NCERT Solutions For Class 7 Maths Chapter 9

NCERT Solutions Class 7 Maths Rational Numbers

NCERT Solutions for Class 7 Maths Chapter 9 Rational Numbers is the best study materials for those students who are finding difficulties in solving problems on Rational Numbers. These solutions include several example problems and are mainly explained by the team of our subject experts to helps students in understanding the topic easily and effectively.

NCERT Solutions for Class 7 Maths Chapter 9 are available for free in PDF format provides solutions for all the questions provided in class 7 math NCERT textbooks. Students can either practice online or download these NCERT Solutions for Class 7 Maths chapter 9 pdf files from our website BYJU’S and have a quick review during their exams.

NCERT Solutions For Class 7 Maths Chapter 9 Exercises

Exercise 9.1

Q1:

List 9 natural numbers between:

(i) -1 and 0

(ii) -2 and -1

(iii) 45and23

(iv) 12and23

Sol:

(i) -1 and 0

Let us write -1 and 0 as rational number with denominator 10.   (as we need 9 number between the  numbers given so 9+1=10).

1=1010 and 0=010

 

 therefore1010<910<810<710<610<510<410<310<210<110<0

 

1<910<45<710<35<12<25<310<15<110<0

 

Therefore 9 rational numbers between -1 and 0 would be

910,45,710,35,12,25,310,15,110

 

(ii) -2 and -1

Let us write -2 and -1 as rational number with denominator 10.   (as we need 9 number between the  numbers given so 9+1=10).

2=2010 and 1=1010

 

 therefore2010<1910<1810<1710<1610<1510<1410<1310<1210<1110<1010

 

2<1910<95<1710<85<32<75<1310<65<1110<1

 

Therefor 9 rational numbers between -2 and -1 would be,

1910,95,1710,85,32,75,1310,65,1110 .

 

(iii) 45and23

Let us write 45and23 as rational number with the same denominator.

45=7290and23=6090.

 

 therefore7290<7190<7090<6990<6890<6790<6690<6590<6490<6390<6090

 

45<7190<79<2330<3445<6790<1115<1318<3245<710<23

 

Therefor 9 rational numbers between  45and23 are

7190,79,2330,3445,6790,1115,1318,3245,710

 

(iv) 12and23

Let us write 12and23 as rational numbers having same denominator.

12=612and23=812

 

 therefore612<512<412<312<212<112<012<112<212<312<812

 

12<512<13<14<16<112<0<112<16<14<23

 

512,13,14,16,112,0,112,16,14

 

Q2: With the pattern given below, write down four more rational number, which comes in continuation:

(i) 35,610,915,1220,..

(ii) 14,28,312,..

(iii) 16,212,318,424,..

(iv) 23,46,69,..

 

Sol:

(i) 35,610,915,1220,..

35,3×25×2,3×35×3,3×45×4,

Therefore, the next four rational numbers following the pattern would be

3×55×5,3×65×6,3×75×7,3×85×8=1525,1830,2135,2440

 

(ii) 14,28,312,..

1×14×1,1×24×2,1×34×3,..

Therefore, the next four rational numbers following the pattern would be

1×44×4,1×54×5,1×64×6,1×74×7 416,520,624,728

 

(iii) 16,212,318,424,..

1×16×1,1×26×2,1×36×3,1×46×4,..

Therefore, the next four rational numbers following the pattern would be

1×56×5,1×66×6,1×76×7,1×86×8=530,636,742,848

 

(iv) 23,46,69,..

2×13×1,2×23×2,2×33×3,..

Therefore, the next four rational numbers following the pattern would be

2×43×4,2×53×5,2×63×6,2×73×7=812,1015,1218,1421

 

Q3: Write five rational number equivalent to the given fraction:

(i) 27

(ii) 53

(iii) 49

Sol:

(i) 27

2×27×2=414,2×37×3=621,2×47×4=828,2×57×5=1035,2×67×6=1242

Thus five rational number equivalent to 27 are

414,621,828,1035,1242

 

(ii) 53

5×23×2=106,5×33×3=159,5×43×4=2012,5×53×5=2515,5×63×6=3018

Thus five rational number equivalent to 53 are

106,159,2012,2515,3018,

 

(iii) 49

4×29×2=818,4×39×3=1227,4×49×4=1636,4×59×5=2045,4×69×6=2454

Thus five rational number equivalent to 53 are

818,1227,1636,2045,2454

 

Q4: Draw the number line and represent the following rational numbers on it:

(i) 34

(ii) 34

(iii) 34

(iv) 34

 

Sol:

(i) 34

(ii)  34

(iii) 34

(iv) 34

 

Q5: The point 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.

Sol:

Each part which is between the two numbers is divided into 3 parts.

Therefore   A=63,P=73,Q=83andB=93

Similarly  T=33,R=43,S=53andU=63

Thus, the rational numbers represented P,Q,RandSare73,83,43,53 respectively.

 

Q6: Which of the following pairs represent the same rational numbers:

(i) 721and39

(ii) 1620and2025

(iii) 23and23

(iv) 35and1220

(v) 85and2415

(vi) 13and19

(vii) 59and59

Sol:

(i)  721and39

721=13and39=13  because1313 72139

 

(ii) 1620and2025

1620=45and2015=45  because45=45 1620=2025

(iii) 23and23

23=23and23  because23=23 23=23

 

(iv) 35and1220

35and1220=35  because35=35 35=1220

 

(v) 85and2415

85and2415=85  because85=85 85=2415

 

(vi) 13and19

13and19  because1319 1319

 

(vii) 59and59

59=59and59  because5959 5959

 

Q7: Rewrite the following rational numbers in the simplest form:

(i) 86

(ii) 2545

(iii) 4472

(iv) 810

Sol:

(i) 86 = 86=8÷26÷2=43  (as 8 and 6 has H.C.F. of 2)

 

(ii) 2545= 2545=25÷545÷5=59  (as 25 and 45 has H.C.F. of 5).

 

(iii) 4472 = 4472=44÷472÷4=1118  (as 44 and 72 has H.C.F. of 4)

 

(iv) 810 = 810=8÷210÷2=45  (as 8 and 10 has H.C.F. of 2).

 

Q8: Fill in the blanks with the correct symbols out of <,>,and = .

(i) 57 ___ 23

(ii) 45 ___ 57

(iii) 78 ___ 1416

(iv) 85 ___ 74

(v) 13 ___ 14

(vi) 511 ___ 511

(vii) 0 ___ 76

Sol:

(i) 57 _<_ 23

(ii) 45 _<_ 57

(iii) 78 _=_ 1416

(iv) 85 _>_ 74

(v) 13 _<_ 14

(vi) 511 _=_ 511

(vii) 0 _>_ 76

 

Q9: Write the following rational number in ascending order:

(i) 35,25,15

(ii) 13,29,43

(iii) 37,32,34

Sol:

(i) 35,25,15

35<25<15

 

(ii)  13,29,43

39,29,129       (converting to same denominator)

129<29<39 43<29<13

 

(iii) 37,32,34

1228,4228,2128 4228<2128<1228 32<34<37

 

Exercise-9.2

 

Q.1.(i) 54+(114)

(ii)53+35

(iii)e910+2215

(iv)311+59

(v)819+(2)57

(vi)23+0

(vii)213+435

Solution:

(i)54+(114)

54+(114)=5114=64=32

(ii)53+35

53+35=5×53×5+3×35×3=2515+915=25+915=3415=2415

(iii)910+2215

910+2215=9×310×3+22×215×2=2730+4430=27+4430=1730

(iv)311+59

311+59=3×911×9+5×119×11=2799+5599=27+5599=8299

(v)819+(2)57

819+(2)57=8×319×3+(2)×157×1=2457+(2)57=24257=2657

(vi)23+0

23+0=23

(vii)213+435

213+43