Properties of Division

The properties of division are discussed here:

1. Division by 1 Property:

If we divide a number by 1 the quotient is the number itself.

In other words, when any number is divided by 1, we always get the number itself as the quotient.

When any number is divided by 1, we always get the number itself.


For example:

(i) 7542 ÷ 1 = 7542

(ii) 372 ÷ 1 = 372

(iii) 1522 ÷ 1 = 1522

(iv) 1502 ÷ 1 = 1502

(v) 34 ÷ 1 = 34

(vi) 16 ÷ 1 = 16

(v) 1084 ÷ 1 = 1084

(vi) 1745 ÷ 1 = 1745

(vii) 28456 ÷ 1 = 28456

(viii) 34 ÷ 1 = 34

(ix) 16 ÷ 1 = 16

Dividing a number by 1 gives the number itself as the quotient.

Example:

5 ÷ 1 = 5 as 5 × 1 = 5,

8 ÷ 1 = 8 as 8 × 1 = 8, etc.


When a number is divided by 1, it gives the number itself.

4 balloons are given to 1 child.

Division of a Number by 1

4 ÷ 1 = 4


2. Division by itself Property:

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

In other words, when any number is divided by the number itself, we always get 1 as the quotient.

When any number is divided by the number itself, we always get 1 as the quotient.

For example: 

(i) 275 ÷ 275 = 1

(ii) 105 ÷ 105 = 1

(iii) 572 ÷ 572 = 1

(iv) 1027 ÷ 1027 = 1

(v) 1426 ÷ 1426 = 1

(vi) 1654 ÷ 1654 = 1

(vii) 18520 ÷ 18520 = 1

(viii) 7 ÷ 7 = 1

(ix) 24 ÷ 24 = 1


When a number is divided by itself, the answer is 1.

  • Divide 5 candies among 5 children.
Division of a Number by Itself

               5 ÷ 5 = 1

       Each child gets 1 candy.


  • Divide 6 apples among 6 children.

Division by Itself Property

               6 ÷ 6 = 1

       Each child gets 1 apple.


Dividing a number by itself, gives 1 as the quotient.

Example:

If we divide six flowers among six vases, how many flowers can we put in each vase?

Dividing a Number by Itself

We put 1 flower in each vase. So, 6 ÷ 6 = 1 because 6 × 1 = 6

3. Division any Number by 0 Property:

Division of a number by 0 is meaningless.

In other words,

Division by 0 is meaningless.

For example: 

(i) 15 ÷ 0 = meaningless

(ii) 35 ÷ 0 = no meaning

(iii) 65 ÷ 0 = no meaning

(iv) 29 ÷ 0 = no meaning

(v) 47 ÷ 0 = no meaning

(vi) 86 ÷ 0 = no meaning

Note: The divisor can never be zero. Division by zero is not possible.



4. Division of 0 by any Number Property:

0 divided by a number gives 0 as the quotient.

In other words, when 0 is divided by any number, we always get 0 as the quotient.

Dividing zero by a number gives zero as the quotient.

0 ÷ 5 = 0 because 5 × 0 = 0

For example: 

(i) 0 ÷ 25 = 0

(ii) 0 ÷ 100 = 0

(iii) 0 ÷ 4255 = 0

(iv) 0 ÷ 15246 = 0

(v) 0 ÷ 2 = 0

(vi) 0 ÷ 75 = 75

Properties of Division


5. Division by 10, 100 and 1000 Property:


For example:

(i) When a number is divide by 10, the digit in the once place is the remainder.

867 ÷ 10;

Quotient = 86 and Remainder =7.

Division by 10

What do we observe?

We see that when a number (dividend) is divided by 10 the quotient is obtained by removing the ones digit from the number (dividend) and the digit at ones place is the remainder. 



(ii) When a number is divided by 100, the number formed by the tens and once place is the remainder.


2764 ÷ 100;

Quotient = 27 and Remainder = 64. 

Division by 100

What do we observe?

We sew that when a number (dividend) is divided by 100 the quotient is obtained by removing the last two digits on the extreme right of the number (dividend). The number formed by these last to digits is the remainder.


Frequently Asked Questions (FAQs)

1. What is Division by 1 Property?

Ans: When divisor is 1, the quotient is the same as the dividend.

For Example:

÷ 1 = 5;     15 ÷ 1 = 15;     50 ÷ 1 = 50.


2. What is Division by itself Property?

Ans: When the divisor and the dividend are the same non-zero numbers, the quotient is 1.

For Example:

÷ 7 = 1;     13 ÷ 13 = 1;     70 ÷ 70 = 1.


3. What is Division of 0?

Ans: When the dividend is 0, the quotient is 0.

For Example:

÷ 6 = 0;     0 ÷ 19 = 0;     0 ÷ 81 = 0


4. What is Division By Zero?

Ans: The divisor can never be 0. Or, division by 0 is meaningless.

For Example:

20 ÷ 0 = no meaning / not defined

52  ÷ 0 = no meaning / not defined

75 ÷ 0 = no meaning / not defined


Worksheet on Properties of Division:

1. Fill in the blanks:

(i) 6 ÷ 6 = ……….

(ii) 5 ÷ 1 = ……….

(iii) 3 ÷ 3 = ……….

(iv) 9 ÷ 1 = ……….

(v) 8 ÷ 8 = ……….

(vi) 10 ÷ 1 = ……….


Answer:

1. (i) 1

(ii) 5

(iii) 1

(iv) 9

(v) 1

(vi) 10


2. Fill in the blanks.

(i) 23 ÷ 23 = ………

(ii) 21 ÷ ……… = 21

(iii) 15 ÷ 1 = ………

(iv) ……… ÷ 15 = 0

(v) 0 ÷ 12 = ………

(vi) 8 ÷ ……… = 1

(vii) 65 ÷ 65 = ………

(viii) ……… ÷ 12 = 1

(ix) 8 ÷ 1 = _____

(x) 6 ÷ 6 = _____

(xi) 0 ÷ 10 = _____

(xii) 21 ÷ 21 = _____

(xiii) 12 ÷ _____ = 1

(xiv) 21 ÷ 1 = _____

(xv) _____ ÷ 12 = 0

(xvi) 12 ÷ 0 = _____


Answer:

2. (i) 1

(ii) 1

(iii) 15

(iv) 0

(v) 0

(vi) 8

(vii) 1

(viii) 12

(ix) 8

(x) 1

(xi) 0

(xii) 1

(xiii) 12

(xiv) 21

(xv) 0

(xvi) undefined / meaningless

You might like these

● Operations On Whole Numbers

● Addition Of Whole Numbers.

● Subtraction Of Whole Numbers.

● Multiplication Of Whole Numbers.

● Properties Of Multiplication.

● Division Of Whole Numbers.

● Properties Of Division.







5th Grade Math Problems 

From Properties of Division to HOME PAGE




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.



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.




Share this page: What’s this?

Recent Articles

  1. Worksheet on Comparing and Ordering Decimals |Arranging Decimals

    Apr 19, 25 12:16 PM

    Arranging Decimals
    Practice different types of math questions given in the worksheet on comparing and ordering decimals. This worksheet contains questions mainly related to compare decimals and then place the decimals i…

    Read More

  2. Comparison of Decimal Fractions | Comparing Decimals Numbers | Decimal

    Apr 19, 25 11:47 AM

    Comparison of Decimal Fractions
    While comparing natural numbers we first compare total number of digits in both the numbers and if they are equal then we compare the digit at the extreme left. If they also equal then we compare the…

    Read More

  3. Expanded form of Decimal Fractions |How to Write a Decimal in Expanded

    Apr 19, 25 11:25 AM

    Expanded form of Decimal
    Decimal numbers can be expressed in expanded form using the place-value chart. In expanded form of decimal fractions we will learn how to read and write the decimal numbers. Note: When a decimal is mi…

    Read More

  4. Missing Numbers up to 10 | Worksheets on Missing Numbers up to 10

    Apr 18, 25 04:53 PM

    missing numbers up to 10
    Printable worksheets on missing numbers up to 10 help the kids to practice counting of the numbers.

    Read More

  5. Ordering Decimals | Comparing Decimals | Ascending & Descending Order

    Apr 18, 25 01:49 PM

    Ordering Decimal Numbers
    In ordering decimals we will learn how to compare two or more decimals. (i) Convert each of them as like decimals. (ii) Compare these decimals just as we compare two whole numbers ignoring

    Read More