# INSERTING RATIONAL NUMBERS BETWEEN TWO GIVEN RATIONAL NUMBERS

## About "Inserting Irrational Numbers Between Two Given Rational Numbers"

Inserting Irrational Numbers Between Two Given Rational Numbers :

Here we are going to see some practice questions on inserting irrational numbers between two given rational numbers.

## Inserting Irrational Numbers Between Two Given Rational Numbers - Practice questions

Question 1 :

List five rational numbers between

(i) –2 and 0

Solution :

-1.9, -1.8, -1.7, -1.6, -1.5

writing the above decimals as rational numbers, we get

-19/10, -18/10, -17/10, -16/10, -15/10

(ii)  -1/2 and 3/5

Solution :

Let us convert the denominators same.

(-1/2) ⋅ (5/5)  =  -5/10

(3/5) ⋅ (2/2)  =  6/10

Rational numbers between them are

-4/10, -3/10, -2/10, -1/10, 0, 1/10, .....

We may choose any five as answer.

(iii)  0.25 and 0.35

Solution :

Writing numbers between 0.25 and 0.35 in decimal form, we get

0.26, 0.27, 0.28, 0.29, 0.30, 0.31, 0.32, 0.33, 0.34

By changing them into fraction, we get

26/100, 27/100, 28/100, 29/100, 30/100

(iv) –1.2 and -2.3

Solution :

-1.3, -1.4, -1.5, -1.6, -1.7, .........., -2.2

By changing them into decimal form, we get

13/10, 14/10, 15/10, 16/10, 17/10.

## Writing Equivalent Rational Numbers of the Given Numbers

Question 1 :

Write four rational numbers equivalent to

(i) −3/5

Solution :

In order to find equivalent fraction, let us multiply both numerator and denominator of the given fraction by 2.

(-3/5) ⋅ (2/2)  =  -6/10

(-3/5) ⋅ (3/3)  =  -9/15

(-3/5) ⋅ (4/4)  =  -12/20

(-3/5) ⋅ (5/5)  =  -15/25

Hence the four equivalent fractions are -6/10, -9/15, -12/20, -15/25.

(ii)  -7/6

Solution :

(-7/6) ⋅ (2/2)  =  -14/12

(-7/6) ⋅ (3/3)  =  -21/18

(-7/6) ⋅ (4/4)  =  -28/24

(-7/6) ⋅ (5/5)  =  -35/30

Hence the four equivalent fractions are -14/12, -21/18, -28/24, -35/30.

(iii)  8/9

Solution :

(-7/6) ⋅ (2/2)  =  -14/12

(-7/6) ⋅ (3/3)  =  -21/18

(-7/6) ⋅ (4/4)  =  -28/24

(-7/6) ⋅ (5/5)  =  -35/30

Hence the four equivalent fractions are -14/12, -21/18, -28/24, -35/30.

Question 2 :

Draw the number line and represent the following rational numbers on it

(i)  9/4   (ii)  -8/3   (iii)  -17/(-5)   (iv)  -15/4

Solution :

(i)  9/4  =  2.25

(ii)  -8/3  =  -2.66

(iii)  -17/(-5)  =  3.4

(iv)  -15/4  =  3.75 Question 3 :

Find the rational numbers for the question marks marked on the number line.

(i) Solution :

The part lies between -3 and -4 is divided into three equal intervals.

Moving from -3 to the indicated arrow, we have to cover 2/3 interval.

=  -3 + (-2/3)

=  -11/3

Hence the indicated arrow represents -11/3.

(ii) Solution :

The portion between 0 and -1 is divided into 5 equal parts.Moving from 0 to the arrow indicated, we have to cover 2/5 part.. Since we move to the left side, we have to take negative sign.

Hence the arrow is indicating the rational number -2/5.

(iii) The portion between 0 and -1 is divided into 4 equal parts.Moving from 1 to the arrow indicated, we have to cover 3/4 part.. Since we move to the right side, we have to take positive sign.

=  1 +  (3/4)

=  7/4

Hence the arrow is indicating the rational number 7/4. After having gone through the stuff given above, we hope that the students would have understood, "Inserting Irrational Numbers Between Two Given Rational Numbers"

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