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 36

q1 =

q2 =

q3 =


Answer:_______________




2)  

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

35 and 37

q1 =

q2 =

q3 =


Answer:_______________




3)  

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

17 and 46

q1 =

q2 =

q3 =


Answer:_______________




4)  

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

36 and 59

q1 =

q2 =

q3 =


Answer:_______________




5)  

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

16 and 58

q1 =

q2 =

q3 =


Answer:_______________




6)  

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

34 and 58

q1 =

q2 =

q3 =


Answer:_______________




7)  

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

37 and 56

q1 =

q2 =

q3 =


Answer:_______________




8)  

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

14 and 38

q1 =

q2 =

q3 =


Answer:_______________




9)  

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

15 and 56

q1 =

q2 =

q3 =


Answer:_______________




10)  

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

36 and 56

q1 =

q2 =

q3 =


Answer:_______________




 

1)  

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

26 and 36

q1 = Answer: 512

q2 = Answer: 38

q3 = Answer: 1748


SOLUTION 1 :

  26 and 36

a = 26 ,  b = 36

Let q1 be the rational number between 26 and 36

q1 = 12 (a+b)

1
x
 
2x6+3x6
26x66x6

 

[LCM of 6 and 6 is 36]

1
x
 
12+18=1x30=30= 512
2363623672

 

q1 = 512

q2 = 12 (a+q1)

1
x
 
2+30 =1x6x30+2x72 =1x180+144 =1x324
267226x726x7224322432

 

1
x
 
324= 38
1864

 

q2 = 38

q3 = (a+q2)

1x2+324=1x6x3242x864 =1x1944+1728=
2686426x8646x86425184

 

1x3672=3672= 1748
2518410368

 

q3 = 1748

Hence, 512 , 38 , 1748 is a rational number between 26 and 36



2)  

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

35 and 37

q1 = Answer: 1835

q2 = Answer: 3970

q3 = Answer: 81140


SOLUTION 1 :

  35 and 37

a = 35 ,  b = 37

Let q1 be the rational number between 35 and 37

q1 = 12 (a+b)

1
x
 
3x7+3x5
25x77x5

 

[LCM of 5 and 7 is 35]

1
x
 
21+15=1x36=36= 1835
2353523570

 

q1 = 1835

q2 = 12 (a+q1)

1
x
 
3+36 =1x5x36+3x70 =1x180+210 =1x390
257025x705x7023502350

 

1
x
 
390= 3970
1700

 

q2 = 3970

q3 = (a+q2)

1x3+390=1x5x3903x700 =1x1950+2100=
2570025x7005x70023500

 

1x4050=4050= 81140
235007000

 

q3 = 81140

Hence, 1835 , 3970 , 81140 is a rational number between 35 and 37



3)  

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

17 and 46

q1 = Answer: 1742

q2 = Answer: 2384

q3 = Answer: 524


SOLUTION 1 :

  17 and 46

a = 17 ,  b = 46

Let q1 be the rational number between 17 and 46

q1 = 12 (a+b)

1
x
 
1x6+4x7
27x66x7

 

[LCM of 7 and 6 is 42]

1
x
 
6+28=1x34=34= 1742
2424224284

 

q1 = 1742

q2 = 12 (a+q1)

1
x
 
1+34 =1x7x34+1x84 =1x238+84 =1x322
278427x847x8425882588

 

1
x
 
322= 2384
11176

 

q2 = 2384

q3 = (a+q2)

1x1+322=1x7x3221x1176 =1x2254+1176=
27117627x11767x117628232

 

1x3430=3430= 524
2823216464

 

q3 = 524

Hence, 1742 , 2384 , 524 is a rational number between 17 and 46



4)  

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

36 and 59

q1 = Answer: 1936

q2 = Answer: 3772

q3 = Answer: 73144


SOLUTION 1 :

  36 and 59

a = 36 ,  b = 59

Let q1 be the rational number between 36 and 59

q1 = 12 (a+b)

1
x
 
3x9+5x6
26x99x6

 

[LCM of 6 and 9 is 54]

1
x
 
27+30=1x57=57= 1936
25454254108

 

q1 = 1936

q2 = 12 (a+q1)

1
x
 
3+57 =1x6x57+3x108 =1x342+324 =1x666
2610826x1086x10826482648

 

1
x
 
666= 3772
11296

 

q2 = 3772

q3 = (a+q2)

1x3+666=1x6x6663x1296 =1x3996+3888=
26129626x12966x129627776

 

1x7884=7884= 73144
2777615552

 

q3 = 73144

Hence, 1936 , 3772 , 73144 is a rational number between 36 and 59



5)  

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

16 and 58

q1 = Answer: 1948

q2 = Answer: 932

q3 = Answer: 43192


SOLUTION 1 :

  16 and 58

a = 16 ,  b = 58

Let q1 be the rational number between 16 and 58

q1 = 12 (a+b)

1
x
 
1x8+5x6
26x88x6

 

[LCM of 6 and 8 is 48]

1
x
 
8+30=1x38=38= 1948
2484824896

 

q1 = 1948

q2 = 12 (a+q1)

1
x
 
1+38 =1x6x38+1x96 =1x228+96 =1x324
269626x966x9625762576

 

1
x
 
324= 932
11152

 

q2 = 932

q3 = (a+q2)

1x1+324=1x6x3241x1152 =1x1944+1152=
26115226x11526x115226912

 

1x3096=3096= 43192
2691213824

 

q3 = 43192

Hence, 1948 , 932 , 43192 is a rational number between 16 and 58



6)  

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

34 and 58

q1 = Answer: 1116

q2 = Answer: 2332

q3 = Answer: 4764


SOLUTION 1 :

  34 and 58

a = 34 ,  b = 58

Let q1 be the rational number between 34 and 58

q1 = 12 (a+b)

1
x
 
3x8+5x4
24x88x4

 

[LCM of 4 and 8 is 32]

1
x
 
24+20=1x44=44= 1116
2323223264

 

q1 = 1116

q2 = 12 (a+q1)

1
x
 
3+44 =1x4x44+3x64 =1x176+192 =1x368
246424x644x6422562256

 

1
x
 
368= 2332
1512

 

q2 = 2332

q3 = (a+q2)

1x3+368=1x4x3683x512 =1x1472+1536=
2451224x5124x51222048

 

1x3008=3008= 4764
220484096

 

q3 = 4764

Hence, 1116 , 2332 , 4764 is a rational number between 34 and 58



7)  

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

37 and 56

q1 = Answer: 5384

q2 = Answer: 89168

q3 = Answer: 2348


SOLUTION 1 :

  37 and 56

a = 37 ,  b = 56

Let q1 be the rational number between 37 and 56

q1 = 12 (a+b)

1
x
 
3x6+5x7
27x66x7

 

[LCM of 7 and 6 is 42]

1
x
 
18+35=1x53=53= 5384
2424224284

 

q1 = 5384

q2 = 12 (a+q1)

1
x
 
3+53 =1x7x53+3x84 =1x371+252 =1x623
278427x847x8425882588

 

1
x
 
623= 89168
11176

 

q2 = 89168

q3 = (a+q2)

1x3+623=1x7x6233x1176 =1x4361+3528=
27117627x11767x117628232

 

1x7889=7889= 2348
2823216464

 

q3 = 2348

Hence, 5384 , 89168 , 2348 is a rational number between 37 and 56



8)  

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

14 and 38

q1 = Answer: 516

q2 = Answer: 932

q3 = Answer: 1764


SOLUTION 1 :

  14 and 38

a = 14 ,  b = 38

Let q1 be the rational number between 14 and 38

q1 = 12 (a+b)

1
x
 
1x8+3x4
24x88x4

 

[LCM of 4 and 8 is 32]

1
x
 
8+12=1x20=20= 516
2323223264

 

q1 = 516

q2 = 12 (a+q1)

1
x
 
1+20 =1x4x20+1x64 =1x80+64 =1x144
246424x644x6422562256

 

1
x
 
144= 932
1512

 

q2 = 932

q3 = (a+q2)

1x1+144=1x4x1441x512 =1x576+512=
2451224x5124x51222048

 

1x1088=1088= 1764
220484096

 

q3 = 1764

Hence, 516 , 932 , 1764 is a rational number between 14 and 38



9)  

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

15 and 56

q1 = Answer: 3160

q2 = Answer: 43120

q3 = Answer: 67240


SOLUTION 1 :

  15 and 56

a = 15 ,  b = 56

Let q1 be the rational number between 15 and 56

q1 = 12 (a+b)

1
x
 
1x6+5x5
25x66x5

 

[LCM of 5 and 6 is 30]

1
x
 
6+25=1x31=31= 3160
2303023060

 

q1 = 3160

q2 = 12 (a+q1)

1
x
 
1+31 =1x5x31+1x60 =1x155+60 =1x215
256025x605x6023002300

 

1
x
 
215= 43120
1600

 

q2 = 43120

q3 = (a+q2)

1x1+215=1x5x2151x600 =1x1075+600=
2560025x6005x60023000

 

1x1675=1675= 67240
230006000

 

q3 = 67240

Hence, 3160 , 43120 , 67240 is a rational number between 15 and 56



10)  

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

36 and 56

q1 = Answer: 23

q2 = Answer: 712

q3 = Answer: 1324


SOLUTION 1 :

  36 and 56

a = 36 ,  b = 56

Let q1 be the rational number between 36 and 56

q1 = 12 (a+b)

1
x
 
3x6+5x6
26x66x6

 

[LCM of 6 and 6 is 36]

1
x
 
18+30=1x48=48= 23
2363623672

 

q1 = 23

q2 = 12 (a+q1)

1
x
 
3+48 =1x6x48+3x72 =1x288+216 =1x504
267226x726x7224322432

 

1
x
 
504= 712
1864

 

q2 = 712

q3 = (a+q2)

1x3+504=1x6x5043x864 =1x3024+2592=
2686426x8646x86425184

 

1x5616=5616= 1324
2518410368

 

q3 = 1324

Hence, 23 , 712 , 1324 is a rational number between 36 and 56