Scroll:Real Number System >> Rational ( Exercise1.2) >> saq (4378)


Written Instructions:

For each Multiple Choice Question (MCQ), four options are given. One of them is the correct answer. Make your choice (1,2,3 or 4). Write your answers in the brackets provided..

For each Short Answer Question(SAQ) and Long Answer Question(LAQ), write your answers in the blanks provided.

Leave your answers in the simplest form or correct to two decimal places.



 

1)  

 Find three rational number between the following pairs of rational numbers. ( ples use / )

26 and 59

q1 =

q2 =

q3 =


Answer:_______________




2)  

 Find three rational number between the following pairs of rational numbers. ( ples use / )

37 and 36

q1 =

q2 =

q3 =


Answer:_______________




3)  

 Find three rational number between the following pairs of rational numbers. ( ples use / )

17 and 59

q1 =

q2 =

q3 =


Answer:_______________




4)  

 Find three rational number between the following pairs of rational numbers. ( ples use / )

35 and 57

q1 =

q2 =

q3 =


Answer:_______________




5)  

 Find three rational number between the following pairs of rational numbers. ( ples use / )

24 and 38

q1 =

q2 =

q3 =


Answer:_______________




6)  

 Find three rational number between the following pairs of rational numbers. ( ples use / )

37 and 38

q1 =

q2 =

q3 =


Answer:_______________




7)  

 Find three rational number between the following pairs of rational numbers. ( ples use / )

26 and 38

q1 =

q2 =

q3 =


Answer:_______________




8)  

 Find three rational number between the following pairs of rational numbers. ( ples use / )

34 and 56

q1 =

q2 =

q3 =


Answer:_______________




9)  

 Find three rational number between the following pairs of rational numbers. ( ples use / )

37 and 49

q1 =

q2 =

q3 =


Answer:_______________




10)  

 Find three rational number between the following pairs of rational numbers. ( ples use / )

27 and 36

q1 =

q2 =

q3 =


Answer:_______________




 

1)  

 Find three rational number between the following pairs of rational numbers. ( ples use / )

26 and 59

q1 = Answer: 49

q2 = Answer: 718

q3 = Answer: 1336


SOLUTION 1 :

  26 and 59

a = 26 ,  b = 59

Let q1 be the rational number between 26 and 59

q1 = 12 (a+b)

1
x
 
2x9+5x6
26x99x6

 

[LCM of 6 and 9 is 54]

1
x
 
18+30=1x48=48= 49
25454254108

 

q1 = 49

q2 = 12 (a+q1)

1
x
 
2+48 =1x6x48+2x108 =1x288+216 =1x504
2610826x1086x10826482648

 

1
x
 
504= 718
11296

 

q2 = 718

q3 = (a+q2)

1x2+504=1x6x5042x1296 =1x3024+2592=
26129626x12966x129627776

 

1x5616=5616= 1336
2777615552

 

q3 = 1336

Hence, 49 , 718 , 1336 is a rational number between 26 and 59



2)  

 Find three rational number between the following pairs of rational numbers. ( ples use / )

37 and 36

q1 = Answer: 1328

q2 = Answer: 2556

q3 = Answer: 716


SOLUTION 1 :

  37 and 36

a = 37 ,  b = 36

Let q1 be the rational number between 37 and 36

q1 = 12 (a+b)

1
x
 
3x6+3x7
27x66x7

 

[LCM of 7 and 6 is 42]

1
x
 
18+21=1x39=39= 1328
2424224284

 

q1 = 1328

q2 = 12 (a+q1)

1
x
 
3+39 =1x7x39+3x84 =1x273+252 =1x525
278427x847x8425882588

 

1
x
 
525= 2556
11176

 

q2 = 2556

q3 = (a+q2)

1x3+525=1x7x5253x1176 =1x3675+3528=
27117627x11767x117628232

 

1x7203=7203= 716
2823216464

 

q3 = 716

Hence, 1328 , 2556 , 716 is a rational number between 37 and 36



3)  

 Find three rational number between the following pairs of rational numbers. ( ples use / )

17 and 59

q1 = Answer: 2263

q2 = Answer: 31126

q3 = Answer: 736


SOLUTION 1 :

  17 and 59

a = 17 ,  b = 59

Let q1 be the rational number between 17 and 59

q1 = 12 (a+b)

1
x
 
1x9+5x7
27x99x7

 

[LCM of 7 and 9 is 63]

1
x
 
9+35=1x44=44= 2263
26363263126

 

q1 = 2263

q2 = 12 (a+q1)

1
x
 
1+44 =1x7x44+1x126 =1x308+126 =1x434
2712627x1267x12628822882

 

1
x
 
434= 31126
11764

 

q2 = 31126

q3 = (a+q2)

1x1+434=1x7x4341x1764 =1x3038+1764=
27176427x17647x1764212348

 

1x4802=4802= 736
21234824696

 

q3 = 736

Hence, 2263 , 31126 , 736 is a rational number between 17 and 59



4)  

 Find three rational number between the following pairs of rational numbers. ( ples use / )

35 and 57

q1 = Answer: 2335

q2 = Answer: 2235

q3 = Answer: 4370


SOLUTION 1 :

  35 and 57

a = 35 ,  b = 57

Let q1 be the rational number between 35 and 57

q1 = 12 (a+b)

1
x
 
3x7+5x5
25x77x5

 

[LCM of 5 and 7 is 35]

1
x
 
21+25=1x46=46= 2335
2353523570

 

q1 = 2335

q2 = 12 (a+q1)

1
x
 
3+46 =1x5x46+3x70 =1x230+210 =1x440
257025x705x7023502350

 

1
x
 
440= 2235
1700

 

q2 = 2235

q3 = (a+q2)

1x3+440=1x5x4403x700 =1x2200+2100=
2570025x7005x70023500

 

1x4300=4300= 4370
235007000

 

q3 = 4370

Hence, 2335 , 2235 , 4370 is a rational number between 35 and 57



5)  

 Find three rational number between the following pairs of rational numbers. ( ples use / )

24 and 38

q1 = Answer: 716

q2 = Answer: 1532

q3 = Answer: 3164


SOLUTION 1 :

  24 and 38

a = 24 ,  b = 38

Let q1 be the rational number between 24 and 38

q1 = 12 (a+b)

1
x
 
2x8+3x4
24x88x4

 

[LCM of 4 and 8 is 32]

1
x
 
16+12=1x28=28= 716
2323223264

 

q1 = 716

q2 = 12 (a+q1)

1
x
 
2+28 =1x4x28+2x64 =1x112+128 =1x240
246424x644x6422562256

 

1
x
 
240= 1532
1512

 

q2 = 1532

q3 = (a+q2)

1x2+240=1x4x2402x512 =1x960+1024=
2451224x5124x51222048

 

1x1984=1984= 3164
220484096

 

q3 = 3164

Hence, 716 , 1532 , 3164 is a rational number between 24 and 38



6)  

 Find three rational number between the following pairs of rational numbers. ( ples use / )

37 and 38

q1 = Answer: 45112

q2 = Answer: 93224

q3 = Answer: 2764


SOLUTION 1 :

  37 and 38

a = 37 ,  b = 38

Let q1 be the rational number between 37 and 38

q1 = 12 (a+b)

1
x
 
3x8+3x7
27x88x7

 

[LCM of 7 and 8 is 56]

1
x
 
24+21=1x45=45= 45112
25656256112

 

q1 = 45112

q2 = 12 (a+q1)

1
x
 
3+45 =1x7x45+3x112 =1x315+336 =1x651
2711227x1127x11227842784

 

1
x
 
651= 93224
11568

 

q2 = 93224

q3 = (a+q2)

1x3+651=1x7x6513x1568 =1x4557+4704=
27156827x15687x1568210976

 

1x9261=9261= 2764
21097621952

 

q3 = 2764

Hence, 45112 , 93224 , 2764 is a rational number between 37 and 38



7)  

 Find three rational number between the following pairs of rational numbers. ( ples use / )

26 and 38

q1 = Answer: 1748

q2 = Answer: 1132

q3 = Answer: 65192


SOLUTION 1 :

  26 and 38

a = 26 ,  b = 38

Let q1 be the rational number between 26 and 38

q1 = 12 (a+b)

1
x
 
2x8+3x6
26x88x6

 

[LCM of 6 and 8 is 48]

1
x
 
16+18=1x34=34= 1748
2484824896

 

q1 = 1748

q2 = 12 (a+q1)

1
x
 
2+34 =1x6x34+2x96 =1x204+192 =1x396
269626x966x9625762576

 

1
x
 
396= 1132
11152

 

q2 = 1132

q3 = (a+q2)

1x2+396=1x6x3962x1152 =1x2376+2304=
26115226x11526x115226912

 

1x4680=4680= 65192
2691213824

 

q3 = 65192

Hence, 1748 , 1132 , 65192 is a rational number between 26 and 38



8)  

 Find three rational number between the following pairs of rational numbers. ( ples use / )

34 and 56

q1 = Answer: 1924

q2 = Answer: 3748

q3 = Answer: 7396


SOLUTION 1 :

  34 and 56

a = 34 ,  b = 56

Let q1 be the rational number between 34 and 56

q1 = 12 (a+b)

1
x
 
3x6+5x4
24x66x4

 

[LCM of 4 and 6 is 24]

1
x
 
18+20=1x38=38= 1924
2242422448

 

q1 = 1924

q2 = 12 (a+q1)

1
x
 
3+38 =1x4x38+3x48 =1x152+144 =1x296
244824x484x4821922192

 

1
x
 
296= 3748
1384

 

q2 = 3748

q3 = (a+q2)

1x3+296=1x4x2963x384 =1x1184+1152=
2438424x3844x38421536

 

1x2336=2336= 7396
215363072

 

q3 = 7396

Hence, 1924 , 3748 , 7396 is a rational number between 34 and 56



9)  

 Find three rational number between the following pairs of rational numbers. ( ples use / )

37 and 49

q1 = Answer: 55126

q2 = Answer: 109252

q3 = Answer: 3172


SOLUTION 1 :

  37 and 49

a = 37 ,  b = 49

Let q1 be the rational number between 37 and 49

q1 = 12 (a+b)

1
x
 
3x9+4x7
27x99x7

 

[LCM of 7 and 9 is 63]

1
x
 
27+28=1x55=55= 55126
26363263126

 

q1 = 55126

q2 = 12 (a+q1)

1
x
 
3+55 =1x7x55+3x126 =1x385+378 =1x763
2712627x1267x12628822882

 

1
x
 
763= 109252
11764

 

q2 = 109252

q3 = (a+q2)

1x3+763=1x7x7633x1764 =1x5341+5292=
27176427x17647x1764212348

 

1x10633=10633= 3172
21234824696

 

q3 = 3172

Hence, 55126 , 109252 , 3172 is a rational number between 37 and 49



10)  

 Find three rational number between the following pairs of rational numbers. ( ples use / )

27 and 36

q1 = Answer: 1128

q2 = Answer: 1956

q3 = Answer: 516


SOLUTION 1 :

  27 and 36

a = 27 ,  b = 36

Let q1 be the rational number between 27 and 36

q1 = 12 (a+b)

1
x
 
2x6+3x7
27x66x7

 

[LCM of 7 and 6 is 42]

1
x
 
12+21=1x33=33= 1128
2424224284

 

q1 = 1128

q2 = 12 (a+q1)

1
x
 
2+33 =1x7x33+2x84 =1x231+168 =1x399
278427x847x8425882588

 

1
x
 
399= 1956
11176

 

q2 = 1956

q3 = (a+q2)

1x2+399=1x7x3992x1176 =1x2793+2352=
27117627x11767x117628232

 

1x5145=5145= 516
2823216464

 

q3 = 516

Hence, 1128 , 1956 , 516 is a rational number between 27 and 36