Exercise 8.1

List five rational numbers between:

Instruction

(i) -1 and 0

So, we multiply the number by 66.

-1 ×66 = −66

0 × 66 = 06

Rational Numbers are , , , ,

(ii) -2 and -1

So, we multiply the number by 66.

-2 × 66 = −126

-1 × 66 = −66

Rational Numbers are , , , ,

(iii) −45 and −23

Commmon denominator = Lcm of 3 & 5 =

So, −45 × 33 = −1215 , −23 × 55 = −1015

So, we multiply the number by 66.

−1215 × 66 = −7290 , −1015 × 66 = −6090

Rational Numbers are , , , ,

(iv) −12 and 23

Commmon denominator = Lcm of 2 & 3 =

So, −12 × 33 = −36 , 23 × 22 = 46

Rational Numbers are , , ,

Write four more rational numbers in each of the following patterns.

(i)−35 , −610 , −915 , −1215

Instruction

−610 = −35 × 22 , −915= −35 × 33 repeat the same process and see the difference with in the numbers.

So,these are equivalent rational numbers of −35.

Rational Numbers are −35 × 55 = , −35 × 66 =

−35 × 77 = , −35 × 88 =

(ii)−14 , −28 , −312

−28 = −14 × 22 , −312 = −14 × 33

So,these are equivalent rational numbers of −14.

Rational Numbers are −14 × 44 = , −14 × 55 =

−14 × 66 = , −14 × 77 =

(iii)−16 , 2−12 , 3−18 , 4−24

We write the numbers as −16 , −212 , −318 , −424

−212 = −16 × 22 , −318 = −16 × 33 repeat the same process for next number also.

So,these are equivalent rational numbers of −16.

Rational NUmbers are −16 × 55 = , −16 × 66 =

−16 × 77 = , −16 × 88 =

(iv)−23 , 2−3 , 4−6 , 6−9

2−3 = −23 × −1−1 , 4−6 = −23 × −2−2

So,these are equivalent rational numbers of −23.

Rational NUmbers are −23 × −4−4 = , −23 × −5−5 =

−23 × −6−6 = , −23 × −7−7 =

Give four rational numbers equivalent to.

(i)−27

Instruction

−27 Equivalent rational numbers are −27 22 =

−27 × 33 =

−27 × 44 =

−27 × 55 =

(ii)5−3

5−3 = −53 Equivalent rational numbers are −53 × 22 =

−53 × 33 =

−53 × 44 =

−53 × 55 =

(iii)49

49 Equivalent rational numbers are 49 × 22 =

49 × 33 =

49 × 44 =

49 × 55 =

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

(i)34

Identify the integers between which the number lies: Here, 34 lies between 0 and 1.

Divide the length between 0 and 1 into equal parts because the denominator of 34 is 4.

Count 3 parts from 0 towards 1 and mark the point. This point represents .

(ii)−58

Identify the integers between which the number lies: Here, -5/8 lies between 0 and -1.

Divide the length between 0 and -1 into equal parts because the denominator of 58 is 8.

Count 5 parts from 0 towards -1 and mark the point. This point represents .

(iii)−74

Identify the integers between which the number lies: Here, -7/4 is an improper fraction. Converting it to a mixed number : -134 . It lies between -2 and -1.

Since the denominator of −74 is 4, divide the length between -1 and -2 into equal parts.

Count 3 parts from -1 towards -2 and mark the point. This point represents .

(iv)78

Identify the integers between which the number lies: Here, 7/8 is an proper fraction. It less than 1 but greater than 0.

Since the denominator of 78 is 8, divide the length between 0 and 1 into equal parts.

Count 7 parts from 0 towards 1 and mark the point. This point represents .

The points P, Q, R, S, T, U, A and B on the number line are such that, TR = RS = SU and AP = PQ = QB. Name the rational numbers represented by P, Q, R and S.

Solution :

Number line between A & B is divided into equal parts. It lines between and 3.

So, Point P = ; Point Q =

Number line between U & T is divided into equal parts. It lines between and .

So, Point R = ; Point S =

Which of the following pairs represent the same rational number?

Instruction

−721 and 39

−1620 and 20−25

−2−3 and 23

−35 and −1220

8−5 and −2415

13 and −19

−5−9 and 5−9

Pair Rational Numbers

Not a Pair Rational Numbers

Rewrite the following rational numbers in the simplest form.

Note: Find the Greatest Common Divisor(GCD) of the every number then it is easy to solve.

(i)−86

GCD of 8 and 6 =

Divide both the numerator and denominator by the GCD.4

−8÷26÷2 =

(ii)2545

GCD of 25 and 45 =

Divide both the numerator and denominator by the GCD.4

25÷545÷5 =

(iii)−4472

GCD of 44 and 72 =

Divide both the numerator and denominator by the GCD.

−44÷472÷4 =

(iv)−810

GCD of 8 and 10 =

Divide both the numerator and denominator by the GCD.4

−8÷210÷2 =

Fill in the boxes with the correct symbol out of >, <, and =.

(i)−57 23

(ii)−45 −57

(iii) −78 14−16

(iv) −85 −74

(v) 1−3 −14

(vi) 5−11 −511

(vii) 0 −76

Which is greater in each of the following.

(i)23 , 52

Instruction

LCM of 3 and 2 is

23 = 2×23×2 =

52 = 5×32×3 =

Since, 46

156

(ii)−56 , −43

LCM of 6 and 3 is

−56 = −5×16×1 =

−43 = −4×23×2 =

Since, −56

−43

(iii)−34 , 2−3

LCM of 4 and 3 is

−34 = −3×34×3 =

2−3 = 2×4−3×4 =

Since, −34

2−3

(iv)−14 , 14

Since, 46 156

(v)-327 , -347

LCM of 7 and 5 is

−237 = −23×57×5 =

−197 = −19×77×5 =

Since, -327 -345

Write the following rational numbers in ascending order.

(i) −35 , −25 , −15

, ,

(ii) −13 , −29 , −43

, ,

(iii) −37 , −32 , −34

, ,

Chapter 8: Rational Numbers

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Exercise 8.1

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Chapter 8: Rational Numbers

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Glossary

Exercise 8.1