What is Division ? Write their prapertis
Answers
The division property of equality states that when we divide both sides of an equation by the same non-zero number, the two sides remain equal. That is, if a, b, and c are real numbers such that a = b and c ≠0, then a c = a c .
Properties of Division:-
Division by 1 Property: If we divide a number by 1 the quotient is the number itself. ...
Division by itself Property: If we divide a number by the number itself, the quotient is 1. ...
Division any Number by 0 Property: ...
Division of 0 by any Number Property: ...
Division by 10, 100 and 1000 Property:
HOPE ITS HELPFUL.
Answer:
The separation of something into different parts; the sharing of something between different people, groups, places, etc is called division
Step-by-step explanation:
Property 1:
If a and b (b not equal to zero) are whole numbers, then a ÷ b (expressed as a/b) is not necessarily a whole number.
In other words, whole numbers are not closed for division.
Verification: We know that dividing a whole number a by a non-zero whole number b means finding a whole numbers c such that a = bc.
Consider the division of 14 by 3. We find that there is no whole number which when multiplied by 3 gives us 14. So, 14 ÷ 3 is not a whole number. Similarly, 12, 5, 9, 4, 37, 6 etc. are not whole numbers.
Property 2:
If a is any whole number, then a ÷ 1 = a.
In other words, any whole number divided by 1 gives the quotient as the number itself.
Verification: We know that
(i) 1 × 5 = 5
Therefore, 5 ÷ 1 = 5
(ii) 1 × 11 = 11
Therefore, 11 ÷ 1 = 11
(iii) 1 × 29 = 29
Therefore, 29 ÷ 1 = 29
(iv) 1 × 116 = 116
Therefore, 116 ÷ 1 = 116
(v) 1 × 101 = 101
Therefore, 101 ÷ 1 = 101
(vi) 1 × 1 = 1
Therefore, 1 ÷ 1 = 1
Property 3:
If a is any whole number other than zero, then a ÷ a = 1.
In other words, any whole number (other than zero) divided by itself gives 1 as the quotient.
Verification: We have,
(i) 13 = 13 × 1
Therefore, 13 ÷ 13 = 1
(ii) 9 = 9 × 1
Therefore, 9 ÷ 9 = 1
(iii) 17 = 17 × 1
Therefore, 17 ÷ 17 = 1
(iv) 123 = 123 × 1
Therefore, 123 ÷ 123 = 1
(v) 21 = 21 × 1
Therefore, 21 ÷ 21 = 1
(vi) 1 = 1 × 1
Therefore, 1 ÷ 1 = 1
Property 4:
Zero divided by any whole number (other than zero) gives the quotient as zero. In other words, if a is a whole numbers other than zero, then 0 ÷ a = 0
Verification : We have,
(i) 0 × 7 = 0
Therefore, 0 ÷ 7 = 0
(ii) 0 × 11 = 0
Therefore, 0 ÷ 11 = 0
(iii) 0 × 17 = 0
Therefore, 0 ÷ 17 = 0
(iv) 0 × 132 = 0
Therefore, 0 ÷ 132 = 0
(v) 0 × 164 = 0
Therefore, 0 ÷ 164 = 0