RD Sharma 2018 Solutions for Class 7 Math Chapter 5 Operations On Rational Numbers are provided here with simple step-by-step explanations. These solutions for Operations On Rational Numbers are extremely popular among class 7 students for Math Operations On Rational Numbers Solutions come handy for quickly completing your homework and preparing for exams. All questions and answers from the RD Sharma 2018 Book of class 7 Math Chapter 5 are provided here for you for free. You will also love the ad-free experience on Meritnation’s RD Sharma 2018 Solutions. All RD Sharma 2018 Solutions for class 7 Math are prepared by experts and are 100% accurate.

Page No 5.10:

Question 1:

Multiply:
(i) 711 by 54
(ii) 57 by -34
(iii) (-2)9 by 511
(iv) -317 by -5-4

Answer:

(i) 711×54= 7×511×4 = 3544(ii) 57×-34=5×-37×4 = -1528(iii) -29×511= -2×59×11 = -1099

(iv) -317×-5-4= -3×517×-4 = -1568

Page No 5.10:

Question 2:

Multiply:
(i) -517 by 51-60
(ii) -611 by -5536
(iii) -825 by -516
(iv) 67 by -4936

Answer:

(i) -517×51-60=-517×17×3-5×3×4=14

(ii) -611×-5536=-611×-5×116×6=56

(iii) -825×-516=-85×5×-58×2=110

(iv) 67×-4936=67×-7×76×6=-76

Page No 5.10:

Question 3:

Simplify peach of the following and express the result as a rational number in standard from:
(i) -1621×145
(ii) 76×-328
(iii) -1936×16
(iv) -139×27-26

Answer:

(i) -1621×145=-16×1421×5=-3215
(ii) 76×-328=7×-36×28=-18(iii) -1936×16=-19×1636=-769

(iv) -139×27-26=-13×279×-26=32

Page No 5.10:

Question 4:

Simplify:
(i) -5×215--6×29
(ii) -94×53+132×56

Answer:

(i) (-5×215)-(-6×29)=(-5×23×5)-(-6×23×3)=(-23)-(-43)=-2+43=23(ii) (-94×53)+(132×56)=(-3×34×53)+(6512)=(-154)+(6512)=-15×34×3+6512=-45+6512=2012=5×43×4=53

Page No 5.10:

Question 5:

Simplify:
(i) 139×-152+73×85+35×12
(ii) 311×56-912×43+513×615

Answer:

(i) (139×-152)+(73×85)+(35×12)=(133×3×-3×52)+(5615)+(310)=-656+5615+310=-65×56×5+56×215×2+3×310×3=-32530+11230+930=-325+112+930=-20430 = -345(ii) (311×56)-(912×43)+(513×615)=(311×52×3)-(3×34×3×43)+(513×3×25×3)=522-11+213=5×1322×13-1×2861×286+2×2213×22=65286-286286+44286=65-286+44286=-177286



Page No 5.13:

Question 1:

Divide:
(i) 1 by 12
(ii) 5 by -57
(iii) -34 by 9-16
(iv) -78 by -2116
(v) 7-4 by 6364
(vi) 0 by -75
(vii) -34 by -6
(viii) 23 by -712

Answer:

(i) 1÷12=1×21=2(ii) 5÷-57=5×7-5=-7(iii) -34÷9-16=-34×-169=-34×-4×43×3=43(iv)  -78÷-2116=-78×-1621=-78×-8×27×3=23

(v)  7-4÷6364=7-4×6463=-74×4×167×9=-169(vi)  0÷-75=0×-75=0(vii)  -34÷-6=-34×-16=-34×-12×3=18(viii)  23÷-712=23×-127=23×-4×37=-87

Page No 5.13:

Question 2:

Find the value and express as a rational number in standard form:
(i) 25÷2615
(ii) 103÷-3512
(iii) -6÷-817
(iv) 4098÷(-20)

Answer:







Page No 5.13:

Question 3:

The product of two rational numbers is 15. If one of the numbers is −10, find the other.

Answer:

Let the first rational number = x.
Second number = −10
Their product = 15

Then, we have
x×-10=15x=15×1-10=5×3×-12×5=-32

Page No 5.13:

Question 4:

The product of two rational numbers is -89. If one of the numbers is -415, find the other.

Answer:

Let the first rational number = x
Second number             = -415
Their product              = -89

Then, we have
x×-415=-89x=-89×-154=-2×43×3×-3×54=103

Page No 5.13:

Question 5:

By what number should we multiply -16 so that the product may be -239?

Answer:

Let x be the number by which we should multiply -16 to get -239.
Then, according to the question, we have
-16×x=-239x=-239×(-6)=463

Page No 5.13:

Question 6:

By what number should we multiply -1528 so that the product may be -57?

Answer:

Let be the number by which we multiply -1528 to get the product -57.
Then, we have

x×-1528=-57x=-57×28-15=-57×7×4-5×3=43



Page No 5.14:

Question 7:

By what number should we multiply -813 so that the product may be 24?

Answer:

Let x be the number required. Then, we have
x×-813=24x=24×-138=-13×3=-39

Page No 5.14:

Question 8:

By what number should -34 be multiplied in order to produce 23?

Answer:

Let be the number by which we should multiply -34 to get 23.
Then, we have
-34×x=23x=23×4-3=-89

Page No 5.14:

Question 9:

Find (x + y) ÷ (x + y), if
(i) x=23, y=32
(ii) x=25, y=12
(iii) x=54, y=-13

Answer:

(i) x = 23, y = 32
Then, (x+y)  = 23+32=2×23×2+3×32×3=46+96=136
(x-y) = 23-32 = 46- 96= -56
Then, (x+y)÷(x-y) = 136÷-56=136×6-5=-135.

(ii) x = 25, y = 12
Then, (x+y) = 25+12=2×25×2+1×52×5=410+510=910
(x-y) = 25-12 = 410- 510= -110

Then, (x+y)÷(x-y) = 910÷-110=-9

(iii) x = 54, y = -13
Then, (x+y) = 54+-13=5×34×3+-1×43×4=1512+-412=1112
(x-y) = 54--13 = 54+ 13= 1912
Then, (x+y)÷(x-y) = 1112÷1912=1112×1219=1119.

Page No 5.14:

Question 10:

The cost of 723 metres of rope is Rs 1234. Find its cost per metre.

Answer:

The cost of 723=233metres  of rope = Rs. 1234=514.
Then, the cost of 1 metre of rope = Rs. 514÷233=514×323=15392= Rs. 16192.

Page No 5.14:

Question 11:

The cost of 213 metres of cloth is Rs 7514. Find the cost of cloth per metre.

Answer:

The cost of 213=73 metres of cloth = Rs. 7514=3014.
The cost of 1 metre of cloth = Rs. 3014÷73=3014×37=43×74×37=1294=3214.

Page No 5.14:

Question 12:

By what number should -3316 be divided to got -114?

Answer:

Let be the number required.

Then, we have

-3316÷x=-114-3316×1x=-114-3316×4-11=xx=-3×114×4×4-11=34

Page No 5.14:

Question 13:

Divide the sum of -135 and 127 by the product of -317 and -12.

Answer:

The sum of -135 and 127 is -135+127=-13×75×7+12×57×5=-9135+6035=-91+6035=-3135

The product of -317 and -12 is-317×-12=3114

Then, according to the question, we have

-3135÷3114=-3135×1431=-25

Page No 5.14:

Question 14:

Divide the sum of 6512  and 83 by their difference.

Answer:

The sum of  6512 and 83 is6512+83=6512+8×43×4=6512+3212=65+3212=9712The difference of  6512 and 83 is6512-83=6512-8×43×4=6512-3212=65-3212=3312

According to the question, we need to divide the first figure by the second:

9712÷3312=9712×1233=9733

Page No 5.14:

Question 15:

If 24 trousers of equal size can be prepared in 54 metres of cloth, what length of cloth is required for each trouser?

Answer:

Total cloth given = 54 metres
Total number of pairs of trousers made = 24
Length of cloth required for each pair of trousers = 5424=9×64×6=94 metres.



Page No 5.16:

Question 1:

Find six rational numbers between -48 and 38.

Answer:

  Since -4<-3<-2<1<0<1<2<3,six rational numbers between-48 and 38 are-38, -28, -18, 08,18,28

Page No 5.16:

Question 2:

Find 10 rational numbers between 713 and -413.

Answer:

Since

-4<-3<-2<-1<0<1<2<3<4<5<6<7,10 rational numbers between 713 and -413are,-313,-213, -113, 013,113,213,313413,513,613

Page No 5.16:

Question 3:

State true or false:
(i) Between any two distinect integers there is always an linteger.
(ii) Between any two distinct rational numbers there is always a rational number.
(iii) Between any two distinct rational numbers there is always a rational number.

Answer:

(i) False, because there is no integer between 2 and 3.
(ii) True
(iii) True

Page No 5.16:

Question 1:

Mark the correct alternative in each of the following:

What should be added to -79 to get 2?

(a) 119                                 (b) -119                                 (c) -259                                 (d) 259

Answer:


Sum of the given number and the required number = 2

Given number = -79

∴ Required number = Sum of the numbers − Given number

                              =2--79=21+79=2×9+7×19=18+79=259

Hence, the correct answer is option (d).

Page No 5.16:

Question 2:

Mark the correct alternative in each of the following:

What should be subtracted from -23 to get 45?

(a) 2215                                 (b) -2215                                 (c) 1522                                 (d) -1522

Answer:


Difference of the given number and required number = 45

Given number = -23

∴ Required number = Given number − Difference of the numbers

                               =-23-45=-23+-45=-2×5+-4×315=-10+-1215=-2215

Hence, the correct answer is option (b).

Page No 5.16:

Question 3:

Mark the correct alternative in each of the following:

Reciprocal of -34 is

(a) 34                                 (b) 43                                 (c) -43                                 (d) None of these

Answer:



We know that the reciprocal of the rational number ab is ab-1=ba.

∴ Reciprocal of -34

=-34-1=4-3=4×-1-3×-1=-43

Hence, the correct answer is option (c).

Page No 5.16:

Question 4:

Mark the correct alternative in each of the following:

The multiplicative inverse of 4-5 is

(a) -45                                 (b) 54                                 (c) 5-4                                 (d) -5-4

Answer:


We know that the multiplicative inverse of the rational number ab is ba.

∴ Multiplicative inverse of 4-5=-54=5-4

Hence, the correct answer is option (c).




 

Page No 5.16:

Question 5:

Mark the correct alternative in each of the following:

1÷-57=

(a) 27                                 (b) 57                                 (c) -27                                 (d) -75

Answer:


1÷-57=1×7-5                       x÷y=x×1y=7-5=7×-1-5×-1=-75

Hence, the correct answer is option (d).



Page No 5.17:

Question 6:

Mark the correct alternative in each of the following:

-513+?=-1

(a) 813                                 (b) -813                                 (c) -1813                                 (d) 1813

Answer:


-513+?=-1?=-1--513?=-1+513                               --513=513?=-1×13+513
?=-13+513?=-813

Hence, the correct answer is option (b).

Page No 5.17:

Question 7:

Mark the correct alternative in each of the following:

0÷35=

(a) 0                                   (b) 53                                   (c) 35                                   (d) -35                                  

Answer:

We know that 0 divided by any non-zero rational number is always 0.

0÷35=0                       0÷ab=0

Hence, the correct answer is option (a).

Page No 5.17:

Question 8:

Mark the correct alternative in each of the following:

-237+4=?

(a) -117                                   (b) 117                                   (c) -457                                   (d) 457

Answer:


?=-237+4?=-177+41?=-17×1+4×77?=-17+287
?=117

Hence, the correct answer is option (b).

Page No 5.17:

Question 9:

Mark the correct alternative in each of the following:

If the product of two non-zero rational numbers is 1, then they are

(a) additve inverse of each other                                 (b) multiplicative inverse of each other

(c) reciprocal of each other                                         (d) both (b) and (c)

Answer:


For every non-zero rational number ab there exists a rational number ba such that

ab×ba=1

Here, the rational number ba is called the multiplicative inverse or reciprocal of ab.

Thus, if the product of two non-zero rational numbers is 1, then they are multiplicative inverse or reciprocal of each other.

Hence, the correct answer is option (d).

Page No 5.17:

Question 10:

Mark the correct alternative in each of the following:

The product 317×156×125×1111 is equal to

(a) 585                                 (b) 545                                   (c) 845                                   (d) 745

Answer:


317×156×125×1111=227×116×75×1211=22×11×7×127×6×5×11                                   ab×cd=a×cb×d=445=8×5+45=845

Hence, the correct answer is option (c).

Page No 5.17:

Question 11:

Mark the correct alternative in each of the following:

-713--815=

(a) -239195                                   (b) 29195                                   (c) -29195                                   (d) None of these

Answer:


-713--815=-713+815                                             --815=815=-7×15+8×13195                                  LCM of 13 and 15=195=-105+104195=-1195

Hence, the correct answer is option (d).

Page No 5.17:

Question 12:

Mark the correct alternative in each of the following:

1÷13=

(a) 13                                  (b) 3                                   (c) 113                                   (d) 313

Answer:


1÷13=1×3                          x÷y=x×1y=3

Hence, the correct answer is option (b).

Page No 5.17:

Question 13:

Mark the correct alternative in each of the following:

-2÷-53=

(a) 56                                  (b) -56                                   (c) 65                                   (d) -65

Answer:


-2÷-53=-2×-35                                  x÷y=x×1y=-21×-35=-2×-31×5                                   ab×cd=a×cb×d=65

Hence, the correct answer is option (c).

Page No 5.17:

Question 14:

Mark the correct alternative in each of the following:

If x2+13=1, then x =

(a) 34                                   (b) 43                                   (c) -34                                   (d) -43

Answer:


x2+13=1x2=1-13x2=3×1-13x2=3-13x2=23
2x2=2×23                       Multiplying both sides by 2x=43

Hence, the correct answer is option (b).

Page No 5.17:

Question 15:

Mark the correct alternative in each of the following:

54-76--23=

(a) 34                                   (b) -34                                   (c) -712                                   (d) 712

Answer:


54-76--23=54+-76+23                          --23=23=5×3+-7×2+2×412                      LCM of 3,4 and 6=12=15-14+812=912

=9÷312÷3                        Dividing numerator and denominator by 3=34

Hence, the correct answer is option (a).



Page No 5.4:

Question 1:

Add the following rational numbers:
(i) -57 and 37
(ii) -154 and 74
(iii) -811 and -411
(iv) 613 and -913

Answer:

 (i)-57+37 = -5+37 = -27(ii) -154+74 = -15+74 = -84 = -2(iii) -811+-411 = -8-411 = -1211(iv) 613+-913 = 6-913 = -313

Page No 5.4:

Question 2:

(i) 34 and -35
(ii) -3 and 35
(iii) -727 and 1118
(iv) 31-4 and -58

Answer:

(i)

34+-35 LCM of the denominators 4 and 5 is 20.  Now, we express 34 and -35 into forms in which both of them have the same denominator 20.34 = 3×54×5 = 1520-35 = -3×45×4 = -1220Therefore, 34+-35 = 1520 + -1220 = 15-1220 = 320

(ii)

-3+35LCM of the denominators 1 and 5 is 5.  Now, we express -3 and 35 into forms in which both of them have the same denominator 5.-31 = 3×51×5 = -15535 = 3×15×1 = 35Therefore, -3+35 = -155 + 35 = -125

(iii)

-727+1118LCM of the denominators 27 and 18 is 54.  Now, we express -727 and 1118 into forms in which both of them have the same denomiator 54.-727 = -7×227×2 = -14541118 = 11×318×3 = 3354Therefore, -727+1118 = -1454 + 3354 = -14+3354 = 1954

(iv)

-314+-58LCM of the denominators 4 and 8 is 8.  Now, we express -314 and -58 into forms in which both of them have the same denomiator 8.-314 = -31×24×2 = -628-58 = -5×18×1 = -58Therefore, -314+-58 = -628 + -58 = -62-58 = -678

Page No 5.4:

Question 3:

Simplify:
(i) 89+-116
(ii) -516+724
(iii) 1-12+2-15
(iv) -819+-457

Answer:

(i) 89+-116LCM of the denominators 9 and 6 is 18.  Now, we express 89 and -116 into forms in which both of them have the same denominator as LCM.  89 = 8×29×2   -116 = -11×36×3 Therefore,8×29×2+-11×36×3=16-3318=-1718

(ii) -516+724LCM of the denominators 16 and 24 is 48.  Now, we express -516 and 724 into forms in which both of them have the same denominator as LCM.-516 = -5×316×3 724 = 7×224×2 Therefore,-5×316×3+7×224×2=-15+1448=-148(iii) 1-12+2-15LCM of the denominators 12 and 15 is 60.  Now, we express -112 and -215 into forms in which both of them have the same denominator as LCM. -112 = -1×512×5 -215 = -2×415×4 Therefore,-1×512×5+-2×415×4=-5-860=-1360


(iv) -819+-457LCM of the denominators 19 and 57 is 57.  Now, we express -819 and -457 into forms in which both of them have the same denominator as LCM.89 = -8×319×3 -457 = -4×157×1 Therefore,-8×319×3+-457=-24-457=-2857

Page No 5.4:

Question 4:

Add and express the sum as a mixed fraction:
(i) -125+4310
(ii) 247+-114
(iii) -316+-278

Answer:

(i) -125+4310LCM of the denominators 5 and 10 is 10.  Now, we express -125 and 4310 into forms in which both of them have the same denominator as LCM.-125 = 12×25×2 4310 = 43×110×1 Therefore,-12×25×2+4310=-24+4310=1910=1910(ii)  247+-114LCM of the denominators 7 and 4 is 28.  Now, we express 247 and -114 into forms in which both of them have the same denominator as LCM.247 = 24×47×4 -114 = -11×74×7 Therefore,24×47×4+-11×74×7=96-7728=1928


(iii) -316+-278LCM of the denominators 6 and 8 is 24.  Now, we express -316 and -278 into forms in which both of them have the same denominator as LCM.-316 = -31×46×4 -278 = -27×38×3 Therefore,-31×46×4+-27×38×3=-124-8124=-20524



Page No 5.7:

Question 1:

Subtract the first rational number from the second in each of the following:
(i) 38, 58
(ii) -79, 49
(iii) -211, -911
(iv) 1113, -413

Answer:

(i) 58-38=28(ii) 49--79=119
(iii) -911--211=-9+211=-711(iv) -413-1113=-4-1113=-1513

Page No 5.7:

Question 2:

Evaluate each of the following:
(i) 23-35
(ii) -47-2-3
(iii) 47--5-7
(iv) -2-59

Answer:

(i) 23-35=2×5-3×315=10-915=115(ii) -47-2-3=-4×3+2×721=-12+1421=221

(iii) 47--5-7=4-57=-17(iv) -21-59=-2×9-59==-18-59=-239

Page No 5.7:

Question 3:

The sum of the two numbers is 59. If one of the numbers is 13, find the other.

Answer:

First number = 13
Let the second number = x.
According to the question, we have
13+x=59x=59-13=5-1×39=5-39=29

Page No 5.7:

Question 4:

The sum of two numbers is -13. If one of the numbers is -123, find the other.

Answer:

First number = -123
Let the second number = x.
Then, according to the question, we have
-123+x=-13x=-13--123=-1+123=113

Page No 5.7:

Question 5:

The sum of two numbers is -43. If one of the numbers is −5, find the other.

Answer:

First number = -5
Let the second number = x.
Then, according to the question, we have
-5+x=-43x=-43--51=-4+5×33=-4+153=113

Page No 5.7:

Question 6:

The sum of two rational numbers is −8. If one of the numbers is -157, find the other.

Answer:

First number = -157
Let the second number = x.
Then, according to the question, we have
-157+x=-8x=-81--157=-8×7+157=-56+157=-417

Page No 5.7:

Question 7:

What should be added to -78 so as to get 59?

Answer:

Let be added to -78 to get 59.
Then, according to the question, we have
x+-78=59=>x = 59--78=5×8+7×972=40+6372=10372

Page No 5.7:

Question 8:

What number should be added to -511 so as to get 2633?

Answer:

Let be added to -511 to get 2633.
Then, according to the question, we have
x+-511=2633=> x = 2633--511              =26+5×333                 =26+1533                 =4133

Page No 5.7:

Question 9:

What number should be added to -57 to get -23?

Answer:

Let be added to -57 to get -23.
Then, according to the question, we have
x+-57=-23x = -23--57=-2×7+5×321=-14+1521=121



Page No 5.8:

Question 10:

What number should be suvtracted from -53 to get 56?

Answer:

Let x be the number that should be subtracted from -53 to get 56.
Then, according to the question, we have
 -53-x=56x = -53-56=-5×23×2-56=-10-56=-156=-52

Page No 5.8:

Question 11:

What number should be subtracted from 37 to get 54?

Answer:

Let x be the number that should be subtracted from 37 to get 54.
Then, according to the question, we have
37-x=54x=37-54=3×4-5×728=12-3528=-2328

Page No 5.8:

Question 12:

What should be added to 23+35 to get -215?

Answer:

23+35=2×53×5+3×35×3=1015+915=1915
Let x be the number that should be added to 1915 to get -215
Then, we have
     1915+x=-215=>x=-215-1915           =-2115            =-7×35×3            =-75

Page No 5.8:

Question 13:

What should be added to 12+13+15 to get 3?

Answer:

Let x be added to (12+13+15)=(1×152×15+1×103×10+1×65×6)=(1530+1030+630)=3130 to get 3.
Then, we have
3130+x=3x=3-3130=3×301×30-3130=9030-3130=5930

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Question 14:

What should be subtracted from 34-23 to get -16?

Answer:

Let  x be the number that should be subtracted from 34-23=3×34×3-2×43×4=912-812=112 to get -16.

Then, we have
112-x=-16x=112--16=112--1×26×2=112--212=312=14

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Question 15:

Simplify:
(i) -32+54-74
(ii) 53-76+-23
(iii) 54-76--23
(iv) -25--310--47

Answer:

(i) -32+54-74=-3×22×2+54-74=-6+5-74=-84=-2(ii) 53-76+-23=5×23×2-76+-2×23×2=10-7-46=-16

(iii) 54-76--23=5×34×3-7×26×2--2×43×4=15-14+812=912=34(iv) -25--310--47=-2×145×14--3×710×7--4×107×10=-28+21+4070=3370

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Question 16:

Fill in the blanks:
(i) -413--326=....
(ii) -914+....=-1
(iii) -79+....=3
(iv) ....+1523=4

Answer:

(i) -413--326=-4×213×2--326=-8+326=-526
(ii) -914+x=-1x=-1--914=-14+914=-514(iii) -79+x=3x=3×91×9--79=27+79=349

(iv)
x+1523=4x=4-1523=4×231×23-1523=92-1523=7723



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