# Dividend, Divisor, Quotient and Remainder

In division we will see the relationship between the dividend, divisor, quotient and remainder. The number which we divide is called the dividend. The number by which we divide is called the divisor. The result obtained is called the quotient. The number left over is called the remainder.

55           ÷         9           =           6           and           1

Dividend             Divisor               Quotient               Remainder

For example:

(i) Divide 217 by 4 Here, Dividend = 217 Divisor = 4 Quotient = 54 Remainder = 1

(ii) Divide 5679 by 7 Here, Dividend = 5679 Divisor = 7 Quotient = 811 Remainder = 2
Remainder, 55 ÷ 9 can also write as 9) 55 ( or 9) 55

Note: dividend = divisor × quotient + remainder

Understanding Remainder:

We know divisor means to split a large group of objects into small equal groups. The large group is called the dividend. The number of smaller equal groups is called the divisor and the number of objects in each smaller group is called the quotient.

Let us Divide 12 cupcakes among 3 children.

Now, let us Divide 9 pencils into 2 equal groups.

When we cannot make equal groups or share equally all the objects, the number which is left undivided is called the remainder. Remainder is always less than the divisor.

So, Dividend = Divisor × Quotient + Remainder

In the above example = 9 × 2 + 1

The dividend, divisor, quotient and remainder will help us to verify the answer of division. Add remainder (if any) with the product of divisor and quotient. The sum we get should be equal to the dividend.

Let us consider some examples to verify the answer of division.

1. Divide 38468 by 17 and verify the answer. Now let us verify the answer; dividend = divisor × quotient + remainder   38468  =   17  ×  2262   +    14              =   38454 + 14              =   38468 So, the answer is correct.

The quotient is 2262 and the remainder is 14.

2. Divide 58791 by 36 and verify the answer. Now let us verify the answer; dividend = divisor × quotient + remainder  58791  =   36   ×  1633   +   3             =   58788 + 3             =   58791 So, the answer is correct.

The quotient is 1633 and the remainder is 3.

3. Divide 94 by 3 and verify the answer.

 Step I: Write 94 inside the bracket and 3 on the left side of the bracket.Step II: Start division from left to right, Divide 9 tens by 3.We know that 3 × 3 = 9Write 3 in the quotient  and 9 below 9.Subtract 9 from 9.Step III: Bring down 4 from ones place. 3 goes into 4, 1 time and gives 1 as remainder.Write 1 in the quotient and subtract 3 from 4. Thus, quotient = 31 and remainder = 1

Check: To check answer, we use the following relationship:

Dividend = Divisor × Quotient + Remainder

94     =     3     ×     31      +       1

94    =           93               +       1

94    =     94

Hence, division is correct.

4. Divide 654 by 7 and verify the answer.

 Step I: Write 654 inside the bracket and 7 on the left side of the bracket.Step II: The divisor 7 is greater than 6. So, consider first two digits 65. 7 goes into 65, 9 times and gives 2 as remainder.Step III: 24 is the new dividend. 7 goes into 24, 3 times and gives 3 as remainder.Write the quotient 3 and subtract 321 from 24. Thus, quotient = 93 and remainder = 3

Check: To check answer, we use the following relationship:

Dividend = Divisor × Quotient + Remainder

654    =     7     ×     93      +       3

654    =           651            +       3

654    =     654

Hence, division is correct.

Therefore, to check a division sum, add the remainder to help product of divisor and quotient. The result should be equal to the dividend.

Properties of division:

When zero is divided by a number the quotient is zero.

For example:

(i) 0 ÷ 4 = 0

(ii) 0 ÷ 12 = 0

(iii) 0 ÷ 25 = 0

(iv) 0 ÷ 314 = 0

(v) 0 ÷ 225 = 0

(vi) 0 ÷ 7135 = 0

Division of a number by zero is not possible.

For example, we cannot divide 74 by 0.

If we divide any number by 1, the quotient is the number itself.

For example:

(i) 28 ÷ 1 = 28

(ii) 4558 ÷ 1 = 4558

(iii) 335 ÷ 1 = 335

(iv) 9387 ÷ 1 = 9387

If we divide a non-zero number by itself, the quotient is 1.

For example:

(i) 45 ÷ 45 = 1

(ii) 98 ÷ 98 = 1

(iii) 1371 ÷ 1371 = 1

(iv) 5138 ÷ 5138 = 1

## You might like these

• ### Money Bills | Prepare a Bill for the Purchases | Copy of an Invoice

We often buy things and then we get money bills of the items. The shopkeeper gives us a bill containing information about what we purchase. Different items purchased by us, their rates and the total

• ### Worksheet on Bills | Bills & Billing of Different Items |Cost of items

We will practice the questions given in the worksheet on bills and billing of different items. We know bill is a slip of paper on which a shopkeeper notes down the requirements of a buyer

• ### Estimating Products | Estimation in Multiplication | Rounding Numbers

To estimate the product, we first round off the multiplier and the multiplicand to the nearest tens, hundreds, or thousands and then multiply the rounded numbers. Estimating products by rounding numbers to the nearest ten, hundred, thousand etc., we know how to estimate

• ### Worksheet on Word Problems on Addition and Subtraction Together | Ans

In 4th grade worksheet on word problems on addition and subtraction, all grade students can practice the questions on word problems based on addition and subtraction. This exercise sheet on

• ### Estimating Sums and Differences | Estimations | Practical Calculations

For estimating sums and differences in the number we use the rounded numbers for estimations to its nearest tens, hundred, and thousand. In many practical calculations, only an approximation is required rather than an exact answer. To do this, numbers are rounded off to a

• ### Worksheet on Forming Numbers with Digits | Smallest & Greatest Numbers

In the worksheet on forming numbers with digits, the questions will help us to practice how to form different types of smallest and greatest numbers using different digits. We know that all the numbers are formed with the digits 0, 1, 2, 3, 4, 5, 6, 7, 8 and 9.

• ### Worksheets on Comparison of Numbers | Find the Greatest Number

In worksheets on comparison of numbers students can practice the questions for fourth grade to compare numbers. This worksheet contains questions on numbers like to find the greatest number, arranging the numbers etc…. Find the greatest number:

• ### Formation of Greatest and Smallest Numbers | Arranging the Numbers

the greatest number is formed by arranging the given digits in descending order and the smallest number by arranging them in ascending order. The position of the digit at the extreme left of a number increases its place value. So the greatest digit should be placed at the

• ### Even and Odd Numbers | Definition | Properties | Examples | Questions

A number which is a multiple of 2 is an even number and that which is not multiple of 2 is an odd number. All those numbers that can be put into pairs are called even numbers, that is, all those numbers which come in the table of two are even numbers.

• ### Successor and Predecessor | Successor of a Whole Number | Predecessor

The number that comes just before a number is called the predecessor. So, the predecessor of a given number is 1 less than the given number. Successor of a given number is 1 more than the given number. For example, 9,99,99,999 is predecessor of 10,00,00,000 or we can also

• ### Worksheets Showing Numbers on Spike Abacus | Number in Figures

Worksheets showing numbers on spike abacus for 4th grade math questions to practice after learning 1 digit, 2 digits, 3 digits, 4 digits and 5 digits numbers on spike abacus.

• ### Numbers Showing on Spike Abacus | Spike Abacus | Name of a Number

Numbers showing on spike abacus helps the students to understand the number and its place value. Spike abacus is very helpful to understand the concept of magnitude and name of a number.

• ### 4th Grade Division Worksheet | Simple Division | Math Division|Answers

In 4th grade division worksheet we will solve division by 2-digit numbers, division by 10 and 100, properties of division, estimation in division and word problems on division.

• ### Worksheet on Word Problems on Division | Solve Division Problems

In worksheet on word problems on division, all grade students can practice the questions on word problems involving division. This exercise sheet on word problems on division can be practiced by the students to get more ideas to solve division problems.

• ### Worksheet on Estimating the Quotient | Questions on Estimate Quotient

In worksheet on estimating the quotient, all grade students can practice the questions on estimate the quotient. This exercise sheet on estimating quotient can be practiced by the students to get more ideas. Find the estimated quotient for the following divisions: