Number System EXERCISE 1.1 (II)

EXERCISE 1.1 (II)

Question – 3 - Find five rational numbers between 3/5 and 4/5.

Answer:

First method to find rational number between two number:

Since we have to find 5 rational numbers between 3/5 and 4/5, so we

will mutiply the numerator and denomirator of or the given numbers by

5+1, i.e. equal to 6.

We get,

Now, we have to find 5 rational numbers between 18/30 and 24/30, which will come as

Thus, five rational numbers between 3/5 and 4/5 are         







You can find as many rational numbers between given numbers using method given above.

Second method to find rational number between two number:

(1) One rational number between given numbers 3/5 and 4/5 will the average between them.

Thus, average between 3/5 and 4/5 will be equals to

(2) Rational number between 3/5 and 7/10 will be the next rational number between 3/5 and 4/5, since 7/10 is a rational number between 3/5 and 4/5. Thus, next rational number between 3/5 and 7/10 can be found by calculating average between them. Calculation is as follows:

(3) Similarly, rational number between 4/5 and 7/10 will be the another rational number between 3/5 and 4/5. This another rational number between 3/5 and 4/5 can be found by calculating average between 4/5 and 7/10, calculation is as follows:

(4) Similarly, rational number between 3/5 and 13/20 will be the another rational number between 3/5 and 4/5, which can be found by calculating average between 3/5 and 13/20, calculation is as follows:

(5) Similarly, rational number between 3/5 and 5/8 will be the another rational number between 3/5 and 4/5, which can be found by calculating average between 3/5 and 5/8, calculation is as follows:

Thus, five rational numbers between 3/5 and 4/5 are 7/10, 13/20, 3/4, 5/8 and 49/80

You can find more rational numbers between the given two numbers 3/5 and 4/5 using above method.

Question – 4 - State whether the following statements are true or false. Give reasons for your answers.

(i) Every natural number is a whole number.

(ii) Every integer is a whole number.

(iii) Every rational number is a whole number.

Answer –

(1) True

Reason: Natural numbers are counting numbers, starting from 1. Example – 1, 2, 3, 4, .. and so on. While whole numbers are all natural numbers including zero. Thus, every natural number is a whole number.

(2) False

Reason: Integers can be positive and negative both. Since whole numbers are only positive, thus every integer is not a whole number, rather only positive integers are whole number.

(3) False

Reason: Numbers are in the form of p/q or can be written in the form of p/q are called rational numbers, while whole numbers are counting numbers including zero. For example 1/2 is a rational number and clearly it is not a whole number. Thus, every rational number is not a whole number.