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 28

q1 =

q2 =


Answer:_______________




2)  

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

26 and 38

q1 =

q2 =


Answer:_______________




3)  

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

36 and 37

q1 =

q2 =


Answer:_______________




4)  

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

35 and 56

q1 =

q2 =


Answer:_______________




5)  

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

26 and 46

q1 =

q2 =


Answer:_______________




6)  

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

35 and 26

q1 =

q2 =


Answer:_______________




7)  

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

46 and 59

q1 =

q2 =


Answer:_______________




8)  

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

46 and 37

q1 =

q2 =


Answer:_______________




9)  

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

35 and 39

q1 =

q2 =


Answer:_______________




10)  

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

25 and 46

q1 =

q2 =


Answer:_______________




 

1)  

 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



2)  

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

26 and 38

q1 = Answer: 1748

q2 = Answer: 1116


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 = 3496 = 1748

q2 = 12 (a+q1)

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

 

1
x
 
396= 1116
11152

 

q2 = 1116

Hence, 1748 , 1116 is a rational number between 26 and 38



3)  

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

36 and 37

q1 = Answer: 1328

q2 = Answer: 2728


SOLUTION 1 :

  36 and 37

a = 36 ,  b = 37

Let q1 be the rational number between 36 and 37

q1 = 12 (a+b)

1
x
 
3x7+3x6
26x77x6

 

[LCM of 6 and 7 is 42]

1
x
 
21+18=1x39=39= 1328
2424224284

 

q1 = 3984 = 1328

q2 = 12 (a+q1)

1
x
 
3+39 =1x6x39+3x84 =1x234+252 =1x486
268426x846x8425042504

 

1
x
 
486= 2728
11008

 

q2 = 2728

Hence, 1328 , 2728 is a rational number between 36 and 37



4)  

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

35 and 56

q1 = Answer: 4360

q2 = Answer: 7960


SOLUTION 1 :

  35 and 56

a = 35 ,  b = 56

Let q1 be the rational number between 35 and 56

q1 = 12 (a+b)

1
x
 
3x6+5x5
25x66x5

 

[LCM of 5 and 6 is 30]

1
x
 
18+25=1x43=43= 4360
2303023060

 

q1 = 4360 = 4360

q2 = 12 (a+q1)

1
x
 
3+43 =1x5x43+3x60 =1x215+180 =1x395
256025x605x6023002300

 

1
x
 
395= 7960
1600

 

q2 = 7960

Hence, 4360 , 7960 is a rational number between 35 and 56



5)  

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

26 and 46

q1 = Answer: 12

q2 = Answer: 56


SOLUTION 1 :

  26 and 46

a = 26 ,  b = 46

Let q1 be the rational number between 26 and 46

q1 = 12 (a+b)

1
x
 
2x6+4x6
26x66x6

 

[LCM of 6 and 6 is 36]

1
x
 
12+24=1x36=36= 12
2363623672

 

q1 = 3672 = 12

q2 = 12 (a+q1)

1
x
 
2+36 =1x6x36+2x72 =1x216+144 =1x360
267226x726x7224322432

 

1
x
 
360= 56
1864

 

q2 = 56

Hence, 12 , 56 is a rational number between 26 and 46



6)  

 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



7)  

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

46 and 59

q1 = Answer: 1118

q2 = Answer: 2318


SOLUTION 1 :

  46 and 59

a = 46 ,  b = 59

Let q1 be the rational number between 46 and 59

q1 = 12 (a+b)

1
x
 
4x9+5x6
26x99x6

 

[LCM of 6 and 9 is 54]

1
x
 
36+30=1x66=66= 1118
25454254108

 

q1 = 66108 = 1118

q2 = 12 (a+q1)

1
x
 
4+66 =1x6x66+4x108 =1x396+432 =1x828
2610826x1086x10826482648

 

1
x
 
828= 2318
11296

 

q2 = 2318

Hence, 1118 , 2318 is a rational number between 46 and 59



8)  

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

46 and 37

q1 = Answer: 2342

q2 = Answer: 1714


SOLUTION 1 :

  46 and 37

a = 46 ,  b = 37

Let q1 be the rational number between 46 and 37

q1 = 12 (a+b)

1
x
 
4x7+3x6
26x77x6

 

[LCM of 6 and 7 is 42]

1
x
 
28+18=1x46=46= 2342
2424224284

 

q1 = 4684 = 2342

q2 = 12 (a+q1)

1
x
 
4+46 =1x6x46+4x84 =1x276+336 =1x612
268426x846x8425042504

 

1
x
 
612= 1714
11008

 

q2 = 1714

Hence, 2342 , 1714 is a rational number between 46 and 37



9)  

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

35 and 39

q1 = Answer: 715

q2 = Answer: 1615


SOLUTION 1 :

  35 and 39

a = 35 ,  b = 39

Let q1 be the rational number between 35 and 39

q1 = 12 (a+b)

1
x
 
3x9+3x5
25x99x5

 

[LCM of 5 and 9 is 45]

1
x
 
27+15=1x42=42= 715
2454524590

 

q1 = 4290 = 715

q2 = 12 (a+q1)

1
x
 
3+42 =1x5x42+3x90 =1x210+270 =1x480
259025x905x9024502450

 

1
x
 
480= 1615
1900

 

q2 = 1615

Hence, 715 , 1615 is a rational number between 35 and 39



10)  

 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