how many glasses of orange juice can she make? (4 Marks)
Ans. Total number of oranges=250
She needs 5 lemons to make a glass of orange juice.
To find how many glasses of orange juice can Nancy make, divide the total number of oranges by the number of oranges needed for each glass of orange juice.
We get, divide 250 by 5
250÷5=50
Therefore, Nancy can make 50 glasses of orange juice.
Ques. In your classes, you counted 120 hands. How many students were in the class? (4 Marks)
Ans. Total number of hands=120
We have 2 hands.
To find how many students were in the class, divide the total number of hands by the number of hands we have.
We get, divide 120 by 2
220÷2=60
Therefore, there were 60 students in the class.
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