NCERT Solutions for Class 7 Maths Chapter 9 Rational Numbers

NCERT solutions for class 7 maths chapter 9 rational numbers banner image
author_logo

Written by Team Trustudies
Updated at 2021-05-07


NCERT solutions for class 7 Maths Chapter 9 Rational Numbers Exercise 9.1

Q.1 List five rational numbers between:
(i) -1 and 0
(ii) -2 and -1
(iii)?45 and ?23
(iv) 12 and 23



NCERT Solutions for Class 7 Maths Chapter 9 Rational Numbers


Answer :

(i) The five rational numbers between -1 and 0 are,
-1< ?12 < ?34 < ?45 < ?13 < ?15 < 0< br> (ii) The five rational numbers between -2 and -1 are,
-2 < ?98 , ?97 , ?96 , ?85 , ?43 < -1
(iii) The five rational numbers between -4/5 and -2/3 are,
-4/5= ?4×65×6 = ?2430
-2/3 = ?2×103×10 = ?2030
-4/5 < (-21/30) , (-22/30) , (-23/30) , (-16/15) , (-17/16) <-2/3
(iv) The five rational numbers between -1/2 and 2/3 are,
-1/2 < (-1/6) < (0) < (1/3) < (1/2) < (20/36) < 2/3

Q.2 . Write four more rational numbers in each of the following patterns:
(i) -3/5, -6/10, -9/15, -12/20, …..
(ii) -1/4, -2/8, -3/12, …..
(iii) -1/6, 2/-12, 3/-18, 4/-24 …..
(iv) -2/3, 2/-3, 4/-6, 6/-9 …..



NCERT Solutions for Class 7 Maths Chapter 9 Rational Numbers


Answer :

(i) In the above question, we can observe that the numerator and denominator are the multiples of 3 and 5.
= (?3×1)(5×1), (?3×2)(5×2), (?3×3)(5×3), (?3×4)(5×4)
Then, next four rational numbers in this pattern are,
= (?3×5)(5×5), (?3×6)(5×6) , (?3×7)(5×7),(?3×8)(5×8)
= -15/25, -18/30, -21/35, -24/40 ….
(ii) In the above question, we can observe that the numerator and denominator are the multiples of 1 and 4.
= (-1 × 1)/ (4 × 1), (-1 × 2)/ (4 × 2), (-1 × 3)/ (1 × 3)
Then, next four rational numbers in this pattern are,
= (-1 × 4)/ (4 × 4), (-1 × 5)/ (4 × 5), (-1 × 6)/ (4 × 6), (-1 × 7)/ (4 × 7)
= -4/16, -5/20, -6/24, -7/28 ….
(iii) In the above question, we can observe that the numerator and denominator are the multiples of 1 and 6.
= (-1 × 1)/ (6 × 1), (1 × 2)/ (-6 × 2), (1 × 3)/ (-6 × 3), (1 × 4)/ (-6 × 4)
Then, next four rational numbers in this pattern are,
= (1 × 5)/ (-6 × 5), (1 × 6)/ (-6 × 6), (1 × 7)/ (-6 × 7), (1 × 8)/ (-6 × 8)
= 5/-30, 6/-36, 7/-42, 8/-48 ….
(iv) In the above question, we can observe that the numerator and denominator are the multiples of 2 and 3.
= (-2 × 1)/ (3 × 1), (2 × 1)/ (-3 × 1), (2 × 2)/ (-3 × 2), (2 × 3)/ (-3 × 3)
Then, next four rational numbers in this pattern are,
= (2 × 4)/ (-3 × 4), (2 × 5)/ (-3 × 5), (2 × 6)/ (-3 × 6), (2 × 7)/ (-3 × 7)
= 8/-12, 10/-15, 12/-18, 14/-21 ….

Q.3 Give four rational numbers equivalent to:
(i) -2/7
(ii) 5/-3
(iii) 4/9



NCERT Solutions for Class 7 Maths Chapter 9 Rational Numbers


Answer :

(i) ?27 = ?2×27×2 =?414
?27 =?2×37×3 = ?621
?27 =?2×47×4 = ?828
?27 =?2×57×5 = ?1035
(ii) 5?3 = 5×2?3×2 =10?6
5?3 =5×3?3×3 = 15?9
5?3 =5×4?3×4 = 20?12
5?3 =5×5?3×5 = 25?15
(iii) 49 = 4×29×2 =818
49 =4×39×3 = 1227
49 =4×49×4 = 1636
49 =4×59×5 = 2045

Q.4 Draw a number line and represent the following rational numbers on it:
(i) 3/4
(ii) -5/8
(iii) -7/4
(iv) 7/8



NCERT Solutions for Class 7 Maths Chapter 9 Rational Numbers


Answer :

(i)
(ii)
(iii)
(iv)

Q.6 Which of the following pairs represent the same rational number?
(i) ?721 and 39
(ii) ?1620 and 20?25
(iii)?2?3 and 23
(iv) ?35 and ?1220
(v) 8?5 and ?2415
(vi) 13 and ?19
(vii) ?5?9 and 5?9



NCERT Solutions for Class 7 Maths Chapter 9 Rational Numbers


Answer :

(i) ?721 and 39
Or, ?7×321×3 and 3×79×7
Or, ?2163 and 2163
Since -21? 21 so ?721 and 39do not represent the same rational number
(ii) ?1620 and 20?25
Or, ?16×520×5 and 20×425×4
Or, ?80100 and 80100
Since -80? 80 so ?1620 and 20?25do not represent the same rational number
(iii) ?2?3 and 23
Or, 23 and 23
so23 and 23 represent the same rational number
(iv) ?35 and ?1220
Or, ?3×45×4 and ?12×120×1
Or, ?1220 and ?1220
Since ?1220 = ?1220
so ?35 and ?1220 represent the same rational number

Q.5 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.



NCERT Solutions for Class 7 Maths Chapter 9 Rational Numbers


Answer :

Rational numbers represented by P, Q, R and S. 73,83,?43and ??53 respectlvely.

Q.7 Rewrite the following rational numbers in the simplest form:
(i) ?86 (ii) ?2545 (iii) ?4472



NCERT Solutions for Class 7 Maths Chapter 9 Rational Numbers


Answer :

(i) ?86= ?8÷26÷2= ?43
(ii) 2545= 25÷545÷5= 59
(iii) ?4472= ?44÷472÷4= ?1118

Q.8 Fill in the boxes with the correct symbol out of >, <
(i) ?57 ? 23
(ii) ?45 ? ?57
(iii) ?78 ? ?1416
(iv) ?85 ? ?74
(v) 1?3 ? ?14
(vi) 5?11 ? ?511
(vii)0 ? ?76



NCERT Solutions for Class 7 Maths Chapter 9 Rational Numbers


Answer :

(i) ?57 < 23
(ii) ?45 > ?57
(iii) ?78 =?1416
(iv) ?85 > ?74
(v) 1?3 < ?14
(vi) 5?11 = ?511
(vii)0 > ?76

Q.9 Which is greater in each of the following:
(i) 23 , 52
(ii) ?56 , ?43
(iii) ?34 , 2?3
(iv) ?14 , 14
(v) ?327 , ?345



NCERT Solutions for Class 7 Maths Chapter 9 Rational Numbers


Answer :

(i) 23 = 2×23×2=46
52 = 5×32×3 = 156
Since, 23 < 52
(ii) ?56 = ?5×16×1=?56
?43 = ?4×23×2 = ?86
Since, ?56 > ?43
(iii) ?34 = ?3×34×3=?912
2?3 = 2×4?3×4 = 8?12
Since, ?34 < 2?3
(iv) ?14 < 14
(v) ?327 = ?237 = ?23×57×5 = ?11535
?345 = ?195 =?19×75×7= ?13335
Since, ?327 > ?345

Q.10 Write the following rational numbers in ascending order:
(i) -3/5, -2/5, -1/5
(ii) -1/3, -2/9, -4/3
(iii) -3/7, -3/2, -3/4



NCERT Solutions for Class 7 Maths Chapter 9 Rational Numbers


Answer :

(i) -3/5, -2/5, -1/5
Here denominator are same then,
Hence, -3/5 < -2/5 < -1/5
(ii) -1/3, -2/9, -4/3
LCM of denominator = 9
(-1×3)/(3×3), (-2×1)/9×1), (-4×3)/(3×3)
=-2/9 > -3/9 > -12/9
= -2/9>-3/9>-4/3
(iii) -3/7, -3/2, -3/4
LCM of denominator = 28
(-3×4)/(7×4), (-3×14)/(2×14), (-3×7)/(4×7)
= -12/28, -42/28, -21/28
= -12/28 < -21/28 < -42/28
= -3/7< -3/4 < -3/2

NCERT solutions for class 7 Maths Chapter 9 Rational Numbers Exercise 9.2

Q.1 Find the sum:
(i) 54 +( ?114)
(ii) 53 + 35
(iii) ?910 + 2215
(iv) ?3?11 + 59
(v) ?8?19 + (?2)57
(vi) ?23 + 0
(vii) ?213 + 435



NCERT Solutions for Class 7 Maths Chapter 9 Rational Numbers


Answer :

(i) 54 +( ?114) =54 -114 = 5?114= ?64
(ii) 53 + 35 = 5×53×5 + 3×35×3
= 2515 + 915 = 25+915 =25+915 =3415 = 2415
(iii) ?910 + 2215 = ?9×310×3 + 22×215×2=?2730 + 4430 = ?27+4430 =1730
(iv) ?3?11 + 59 = 3×911×9 + 5×119×11 =2799 + 5599 = 27+5599 =8299
(v) ?8?19 + (?2)57 =819 - 257 = 8×319×3 - 257=24?257 =2257
(vi) ?23 + 0 = ?23
(vii) ?213 + 435= ?73 + 235
= ?7×53×5 + 23×35×3 = ?3515 + 6915
= ?35+6915=3415=2415

Q.2 Find :
(i) 724 - 1736
(ii) 563 - (?621)
(iii) ?613 - (?715)
(iv) ?38 - 711
(v) ?219 - 6



NCERT Solutions for Class 7 Maths Chapter 9 Rational Numbers


Answer :

(i) 724 - 1736 = 7×324×3 - 17×236×2 =2172 - 3472 = 21?3472 =?1372
(ii) 563 + 621 = 563 + 6×321×3= 5+1863= 2363
(iii) ?613 - (?715)= ?613 + 715
= ?6×1513×15 + 7×1315×13 = ?90195 + 91195 = ?90+91195 = 1195
(iv) ?38 - 711 = ?3×118×11 - 7×811×8
=?3388 - 5688= ?33?5688 =?8988= ?1188
(v) ?199 - 6 = ?19?549 = ?739 = ?819

Q.3 Find the product:
(i) 92 × (?74)
(ii) 92 × (-9 )
(iii) ?65× 911
(iv) 37 × (?25)
(v) 311× 25
(vi) 3?5× ?53



NCERT Solutions for Class 7 Maths Chapter 9 Rational Numbers


Answer :

(i) 92× ?74 = 9×?72×4= ?638 = ?778
(ii) 92 × (-9 )= ?812 =?4012
(iii) ?65× 911 = ?6×95×11= ?5455
(iv) 37 × (?25)= ?3×27×5 = ?635
(v) 311× 25 = 3×211×5=655
(vi) 3?5× ?53 = 3×(?5)?5×3 =?15?15= 1

Q.4 Find the value of:
(i) -4 ÷ 23
(ii) ?35 ÷ 2
(iii) ?45 ÷ (-3)
(iv) ?18 ÷ 34
(v) ?213 ÷ 17
(vi) ?712 ÷ (?213)
(vii) 313 ÷ (?465)



NCERT Solutions for Class 7 Maths Chapter 9 Rational Numbers


Answer :

(i) -4 ÷ 23= -4 × 32 = ?122= -6
(ii) ?35 ÷ 2 = ?35 ×12= ?310
(iii) ?45 ÷ (-3) = ?45× ?13 =415
(iv) ?18 ÷