Worksheet on Equivalent Rational Numbers

Practice the questions given in the worksheet on equivalent rational numbers. We know, to convert a rational number to an equivalent rational number, either multiply or divide both its numerator and denominator by a non-zero integer.

1. Express each of the following as a rational number with positive denominator:

(i) 15/(-28)

(ii) 6/(-9)

(iii) -28/(-11)

(iv) 19/(-7)

2. Express 3/5 as a rational number with numerator:

(i) 6

(ii) -15

(iii) 21

(iv) -27

3. Express (-3)/5 as a rational number with denominator.

(i) 20

(ii) -30

(iii) 35

(iv) -40

4. Express 5/7 as a rational number with denominator:

(i) -14

(ii) 70

(iii) -28

(iv) -84

5. Express 3/4 as a rational number with denominator:

(i) 20

(ii) 36

(iii) 44

(iv) -80

6. Express 2/5 as a rational number with numerator

(i) -56

(ii) 154

(iii) -750

(iv) 500

7. Express (-192)/108 as a rational number with numerator:

(i) 64

(ii) -16

(iii) 32

(iv) -48

8. Express 168/(-294) as a rational number with denominator :

(i) 14

(ii) -7

(iii) -49

(iv) 1470

9. Write (-14)/42 in a form so that the numerator is equal to:

(i) -2

(ii) 7

(iii) 42

(iv) -70

10. Express (-42)/98 as a rational number with denominator 7.

11. Express (-48)/60 as a rational number with denominator 5.

12. Select those rational numbers which can be written as a rational number with numerator 6:
1/22, 2/3, 3/4, 4/(-5), 5/6, (-6)/7, (-7)/8

13. Select those rational numbers which can be written as a rational number with denominator 4:

7/8, 64/16, 36/(-12), (-16)/17, 5/(-4), 140/28

14. In each of the following, find an equivalent form of the rational number having a common denominator:

(i) 3/4 and 5/12

(ii) 2/3, 7/6 and 11/12

(iii) 5/7, 3/8, 9/14 and 20/21

Answers for the worksheet on equivalent rational numbers are given below to check the exact answers of the above questions on converting a rational number to its equivalent rational number.

Answers:

1. (i) 15

(ii) (-6)/9

(iii) 28/11

(iv) (-19)/7

2. (i) 6/10

(ii) (-15)/(-25)

(iii) 21/35

(iv) (-27)/(-45)

3. (i) (-12)/20

(ii) 18/(-30)

(iii) (-21)/35

(iv) 24/(-40)

4. (i) (-10)/(-14)

(ii) 50/70

(iii) (-20)/28

(iv) (-60)/(-84)

5. (i) 15/20

(ii) 27/36

(iii) 33/44

(iv) (-60)/(-80)

6. (i) (-56)/(-140)

(ii) 154/385

(iii) (-750)/(-1875)

(iv) 500/1250

7. (i) 64/(-36)

(ii) (-16)/9

(iii) 32/(-18)

(iv) (-48)/27

8. (i) (-8)/14

(ii) 4/(-7)

(iii) 28/(-49)

(iv) (-840)/1470

9. (i) (-2)/6

(ii) 7/(-21)

(iii) 42/(-126)

(iv) (-70)/210

10. (-3)/7

11. (-4)/5

12. 1/22, 2/3, 3/4, (-6)/7

13. 7/8, 64/16, 36/(-12), 5/(-4), 140/28

14. (i) 9/12 and 5/12

(ii) 8/12, 14/12 and 11/12

(iii) 120/168, 63/168, 108/168 and 160/168

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