# CLASS-7PROPERTY OF 1 OF DIVISION OF RATIONAL NUMBER

PROPERTY OF 1 OF DIVISION OF RATIONAL NUMBER -

The "Property of 1" in the context of division of rational numbers states that any rational number divided by 1 remains unchanged. This property can be formally stated as follows:

Property of 1:-

For any rational number a,

a

------- = a

1

Explanation:-

• Rational Numbers:-

A rational number is any number that can be written as p/q, where p and q are integers and q โ  0.

• When you divide a rational number by 1, you are essentially saying that the number is being split into one part, which is itself.

Examples:-

1. Positive Rational Number:-

Let, a = 3/4

3               3

a รท 1 = ------ รท 1 = ------

4               4

2. Negative Rational Number:-

Let, a = - 5/7

- 5            - 5

a รท 1 = ------ รท 1 = ------

7               7

3. Whole Number:-

Let, a = 99

99               99

a รท 1 = -------  รท 1 = ------ = 99

1                1

4. Zero:-

Let, a =

a รท 1 = 0 รท 1 = 0

Proof:-

To understand why this property holds, consider the definition of division and rational numbers. Any rational number a can be expressed as p/q. Dividing p/q by 1 means multiplying by the reciprocal of 1, which is still 1:-

a          p/q          p              p          1          p

------ = ------- = ------ รท 1 = ------ x ------ = ------ = a

1           1           q              q          1          q

Thus, for any rational number a, dividing it by 1 results in the number itself. This demonstrates the "Property of 1" for division of rational numbers.

Importance:-

The identity property of division is fundamental because it helps in simplifying expressions and solving equations. Knowing that dividing by 1 does not change the value of a number allows us to manipulate and simplify rational expressions more easily.

In summary, the property of 1 in the division of rational numbers states that any rational number divided by 1 remains the same, highlighting the identity property of division.