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 / )

26 and 47

q1 =

q2 =


Answer:_______________




2)  

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

25 and 46

q1 =

q2 =


Answer:_______________




3)  

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

36 and 26

q1 =

q2 =


Answer:_______________




4)  

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

36 and 47

q1 =

q2 =


Answer:_______________




5)  

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

46 and 28

q1 =

q2 =


Answer:_______________




6)  

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

36 and 56

q1 =

q2 =


Answer:_______________




7)  

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

45 and 47

q1 =

q2 =


Answer:_______________




8)  

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

26 and 26

q1 =

q2 =


Answer:_______________




9)  

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

35 and 26

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 / )

26 and 47

q1 = Answer: 1942

q2 = Answer: 1114


SOLUTION 1 :

  26 and 47

a = 26 ,  b = 47

Let q1 be the rational number between 26 and 47

q1 = 12 (a+b)

1
x
 
2x7+4x6
26x77x6

 

[LCM of 6 and 7 is 42]

1
x
 
14+24=1x38=38= 1942
2424224284

 

q1 = 3884 = 1942

q2 = 12 (a+q1)

1
x
 
2+38 =1x6x38+2x84 =1x228+168 =1x396
268426x846x8425042504

 

1
x
 
396= 1114
11008

 

q2 = 1114

Hence, 1942 , 1114 is a rational number between 26 and 47



2)  

 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



3)  

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

36 and 26

q1 = Answer: 512

q2 = Answer: 1112


SOLUTION 1 :

  36 and 26

a = 36 ,  b = 26

Let q1 be the rational number between 36 and 26

q1 = 12 (a+b)

1
x
 
3x6+2x6
26x66x6

 

[LCM of 6 and 6 is 36]

1
x
 
18+12=1x30=30= 512
2363623672

 

q1 = 3072 = 512

q2 = 12 (a+q1)

1
x
 
3+30 =1x6x30+3x72 =1x180+216 =1x396
267226x726x7224322432

 

1
x
 
396= 1112
1864

 

q2 = 1112

Hence, 512 , 1112 is a rational number between 36 and 26



4)  

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

36 and 47

q1 = Answer: 1528

q2 = Answer: 2928


SOLUTION 1 :

  36 and 47

a = 36 ,  b = 47

Let q1 be the rational number between 36 and 47

q1 = 12 (a+b)

1
x
 
3x7+4x6
26x77x6

 

[LCM of 6 and 7 is 42]

1
x
 
21+24=1x45=45= 1528
2424224284

 

q1 = 4584 = 1528

q2 = 12 (a+q1)

1
x
 
3+45 =1x6x45+3x84 =1x270+252 =1x522
268426x846x8425042504

 

1
x
 
522= 2928
11008

 

q2 = 2928

Hence, 1528 , 2928 is a rational number between 36 and 47



5)  

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

46 and 28

q1 = Answer: 1124

q2 = Answer: 98


SOLUTION 1 :

  46 and 28

a = 46 ,  b = 28

Let q1 be the rational number between 46 and 28

q1 = 12 (a+b)

1
x
 
4x8+2x6
26x88x6

 

[LCM of 6 and 8 is 48]

1
x
 
32+12=1x44=44= 1124
2484824896

 

q1 = 4496 = 1124

q2 = 12 (a+q1)

1
x
 
4+44 =1x6x44+4x96 =1x264+384 =1x648
269626x966x9625762576

 

1
x
 
648= 98
11152

 

q2 = 98

Hence, 1124 , 98 is a rational number between 46 and 28



6)  

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

36 and 56

q1 = Answer: 23

q2 = Answer: 76


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 = 4872 = 23

q2 = 12 (a+q1)

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

 

1
x
 
504= 76
1864

 

q2 = 76

Hence, 23 , 76 is a rational number between 36 and 56



7)  

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

45 and 47

q1 = Answer: 2435

q2 = Answer: 5235


SOLUTION 1 :

  45 and 47

a = 45 ,  b = 47

Let q1 be the rational number between 45 and 47

q1 = 12 (a+b)

1
x
 
4x7+4x5
25x77x5

 

[LCM of 5 and 7 is 35]

1
x
 
28+20=1x48=48= 2435
2353523570

 

q1 = 4870 = 2435

q2 = 12 (a+q1)

1
x
 
4+48 =1x5x48+4x70 =1x240+280 =1x520
257025x705x7023502350

 

1
x
 
520= 5235
1700

 

q2 = 5235

Hence, 2435 , 5235 is a rational number between 45 and 47



8)  

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

26 and 26

q1 = Answer: 13

q2 = Answer: 23


SOLUTION 1 :

  26 and 26

a = 26 ,  b = 26

Let q1 be the rational number between 26 and 26

q1 = 12 (a+b)

1
x
 
2x6+2x6
26x66x6

 

[LCM of 6 and 6 is 36]

1
x
 
12+12=1x24=24= 13
2363623672

 

q1 = 2472 = 13

q2 = 12 (a+q1)

1
x
 
2+24 =1x6x24+2x72 =1x144+144 =1x288
267226x726x7224322432

 

1
x
 
288= 23
1864

 

q2 = 23

Hence, 13 , 23 is a rational number between 26 and 26



9)  

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

35 and 26

q1 = Answer: 715

q2 = Answer: 1615


SOLUTION 1 :

  35 and 26

a = 35 ,  b = 26

Let q1 be the rational number between 35 and 26

q1 = 12 (a+b)

1
x
 
3x6+2x5
25x66x5

 

[LCM of 5 and 6 is 30]

1
x
 
18+10=1x28=28= 715
2303023060

 

q1 = 2860 = 715

q2 = 12 (a+q1)

1
x
 
3+28 =1x5x28+3x60 =1x140+180 =1x320
256025x605x6023002300

 

1
x
 
320= 1615
1600

 

q2 = 1615

Hence, 715 , 1615 is a rational number between 35 and 26



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