Ncert Solutions For Class 7 Maths Ex 9.1

Ncert Solutions For Class 7 Maths Chapter 9 Ex 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