Scroll:Real Number System >> Rational ( Exercise1.2) >> saq (4379)


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

46 and 26

q1 =

q2 =


Answer:_______________




2)  

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

36 and 38

q1 =

q2 =


Answer:_______________




3)  

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

35 and 58

q1 =

q2 =


Answer:_______________




4)  

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

25 and 46

q1 =

q2 =


Answer:_______________




5)  

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

46 and 48

q1 =

q2 =


Answer:_______________




6)  

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

25 and 37

q1 =

q2 =


Answer:_______________




7)  

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

25 and 56

q1 =

q2 =


Answer:_______________




8)  

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

25 and 58

q1 =

q2 =


Answer:_______________




9)  

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

46 and 57

q1 =

q2 =


Answer:_______________




10)  

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

36 and 58

q1 =

q2 =


Answer:_______________




 

1)  

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

46 and 26

q1 = Answer: 12

q2 = Answer: 76


SOLUTION 1 :

  46 and 26

a = 46 ,  b = 26

Let q1 be the rational number between 46 and 26

q1 = 12 (a+b)

1
x
 
4x6+2x6
26x66x6

 

[LCM of 6 and 6 is 36]

1
x
 
24+12=1x36=36= 12
2363623672

 

q1 = 3672 = 12

q2 = 12 (a+q1)

1
x
 
4+36 =1x6x36+4x72 =1x216+288 =1x504
267226x726x7224322432

 

1
x
 
504= 76
1864

 

q2 = 76

Hence, 12 , 76 is a rational number between 46 and 26



2)  

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

36 and 38

q1 = Answer: 716

q2 = Answer: 1516


SOLUTION 1 :

  36 and 38

a = 36 ,  b = 38

Let q1 be the rational number between 36 and 38

q1 = 12 (a+b)

1
x
 
3x8+3x6
26x88x6

 

[LCM of 6 and 8 is 48]

1
x
 
24+18=1x42=42= 716
2484824896

 

q1 = 4296 = 716

q2 = 12 (a+q1)

1
x
 
3+42 =1x6x42+3x96 =1x252+288 =1x540
269626x966x9625762576

 

1
x
 
540= 1516
11152

 

q2 = 1516

Hence, 716 , 1516 is a rational number between 36 and 38



3)  

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

35 and 58

q1 = Answer: 4980

q2 = Answer: 9780


SOLUTION 1 :

  35 and 58

a = 35 ,  b = 58

Let q1 be the rational number between 35 and 58

q1 = 12 (a+b)

1
x
 
3x8+5x5
25x88x5

 

[LCM of 5 and 8 is 40]

1
x
 
24+25=1x49=49= 4980
2404024080

 

q1 = 4980 = 4980

q2 = 12 (a+q1)

1
x
 
3+49 =1x5x49+3x80 =1x245+240 =1x485
258025x805x8024002400

 

1
x
 
485= 9780
1800

 

q2 = 9780

Hence, 4980 , 9780 is a rational number between 35 and 58



4)  

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

25 and 46

q1 = Answer: 815

q2 = Answer: 1415


SOLUTION 1 :

  25 and 46

a = 25 ,  b = 46

Let q1 be the rational number between 25 and 46

q1 = 12 (a+b)

1
x
 
2x6+4x5
25x66x5

 

[LCM of 5 and 6 is 30]

1
x
 
12+20=1x32=32= 815
2303023060

 

q1 = 3260 = 815

q2 = 12 (a+q1)

1
x
 
2+32 =1x5x32+2x60 =1x160+120 =1x280
256025x605x6023002300

 

1
x
 
280= 1415
1600

 

q2 = 1415

Hence, 815 , 1415 is a rational number between 25 and 46



5)  

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

46 and 48

q1 = Answer: 712

q2 = Answer: 54


SOLUTION 1 :

  46 and 48

a = 46 ,  b = 48

Let q1 be the rational number between 46 and 48

q1 = 12 (a+b)

1
x
 
4x8+4x6
26x88x6

 

[LCM of 6 and 8 is 48]

1
x
 
32+24=1x56=56= 712
2484824896

 

q1 = 5696 = 712

q2 = 12 (a+q1)

1
x
 
4+56 =1x6x56+4x96 =1x336+384 =1x720
269626x966x9625762576

 

1
x
 
720= 54
11152

 

q2 = 54

Hence, 712 , 54 is a rational number between 46 and 48



6)  

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

25 and 37

q1 = Answer: 2970

q2 = Answer: 5770


SOLUTION 1 :

  25 and 37

a = 25 ,  b = 37

Let q1 be the rational number between 25 and 37

q1 = 12 (a+b)

1
x
 
2x7+3x5
25x77x5

 

[LCM of 5 and 7 is 35]

1
x
 
14+15=1x29=29= 2970
2353523570

 

q1 = 2970 = 2970

q2 = 12 (a+q1)

1
x
 
2+29 =1x5x29+2x70 =1x145+140 =1x285
257025x705x7023502350

 

1
x
 
285= 5770
1700

 

q2 = 5770

Hence, 2970 , 5770 is a rational number between 25 and 37



7)  

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

25 and 56

q1 = Answer: 3760

q2 = Answer: 6160


SOLUTION 1 :

  25 and 56

a = 25 ,  b = 56

Let q1 be the rational number between 25 and 56

q1 = 12 (a+b)

1
x
 
2x6+5x5
25x66x5

 

[LCM of 5 and 6 is 30]

1
x
 
12+25=1x37=37= 3760
2303023060

 

q1 = 3760 = 3760

q2 = 12 (a+q1)

1
x
 
2+37 =1x5x37+2x60 =1x185+120 =1x305
256025x605x6023002300

 

1
x
 
305= 6160
1600

 

q2 = 6160

Hence, 3760 , 6160 is a rational number between 25 and 56



8)  

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

25 and 58

q1 = Answer: 4180

q2 = Answer: 7380


SOLUTION 1 :

  25 and 58

a = 25 ,  b = 58

Let q1 be the rational number between 25 and 58

q1 = 12 (a+b)

1
x
 
2x8+5x5
25x88x5

 

[LCM of 5 and 8 is 40]

1
x
 
16+25=1x41=41= 4180
2404024080

 

q1 = 4180 = 4180

q2 = 12 (a+q1)

1
x
 
2+41 =1x5x41+2x80 =1x205+160 =1x365
258025x805x8024002400

 

1
x
 
365= 7380
1800

 

q2 = 7380

Hence, 4180 , 7380 is a rational number between 25 and 58



9)  

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

46 and 57

q1 = Answer: 2942

q2 = Answer: 1914


SOLUTION 1 :

  46 and 57

a = 46 ,  b = 57

Let q1 be the rational number between 46 and 57

q1 = 12 (a+b)

1
x
 
4x7+5x6
26x77x6

 

[LCM of 6 and 7 is 42]

1
x
 
28+30=1x58=58= 2942
2424224284

 

q1 = 5884 = 2942

q2 = 12 (a+q1)

1
x
 
4+58 =1x6x58+4x84 =1x348+336 =1x684
268426x846x8425042504

 

1
x
 
684= 1914
11008

 

q2 = 1914

Hence, 2942 , 1914 is a rational number between 46 and 57



10)  

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

36 and 58

q1 = Answer: 916

q2 = Answer: 1716


SOLUTION 1 :

  36 and 58

a = 36 ,  b = 58

Let q1 be the rational number between 36 and 58

q1 = 12 (a+b)

1
x
 
3x8+5x6
26x88x6

 

[LCM of 6 and 8 is 48]

1
x
 
24+30=1x54=54= 916
2484824896

 

q1 = 5496 = 916

q2 = 12 (a+q1)

1
x
 
3+54 =1x6x54+3x96 =1x324+288 =1x612
269626x966x9625762576

 

1
x
 
612= 1716
11152

 

q2 = 1716

Hence, 916 , 1716 is a rational number between 36 and 58