Sasi Math (Revised for 1024)

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.

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

$\frac{3}{6}$ and $\frac{5}{9}$

q1 =

q2 =

q3 =

Answer:_______________

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

$\frac{2}{5}$ and $\frac{4}{8}$

q1 =

q2 =

q3 =

Answer:_______________

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

$\frac{2}{5}$ and $\frac{3}{8}$

q1 =

q2 =

q3 =

Answer:_______________

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

$\frac{2}{7}$ and $\frac{5}{9}$

q1 =

q2 =

q3 =

Answer:_______________

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

$\frac{2}{7}$ and $\frac{3}{8}$

q1 =

q2 =

q3 =

Answer:_______________

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

$\frac{3}{4}$ and $\frac{5}{8}$

q1 =

q2 =

q3 =

Answer:_______________

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

$\frac{1}{5}$ and $\frac{5}{6}$

q1 =

q2 =

q3 =

Answer:_______________

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

$\frac{2}{4}$ and $\frac{4}{9}$

q1 =

q2 =

q3 =

Answer:_______________

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

$\frac{2}{5}$ and $\frac{5}{8}$

q1 =

q2 =

q3 =

Answer:_______________

10)

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

$\frac{2}{6}$ and $\frac{3}{7}$

q1 =

q2 =

q3 =

Answer:_______________

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

$\frac{3}{6}$ and $\frac{5}{9}$

q1 = Answer: $\frac{19}{36}$

q2 = Answer: $\frac{37}{72}$

q3 = Answer: $\frac{73}{144}$

SOLUTION 1 :

$\frac{3}{6}$ and $\frac{5}{9}$

a = $\frac{3}{6}$ , b = $\frac{5}{9}$

Let q1 be the rational number between $\frac{3}{6}$ and $\frac{5}{9}$

q1 = $\frac{1}{2}$ (a+b)

1	x	3x9	+	5x6
2	x	6x9	+	9x6

[LCM of 6 and 9 is 54]

1	x	27	+	30	=	1	x	57	=	57	=	$\frac{19}{36}$
2		54		54		2		54		108

q1 = $\frac{19}{36}$

q2 = $\frac{1}{2}$ (a+q1)

1	x	3	+	57	=	1	x	6x57	+	3x108	=	1	x	342+324	=	1	x	666
2		6		108		2		6x108		6x108		2		648		2		648

1	x	666	=	$\frac{37}{72}$
1		1296

q2 = $\frac{37}{72}$

q3 = (a+q2)

1	x	3	+	666	=	1	x	6x666	3x1296	=	1	x	3996+3888	=
2		6		1296		2		6x1296	6x1296		2		7776

1	x	7884	=	7884	=	$\frac{73}{144}$
2		7776		15552

q3 = $\frac{73}{144}$

Hence, $\frac{19}{36}$ , $\frac{37}{72}$ , $\frac{73}{144}$ is a rational number between $\frac{3}{6}$ and $\frac{5}{9}$

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

$\frac{2}{5}$ and $\frac{4}{8}$

q1 = Answer: $\frac{9}{20}$

q2 = Answer: $\frac{17}{40}$

q3 = Answer: $\frac{33}{80}$

SOLUTION 1 :

$\frac{2}{5}$ and $\frac{4}{8}$

a = $\frac{2}{5}$ , b = $\frac{4}{8}$

Let q1 be the rational number between $\frac{2}{5}$ and $\frac{4}{8}$

q1 = $\frac{1}{2}$ (a+b)

1	x	2x8	+	4x5
2	x	5x8	+	8x5

[LCM of 5 and 8 is 40]

1	x	16	+	20	=	1	x	36	=	36	=	$\frac{9}{20}$
2		40		40		2		40		80

q1 = $\frac{9}{20}$

q2 = $\frac{1}{2}$ (a+q1)

1	x	2	+	36	=	1	x	5x36	+	2x80	=	1	x	180+160	=	1	x	340
2		5		80		2		5x80		5x80		2		400		2		400

1	x	340	=	$\frac{17}{40}$
1		800

q2 = $\frac{17}{40}$

q3 = (a+q2)

1	x	2	+	340	=	1	x	5x340	2x800	=	1	x	1700+1600	=
2		5		800		2		5x800	5x800		2		4000

1	x	3300	=	3300	=	$\frac{33}{80}$
2		4000		8000

q3 = $\frac{33}{80}$

Hence, $\frac{9}{20}$ , $\frac{17}{40}$ , $\frac{33}{80}$ is a rational number between $\frac{2}{5}$ and $\frac{4}{8}$

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

$\frac{2}{5}$ and $\frac{3}{8}$

q1 = Answer: $\frac{31}{80}$

q2 = Answer: $\frac{63}{160}$

q3 = Answer: $\frac{127}{320}$

SOLUTION 1 :

$\frac{2}{5}$ and $\frac{3}{8}$

a = $\frac{2}{5}$ , b = $\frac{3}{8}$

Let q1 be the rational number between $\frac{2}{5}$ and $\frac{3}{8}$

q1 = $\frac{1}{2}$ (a+b)

1	x	2x8	+	3x5
2	x	5x8	+	8x5

[LCM of 5 and 8 is 40]

1	x	16	+	15	=	1	x	31	=	31	=	$\frac{31}{80}$
2		40		40		2		40		80

q1 = $\frac{31}{80}$

q2 = $\frac{1}{2}$ (a+q1)

1	x	2	+	31	=	1	x	5x31	+	2x80	=	1	x	155+160	=	1	x	315
2		5		80		2		5x80		5x80		2		400		2		400

1	x	315	=	$\frac{63}{160}$
1		800

q2 = $\frac{63}{160}$

q3 = (a+q2)

1	x	2	+	315	=	1	x	5x315	2x800	=	1	x	1575+1600	=
2		5		800		2		5x800	5x800		2		4000

1	x	3175	=	3175	=	$\frac{127}{320}$
2		4000		8000

q3 = $\frac{127}{320}$

Hence, $\frac{31}{80}$ , $\frac{63}{160}$ , $\frac{127}{320}$ is a rational number between $\frac{2}{5}$ and $\frac{3}{8}$

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

$\frac{2}{7}$ and $\frac{5}{9}$

q1 = Answer: $\frac{53}{126}$

q2 = Answer: $\frac{89}{252}$

q3 = Answer: $\frac{23}{72}$

SOLUTION 1 :

$\frac{2}{7}$ and $\frac{5}{9}$

a = $\frac{2}{7}$ , b = $\frac{5}{9}$

Let q1 be the rational number between $\frac{2}{7}$ and $\frac{5}{9}$

q1 = $\frac{1}{2}$ (a+b)

1	x	2x9	+	5x7
2	x	7x9	+	9x7

[LCM of 7 and 9 is 63]

1	x	18	+	35	=	1	x	53	=	53	=	$\frac{53}{126}$
2		63		63		2		63		126

q1 = $\frac{53}{126}$

q2 = $\frac{1}{2}$ (a+q1)

1	x	2	+	53	=	1	x	7x53	+	2x126	=	1	x	371+252	=	1	x	623
2		7		126		2		7x126		7x126		2		882		2		882

1	x	623	=	$\frac{89}{252}$
1		1764

q2 = $\frac{89}{252}$

q3 = (a+q2)

1	x	2	+	623	=	1	x	7x623	2x1764	=	1	x	4361+3528	=
2		7		1764		2		7x1764	7x1764		2		12348

1	x	7889	=	7889	=	$\frac{23}{72}$
2		12348		24696

q3 = $\frac{23}{72}$

Hence, $\frac{53}{126}$ , $\frac{89}{252}$ , $\frac{23}{72}$ is a rational number between $\frac{2}{7}$ and $\frac{5}{9}$

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

$\frac{2}{7}$ and $\frac{3}{8}$

q1 = Answer: $\frac{37}{112}$

q2 = Answer: $\frac{69}{224}$

q3 = Answer: $\frac{19}{64}$

SOLUTION 1 :

$\frac{2}{7}$ and $\frac{3}{8}$

a = $\frac{2}{7}$ , b = $\frac{3}{8}$

Let q1 be the rational number between $\frac{2}{7}$ and $\frac{3}{8}$

q1 = $\frac{1}{2}$ (a+b)

1	x	2x8	+	3x7
2	x	7x8	+	8x7

[LCM of 7 and 8 is 56]

1	x	16	+	21	=	1	x	37	=	37	=	$\frac{37}{112}$
2		56		56		2		56		112

q1 = $\frac{37}{112}$

q2 = $\frac{1}{2}$ (a+q1)

1	x	2	+	37	=	1	x	7x37	+	2x112	=	1	x	259+224	=	1	x	483
2		7		112		2		7x112		7x112		2		784		2		784

1	x	483	=	$\frac{69}{224}$
1		1568

q2 = $\frac{69}{224}$

q3 = (a+q2)

1	x	2	+	483	=	1	x	7x483	2x1568	=	1	x	3381+3136	=
2		7		1568		2		7x1568	7x1568		2		10976

1	x	6517	=	6517	=	$\frac{19}{64}$
2		10976		21952

q3 = $\frac{19}{64}$

Hence, $\frac{37}{112}$ , $\frac{69}{224}$ , $\frac{19}{64}$ is a rational number between $\frac{2}{7}$ and $\frac{3}{8}$

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

$\frac{3}{4}$ and $\frac{5}{8}$

q1 = Answer: $\frac{11}{16}$

q2 = Answer: $\frac{23}{32}$

q3 = Answer: $\frac{47}{64}$

SOLUTION 1 :

$\frac{3}{4}$ and $\frac{5}{8}$

a = $\frac{3}{4}$ , b = $\frac{5}{8}$

Let q1 be the rational number between $\frac{3}{4}$ and $\frac{5}{8}$

q1 = $\frac{1}{2}$ (a+b)

1	x	3x8	+	5x4
2	x	4x8	+	8x4

[LCM of 4 and 8 is 32]

1	x	24	+	20	=	1	x	44	=	44	=	$\frac{11}{16}$
2		32		32		2		32		64

q1 = $\frac{11}{16}$

q2 = $\frac{1}{2}$ (a+q1)

1	x	3	+	44	=	1	x	4x44	+	3x64	=	1	x	176+192	=	1	x	368
2		4		64		2		4x64		4x64		2		256		2		256

1	x	368	=	$\frac{23}{32}$
1		512

q2 = $\frac{23}{32}$

q3 = (a+q2)

1	x	3	+	368	=	1	x	4x368	3x512	=	1	x	1472+1536	=
2		4		512		2		4x512	4x512		2		2048

1	x	3008	=	3008	=	$\frac{47}{64}$
2		2048		4096

q3 = $\frac{47}{64}$

Hence, $\frac{11}{16}$ , $\frac{23}{32}$ , $\frac{47}{64}$ is a rational number between $\frac{3}{4}$ and $\frac{5}{8}$

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

$\frac{1}{5}$ and $\frac{5}{6}$

q1 = Answer: $\frac{31}{60}$

q2 = Answer: $\frac{43}{120}$

q3 = Answer: $\frac{67}{240}$

SOLUTION 1 :

$\frac{1}{5}$ and $\frac{5}{6}$

a = $\frac{1}{5}$ , b = $\frac{5}{6}$

Let q1 be the rational number between $\frac{1}{5}$ and $\frac{5}{6}$

q1 = $\frac{1}{2}$ (a+b)

1	x	1x6	+	5x5
2	x	5x6	+	6x5

[LCM of 5 and 6 is 30]

1	x	6	+	25	=	1	x	31	=	31	=	$\frac{31}{60}$
2		30		30		2		30		60

q1 = $\frac{31}{60}$

q2 = $\frac{1}{2}$ (a+q1)

1	x	1	+	31	=	1	x	5x31	+	1x60	=	1	x	155+60	=	1	x	215
2		5		60		2		5x60		5x60		2		300		2		300

1	x	215	=	$\frac{43}{120}$
1		600

q2 = $\frac{43}{120}$

q3 = (a+q2)

1	x	1	+	215	=	1	x	5x215	1x600	=	1	x	1075+600	=
2		5		600		2		5x600	5x600		2		3000

1	x	1675	=	1675	=	$\frac{67}{240}$
2		3000		6000

q3 = $\frac{67}{240}$

Hence, $\frac{31}{60}$ , $\frac{43}{120}$ , $\frac{67}{240}$ is a rational number between $\frac{1}{5}$ and $\frac{5}{6}$

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

$\frac{2}{4}$ and $\frac{4}{9}$

q1 = Answer: $\frac{17}{36}$

q2 = Answer: $\frac{35}{72}$

q3 = Answer: $\frac{71}{144}$

SOLUTION 1 :

$\frac{2}{4}$ and $\frac{4}{9}$

a = $\frac{2}{4}$ , b = $\frac{4}{9}$

Let q1 be the rational number between $\frac{2}{4}$ and $\frac{4}{9}$

q1 = $\frac{1}{2}$ (a+b)

1	x	2x9	+	4x4
2	x	4x9	+	9x4

[LCM of 4 and 9 is 36]

1	x	18	+	16	=	1	x	34	=	34	=	$\frac{17}{36}$
2		36		36		2		36		72

q1 = $\frac{17}{36}$

q2 = $\frac{1}{2}$ (a+q1)

1	x	2	+	34	=	1	x	4x34	+	2x72	=	1	x	136+144	=	1	x	280
2		4		72		2		4x72		4x72		2		288		2		288

1	x	280	=	$\frac{35}{72}$
1		576

q2 = $\frac{35}{72}$

q3 = (a+q2)

1	x	2	+	280	=	1	x	4x280	2x576	=	1	x	1120+1152	=
2		4		576		2		4x576	4x576		2		2304

1	x	2272	=	2272	=	$\frac{71}{144}$
2		2304		4608

q3 = $\frac{71}{144}$

Hence, $\frac{17}{36}$ , $\frac{35}{72}$ , $\frac{71}{144}$ is a rational number between $\frac{2}{4}$ and $\frac{4}{9}$

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

$\frac{2}{5}$ and $\frac{5}{8}$

q1 = Answer: $\frac{41}{80}$

q2 = Answer: $\frac{73}{160}$

q3 = Answer: $\frac{137}{320}$

SOLUTION 1 :

$\frac{2}{5}$ and $\frac{5}{8}$

a = $\frac{2}{5}$ , b = $\frac{5}{8}$

Let q1 be the rational number between $\frac{2}{5}$ and $\frac{5}{8}$

q1 = $\frac{1}{2}$ (a+b)

1	x	2x8	+	5x5
2	x	5x8	+	8x5

[LCM of 5 and 8 is 40]

1	x	16	+	25	=	1	x	41	=	41	=	$\frac{41}{80}$
2		40		40		2		40		80

q1 = $\frac{41}{80}$

q2 = $\frac{1}{2}$ (a+q1)

1	x	2	+	41	=	1	x	5x41	+	2x80	=	1	x	205+160	=	1	x	365
2		5		80		2		5x80		5x80		2		400		2		400

1	x	365	=	$\frac{73}{160}$
1		800

q2 = $\frac{73}{160}$

q3 = (a+q2)

1	x	2	+	365	=	1	x	5x365	2x800	=	1	x	1825+1600	=
2		5		800		2		5x800	5x800		2		4000

1	x	3425	=	3425	=	$\frac{137}{320}$
2		4000		8000

q3 = $\frac{137}{320}$

Hence, $\frac{41}{80}$ , $\frac{73}{160}$ , $\frac{137}{320}$ is a rational number between $\frac{2}{5}$ and $\frac{5}{8}$

10)

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

$\frac{2}{6}$ and $\frac{3}{7}$

q1 = Answer: $\frac{8}{21}$

q2 = Answer: $\frac{5}{14}$

q3 = Answer: $\frac{29}{84}$

SOLUTION 1 :

$\frac{2}{6}$ and $\frac{3}{7}$

a = $\frac{2}{6}$ , b = $\frac{3}{7}$

Let q1 be the rational number between $\frac{2}{6}$ and $\frac{3}{7}$

q1 = $\frac{1}{2}$ (a+b)

1	x	2x7	+	3x6
2	x	6x7	+	7x6

[LCM of 6 and 7 is 42]

1	x	14	+	18	=	1	x	32	=	32	=	$\frac{8}{21}$
2		42		42		2		42		84

q1 = $\frac{8}{21}$

q2 = $\frac{1}{2}$ (a+q1)

1	x	2	+	32	=	1	x	6x32	+	2x84	=	1	x	192+168	=	1	x	360
2		6		84		2		6x84		6x84		2		504		2		504

1	x	360	=	$\frac{5}{14}$
1		1008

q2 = $\frac{5}{14}$

q3 = (a+q2)

1	x	2	+	360	=	1	x	6x360	2x1008	=	1	x	2160+2016	=
2		6		1008		2		6x1008	6x1008		2		6048

1	x	4176	=	4176	=	$\frac{29}{84}$
2		6048		12096

q3 = $\frac{29}{84}$

Hence, $\frac{8}{21}$ , $\frac{5}{14}$ , $\frac{29}{84}$ is a rational number between $\frac{2}{6}$ and $\frac{3}{7}$