Division of Whole Numbers

Division of whole numbers is discussed here step by step.


1. Division is repeated subtraction.

(a) 25 ÷ 5 = 5

(Repeated Subtraction)

(i) 25 - 5 = 20

(ii) 20 - 5 = 15

(iii) 15 - 5 =10

(iv) 10 - 5 = 5

(v) 5 - 5 = 0 

(b) 10 ÷ 2 = 5

(Repeated Subtraction)

(i) 10 - 2 = 8

(ii) 8 - 2 = 6

(iii) 6 - 2 = 4

(iv) 4 - 2 = 2

(v) 2 - 2 = 0 



(c) 50 ÷ 10 = 5

(Repeated Subtraction)

(i) 50 - 10 = 40.

(ii) 40 - 10 = 30

(iii) 30 - 10 = 20

(iv) 20 - 10 = 10

(v) 10 - 10 = 0 



2. Division is the inverse of multiplication.

(a) (i) 12 × 10 = 120

(ii) 120 ÷ 10= 12

(iii) 120 ÷ 12 = 10 



(b) (i) 25 × 5 = 125

(ii) 125 ÷ 5 = 25

(iii) 125 ÷ 25 = 5 



3. Relation between Dividend, Divisor, Quotient and Remainder is.

Dividend = Divisor × Quotient + Remainder


To understand the relation between dividend, divisor, quotient and remainder let us follow the following examples:

(a) Divide 537809 by 35 and find the quotient and remainder.

We need to divide the dividend i.e. 537809 by the divisor i.e. 35 to get the quotient and remainder.

5 cannot be divided by 35 as 5 < 35. So, we will move to the next digit of the dividend i.e. 3 and now we have 53 which can be divided by 35 as 53 > 35. We first divide 53 by 35. 35 into 53 is 1 leaving 18.

Then we bring down the next digit of the dividend i.e. 7 and we have 187. Now we divide 187 by 35 so, 35 into 187 is 5 leaving 12.

Again we bring down the next digit of the dividend i.e. 8 and we have 128. Now we divide 128 by 35 so, 35 into 128 is 3 leaving 23.

Similarly, again we bring down the next digit of the dividend i.e. 0 and we have 230. Now we divide 230 by 35 so, 35 into 230 is 6 leaving 20.

And at last we bring down the last digit of the dividend i.e. 9 and we have 209. So, we divide 209 by 35 then, 35 into 209 is 5 leaving 34.

Division of Whole Numbers

Check the answer of the division:

Dividend = Divisor × Quotient + Remainder

537809 = 35 × 15365 + 34

537809 = 537775 + 34

537809 = 537809


(b) Divide 86228364 by 2768 and check the answer.

We need to divide the dividend i.e. 86228364 by the divisor i.e. 2768 to get the quotient and remainder.

8 cannot be divided by 2768 as 8 < 2768. So, we will move to the second digit of the dividend i.e. 6 and now we have 86 which cannot be divided by 2768 as 86 < 2768. So, we will move to the third digit of the dividend i.e. 2 and now we have 862 which also cannot be divided by 2768 as 862 < 2768. So, we will move to the fourth digit of the dividend i.e. 2 and now we have 8622 which can be divided by 2768 as 8622 > 2768. We first divide 8622 by 2768. 2768 into 8622 is 3 leaving 318.

Then we bring down the fifth digit of the dividend i.e. 8 and we have 3188. Now we divide 3188 by 2768 so, 2768 into 3188 is 1 leaving 420.

Again we bring down the sixth digit of the dividend i.e. 3 and we have 4203. Now we divide 4203 by 2768 so, 2768 into 4203 is 1 leaving 1435.

Similarly, again we bring down the seventh digit of the dividend i.e. 6 and we have 14356. Now we divide 14356 by 2768 so, 2768 into 14356 is 5 leaving 516.

And at last we bring down the last digit of the dividend i.e. 4 and we have 5164. So, we divide 5164 by 2768 then, 2768 into 5164 is 1 leaving 2396.

Relation between Dividend, Divisor, Quotient and Remainder

Now to check the answer of the division:

Dividend = Divisor × Quotient + Remainder

86228364 = 2768 × 31151 + 2396

86228364 = 86225968 + 2396

86228364 = 86228364


4. Divide 682592 by 32 and verify the answer.

Solution:

Dividing Whole Numbers

Hence, 682592 ÷ 32 =21331


Now to check the answer of the division:

Divisor × Quotient + Remainder = Dividend

    32   ×   21331   +      0         = 682592


Division by numerals ending with zeroes:

We know that division is the inverse operation of multiplication. When we divide a number by 10, 100 or 1000, we take away as many zeroes from dividend as in the divisor.

For example:

60 ÷ 10 = 6

600 ÷ 10 = 60

6000 ÷ 10 = 600

60000 ÷ 10 = 6000

600 ÷ 100 = 6

6000 ÷ 100 = 60

60000 ÷ 100 = 600

600000 ÷ 100 = 6000

6000 ÷ 1000 = 6

60000 ÷ 1000 = 60

600000 ÷ 1000 = 600

6000000 ÷ 1000 = 6000


Questions and Answers on Division of Whole Numbers:

I. Find the quotient and check the answers in each of the following:

(i) 22786 ÷ 3

(ii) 389458 ÷ 7

(iii) 6872419 ÷ 24

(iv) 7714592 ÷ 32

(v) 9600729 ÷ 84

(vi) 11682000 ÷ 125

(vii) 66921036 ÷ 170

(viii) 6017635 ÷ 580

(ix) 7654981 ÷ 53


Answers:

(i) Quotient = 7595; Remainder = 1.

(ii) Quotient = 55636; Remainder = 6.

(iii) Quotient = 286350; Remainder = 19.

(iv) Quotient = 241081; Remainder = 0.

(v) Quotient = 114294; Remainder = 33.

(vi) Quotient = 93456; Remainder = 0.

(vii) Quotient = 393653; Remainder = 26.

(viii) Quotient = 10375; Remainder = 135.

(ix) Quotient = 144433; Remainder = 32.


2. Find the quotient and remainder for the given.

(i) 8703364 ÷ 10

(ii) 6933453 ÷ 10000

(iii) 459827 ÷ 100

(iv) 7768232 ÷ 100000

(v) 5672861 ÷ 1000

(vi) 97367140 ÷ 10000


Answers:

(i) Quotient = 870336; Remainder = 4.

(ii) Quotient = 693; Remainder = 3453.

(iii) Quotient = 4598; Remainder = 27.

(iv) Quotient = 77; Remainder = 68232.

(v) Quotient = 5672; Remainder = 861.

(vi) Quotient = 9736; Remainder = 7140.


3. Fill In the blanks.

(i) 4928831 ÷ 1 = ________

(ii) 6582110 × ________ = 6582110

(iii) 5082240 ÷ 10 = ________

(iv) ________ × 0 = 0

(v) 7433925 ÷ 7433925 = ________

(vi) 8953022 + ________ = 8953023

(vii) 3800452 × (0 × 883245) = ________


Answers:

(i) 4928831

(ii) 1

(iii) 508224

(iv) Any number

(v) 1

(vi) 1

(vii) 0


Word Problems on Division of Whole Numbers:

4. 125896 tiles are to be loaded in 8 vehicles equally. How many tiles are loaded in each vehicle?

Answer: 15737 tiles


5. 3792780 voters are to be equally distributed in 18 blocks. How many voters will there be in each block?

Answer: 210710 voters

● Operations On Whole Numbers







5th Grade Math Problems

From Division of Whole Numbers to HOME PAGE


New! Comments

Have your say about what you just read! Leave me a comment in the box below. Ask a Question or Answer a Question.



Didn't find what you were looking for? Or want to know more information about Math Only Math. Use this Google Search to find what you need.



Share this page: What’s this?

Recent Articles

  1. Method of H.C.F. |Highest Common Factor|Factorization &Division Method

    Apr 13, 24 05:12 PM

    HCF by Short Division Method
    We will discuss here about the method of h.c.f. (highest common factor). The highest common factor or HCF of two or more numbers is the greatest number which divides exactly the given numbers. Let us…

    Read More

  2. Factors | Understand the Factors of the Product | Concept of Factors

    Apr 13, 24 03:29 PM

    Factors
    Factors of a number are discussed here so that students can understand the factors of the product. What are factors? (i) If a dividend, when divided by a divisor, is divided completely

    Read More

  3. Methods of Prime Factorization | Division Method | Factor Tree Method

    Apr 13, 24 01:27 PM

    Factor Tree Method
    In prime factorization, we factorise the numbers into prime numbers, called prime factors. There are two methods of prime factorization: 1. Division Method 2. Factor Tree Method

    Read More

  4. Divisibility Rules | Divisibility Test|Divisibility Rules From 2 to 18

    Apr 13, 24 12:41 PM

    Divisibility Rules
    To find out factors of larger numbers quickly, we perform divisibility test. There are certain rules to check divisibility of numbers. Divisibility tests of a given number by any of the number 2, 3, 4…

    Read More

  5. Even and Odd Numbers Between 1 and 100 | Even and Odd Numbers|Examples

    Apr 12, 24 04:22 PM

    even and odd numbers
    All the even and odd numbers between 1 and 100 are discussed here. What are the even numbers from 1 to 100? The even numbers from 1 to 100 are:

    Read More