The quotient is the number obtained by dividing one number by another. For example, if we divide the number 6 by 3, the result so obtained is 2, which is the quotient. It is the answer from the division process. The quotient can be an integer or a decimal number. For exact divisions such as 10 ÷ 5 = 2, we have an integer as a quotient, and for divisions such as 12 ÷ 5 = 2.4, the quotient is a decimal. In the division process with decimal quotient as the answer, the decimal part of the quotient is the remainder of the division.
Generally, knowing the quotient helps in understanding the size of the dividend compared to the divisor. The formula for quotient is dividend by the divisor. A quotient can be larger than the divisor but lesser than the dividend. Let us explore and know more about the quotient and the methods to find the quotient.
|1.||What is Quotient in Division?|
|2.||Finding Quotient using Division|
|3.||Terms related to Quotient|
|4.||Know About Quotients|
|5.||Division Method to Find Quotient|
|6.||FAQs on Quotient|
What is Quotient in Division?
The division is the process of repetitive subtraction. The number of times of subtraction is equal to the quotient. The division is denoted by a mathematical symbol(÷) which consists of a short horizontal line with a dot each above and below the line. The quotient is the final answer of this division process. Let us explore with an example to understand the quotient in division. The example shows division as a method of grouping objects equally in groups. The box below contains 16 balls. Let us divide them into 4 equal groups. We can see that there are 4 balls placed in each group. The division statement for the picture below can be written as 16/4 = 4.
Finding Quotient Using Division
The division is one of the four basic mathematical operations, the other three being Addition, Subtraction, and Multiplication. In simple words, division can be defined as the splitting of a large group into equal smaller groups. The quotient is the result of the division process. On completion of the division process, the quotient is obtained. Division can be introduced by considering objects from our daily life like slices of a pizza or a bar of chocolate. We can see that a pizza can be divided into 4 slices, or a bar of chocolate can be divided and the number of pieces obtained is the quotient.
Terms Related to Quotient
Imagine you have a chocolate bar with 12 pieces. You want to share it with your friend. Can the bar be divided equally between the two? Will there be any leftover pieces? As you can see here, we have divided this bar of chocolate into 2 parts. Both you and your friend will get 6 pieces of chocolate each. Did you notice? No piece of chocolate remains unshared. Hence, there is no remainder. We can write the division statement for the example above as 12 ÷ 2 = 6. Here each of the numbers in the division can be designated with special terms. Let us check the following terms closely related to the quotient.
|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 that is not part of any group.||0|
This example can also be mathematically represented as below:
Know about Quotients
Quotient in mathematics can be defined as the result of the division of a number by any divisor. It is the number of times the divisor is contained in the dividend without the remainder being negative. In the image given below, divisor 2 is contained 6 times in the dividend 12. The quotient is larger or smaller than the divisor but is always smaller than the dividend.
Division Method To Find Quotient
Division method follows the use of the divisor and the dividend to find the quotient. The quotient can be calculated by dividing dividend with divisor. Quotient = Dividend ÷ Divisor. This is the most common method used to solve problems on division. Let us understand this with the help of examples. Let us solve 435 ÷ 4. The number 435 can be represented on an abacus with its hundredth, tens, and unit place respectively.
The following two steps are helpful to understand the division process and to find the quotient.
- Step 1:Take the first digit of the dividend. If this digit is greater than or equal to the divisor, then divide it by the divisor and write the answer on top. Subtract the result from the digit and write below. Here, the first digit is 4 and it is equal to the divisor. So, 4 ÷ 4 = 1 is written on top of the bar. The result 4×4 = 1 is subtracted from the digit and 0 is written below. Next drop the second digit or the digit in the ten’s place beside 0.
- Step 2: We can see that we have 03 as the result of step 1. Repeat the same step of checking if this number is greater or smaller than the divisor. Since 03 is less than 4, we cannot divide this number. Hence, we write a 0 on the top and drop the digit on the unit place beside 3. Now, we have 35. As 35 > 4, we can divide this number and write 35 ÷ 4 = 8 on top. Subtract the result 4 × 8 = 32 from 35 and write 3. 3 is known as the remainder and 108 is called the quotient.
Verification of Division Result: We can easily verify if our answer is correct or wrong. As the process of division is the reverse of multiplication, let us find out how we can verify our answer using this information.For example, 6/2 = 3 and remainder is 0. In other words, 6 = 2 × 3 + 0. This can be expressed as Dividend = Divisor × Quotient + Remainder. Let us reconsider the example discussed above. Here the dividend is 435, the divisor is 4, the quotient is 108, and the remainder is 3. Substituting the value in the formula, we get 435 = 4 × 108 + 3. Therefore, our answer is correct.
Examples on Quotient
Example 1: $4000 is distributed among 25 women for the work completed by them at a construction site. Calculate the amount given to each woman.
The total amount is $4000. The number of women at work is 25. We have to calculate the amount given to each woman. To do so, we have to divide 4000 by 25 using the long division method and find the quotient.
Each woman will be given $160. Therefore, the amount given to each woman is 160.
Example 2: 66 people are invited to a birthday party. The suppliers have to arrange tables for the invitees. 7 people can sit around a table. How many tables should the suppliers arrange for the invitees?
The total number of invitees is 66. The number of people who can sit around one table is 7. We divide 66 by 7 using the long division method and find the quotient.
Since 9 is the quotient, we need 9 tables. With 9 tables, we will still have 3 (which is the remainder) people without a place to sit. Hence, the suppliers should arrange one more table for them. The total number of tables to be arranged by the suppliers = 9 + 1 = 10. Therefore, the required number of tables is 10.
Example 3: Calculate the number of hours in 2100 minutes.
We know that 1 hour is equal to 60 minutes. To find the number of hours in 2100 minutes, we have to divide 2100 by 60 and find the quotient.
Therefore, there are 35 hours in 2100 minutes.
Example 4: When the teacher of class 6 asked a question, some students raised their hands. But instead of raising one hand, each student raised both their hands. If there are 56 hands in total, how many students raised their hands?
The number of hands raised is 56. To find the number of students who raised their hands, we have to divide 56 by 2 and find the quotient, because each student raised both hands.
Therefore, 28 students raised their hands.
Example 5: Emma needs 3 apples to make a big glass of apple juice. If she has 51 apples, how many glasses of juice can she make?
The total number of apples with Emma is 51. The number of apples needed for one glass of juice 3. To find the number of glasses of juice, we divide 51 by 3 and find the quotient.
Emma can make 17 glasses of juice with 51 apples. Therefore, the number of glasses of juice is 17.
FAQs on Quotient
What Is Quotient in Math?
The result of the division is known as a quotient in math. In the example, 63/9 = 7. 7 will be the quotient since 7 groups can be formed with 9 units in each group. The quotient can be larger or smaller than the divisor but lesser than the dividend.
How Do You Find Quotient in Division?
The quotient in the division can be found by the formula, Dividend ÷ Divisor = Quotient. Let us understand this by a simple example of 12÷ 4 = 3. Here 12 is the dividend, 4 is the divisor, and 3 is the quotient.
Is Quotient Always a Whole Number?
The quotient is not always a whole number. The quotient can be a whole number or a decimal number. For perfect division, such as 16 ÷ 2 = 8, a quotient is a whole number and for divisions having remainder the quotient is a decimal number, such as 16 ÷ 5 = 3.2 has a decimal number as a quotient.
What Is the Difference Between Quotient and Remainder?
The number of remaining units which cannot be part of any smaller group is known as the remainder. The quotient is equal to the number of times the divisor goes in the dividend. For perfect divisions, a quotient is a whole number, and the remainder is zero. In general, a remainder is sometimes accounted in a quotient and a quotient is then a decimal number.
How Can We Verify the Quotient in Division?
The division is also known as inverse multiplication. We can verify our results by using the following formula:
Dividend = (Divisor x Quotient) + Remainder
How Do You Find the Quotient Through Long Division?
To find quotient through the long division method check the number of times the divisor goes in the dividend. Subtract the answer of the product of the divisor and the quotient from the dividend. This difference gives the remainder. The entire terms involved in the division process can be presented in the form of an equation as Dividend = Divisor ×Quotient + Remainder.
What Is the Quotient of 14 Divided by 7?
When 14 is divided by 7 the quotient is 2. The number 14 is the dividend and the number 7 is the divisor and we have 14 ÷ 7 = 2.
What Is the Difference Between Quotient and Product?
The quotient is the result of a division process and the product is the result of the multiplication process. The quotient is smaller than the dividend and the divisor. The product is larger than the given two numbers.