# Worksheet on Comparison of Rational Numbers

Practice the questions given in the worksheet on comparison of rational numbers.

We know, if there are two rational numbers with common denominator, then one with the larger numerator is larger than the other.

The questions are based on finding the greater and the smaller rational number among the given pairs of rational numbers, arranging the rational numbers in ascending order and descending order.

1. Which of the two rational numbers in each of the following pairs of rational numbers is greater?

 (i) 3/8 or 0 (ii) (-3)/8 or 0 (iii) (-2)/9 or 0 (iv) 2/5 or 0 (v) (-3)/4 or ¼ (vi) (-4)/11 or 3/11 (vii) (-5)/7 or (-4)/7 (viii) (-7)/12 or 5/(-8) (ix) 2/3 or 3/4 (x) 4/(-9) or (-3)/(-7) (xi) (-1)/2 or -1 (xii) (-5)/8 or 3/(-4) (xiii) 5/9 or (-3)/(-8) (xiv) 5/(-8) or (-7)/12

2. Which of the two rational numbers in each of the following pairs of rational numbers is smaller?

 (i) -4/3 or -8/7 (ii) (-6)/(-13) or 7/13 (iii) 7/-9 or -5/8 (iv) 16/(-5) or 3 (v) -1/3 or 4/-5 (vi) (-4)/3 or 8/(-7) (vii) 9/-13 or 7/-12 (viii) (-12)/5 or -3 (ix) 4/-5 or -7/10  (x) -12/5 or -3

3. Fill in the blanks with the correct symbol out of >, = and <:

 (i) (-6)/7 ____ 7/13 (ii) (-3)/7 ____ 6/(-13) (iii) (-3)/5 ____ (-5)/6 (iv) 5/(-13) ____ (-35)/91 (v) (-2)/3 ____ 5/(-8) (vi) -2 ____ (-13)/5 (vii) 0 ____ (-2)/5 (viii) (-2)/3 ____ 5/(-8) (ix) 0 ____ (-3)/(-5) (x) (-8)/9 ____ (-9)/10

4. Arrange the following rational number ascending order:

(i) 2/3, 5/7, (-4)/(-9), 1/4

(ii) 4/(-9), (-5)/12, 7/(-18), (-2)/3

(iii) 3/5, (-17)/(-30), 8/(-15), (-7)/10

(iv) (-3)/4, 5/(-12), (-7)/16, 9/(-24)

(v) (-4)/9, 5/(-12), 7/(-18), 2/(-3)

(vi) 3/(-5), (-7)/10, (-11)/15, (-13)/20

(vii) 2/3, (-4)/7, (-8)/3, 6/(-9)

(viii) (-4)/7, (-9)/14, 13/(-28), (-23)/42

5. Arrange the following rational number descending order:

(i) -2, (-13)/6, 8/(-3), 1/3

(ii) (-3)/(-5), 17/30, (-8)/15, 7/(-10)

(iii) (-3)/10, 7/(-15), (-11)/20, 17/(-30)

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

(v) (-5)/6, (-7)/12, (-13)/18, 23/(-24)

(vi) (-3)/10, 17/(-30), 7/(-15), (-11)/20

(vii) (-10)/11, (-19)/22, (-23)/33, (-39)/44

(viii) 2/5, (-3)/(-4), ½, (-7)/(-6), 0

Answers for the worksheet on comparison of rational numbers are given below to check the exact answers of the above questions on comparing rational number.

 1. (i) 3/8 (ii) 0 (iii) 0 (iv) 2/5 (v) 1/4 (vi) 3/11 (vii) (-4)/7 (viii) (-7)/12 (ix) 3/4 (x) (-3)/(-7) (xi) (-1)/2  (xii) (-5)/8 (xiii) 5/9 (xiv) (-7)/12
 2. (i) -4/3 (ii) (-6)/(-13) (iii) 7/-9 (iv) 16/(-5) (v) 4/-5 (vi) (-4)/3 (vii) 9/-13 (viii) -3 (ix) 4/-5 (x) -3
 3. (i) < (ii) > (iii) > (iv) = (v) < (vi) > (vii) > (viii) < (ix) < (x) >

4. (i) 1/4 < (-4)/9 < 2/3 < 5/7

(ii) (-2)/3 < 4/(-9) <(-5)/12 < 7/(-18)

(iii) (-7)/10 < 8/(-15) < (-17)/(-30) < 3/5

(iv) (-3)/4 < (-7)/16 < 5/(-12) < 9/(-24)

(v) 2/(-3) < (-4)/9 < 5/(-12) < 7/(-18)

(vi) (-11)/15 < (-7)/10 < (-13)/20 < 3/(-5)

(vii) (-8)/3, 6/(-9), (-4)/7, 2/3

(viii) (-9)/14 < (-4)/7 < (-23)/42 < 13/(-28)

5. (i) 1/3 > -2 > (-13)/6 > 8/(-3)

(ii) (-3)/(-5) > 17/30 > (-8)/15 > 7/(-10)

(iii) (-3)/10 > 7/(-15) > (-11)/20 > 17/(-30)

(iv) 140/28 > 64/16 > 7/8 > 5/(-4) > 36/(-12)

(v) (-7)/12 > (-13)/18 > (-5)/6 > 23/(-24)

(vi) (-3)/10 > 7/(-15) > (-11)/20 > 17/(-30)

(vii) (-23)/33 > (-19)/22 > (-39)/44 > (-10)/11

(viii) (-7)/(-6) > (-3)/(-4) > 1/2 > 2/5 > 0

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