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 / )

$\frac{3}{5}$ and $\frac{4}{7}$

q1 =

q2 =

q3 =

Answer:_______________

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

$\frac{2}{7}$ and $\frac{5}{8}$

q1 =

q2 =

q3 =

Answer:_______________

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

$\frac{1}{4}$ and $\frac{5}{8}$

q1 =

q2 =

q3 =

Answer:_______________

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

$\frac{2}{7}$ and $\frac{4}{9}$

q1 =

q2 =

q3 =

Answer:_______________

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

$\frac{1}{7}$ and $\frac{5}{6}$

q1 =

q2 =

q3 =

Answer:_______________

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

$\frac{2}{5}$ and $\frac{3}{7}$

q1 =

q2 =

q3 =

Answer:_______________

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

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

q1 =

q2 =

q3 =

Answer:_______________

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

$\frac{2}{4}$ and $\frac{4}{6}$

q1 =

q2 =

q3 =

Answer:_______________

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

$\frac{3}{5}$ and $\frac{5}{7}$

q1 =

q2 =

q3 =

Answer:_______________

10)

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

$\frac{2}{6}$ and $\frac{3}{8}$

q1 =

q2 =

q3 =

Answer:_______________

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

$\frac{3}{5}$ and $\frac{4}{7}$

q1 = Answer: $\frac{41}{70}$

q2 = Answer: $\frac{83}{140}$

q3 = Answer: $\frac{167}{280}$

SOLUTION 1 :

$\frac{3}{5}$ and $\frac{4}{7}$

a = $\frac{3}{5}$ , b = $\frac{4}{7}$

Let q1 be the rational number between $\frac{3}{5}$ and $\frac{4}{7}$

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

1	x	3x7	+	4x5
2	x	5x7	+	7x5

[LCM of 5 and 7 is 35]

1	x	21	+	20	=	1	x	41	=	41	=	$\frac{41}{70}$
2		35		35		2		35		70

q1 = $\frac{41}{70}$

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

1	x	3	+	41	=	1	x	5x41	+	3x70	=	1	x	205+210	=	1	x	415
2		5		70		2		5x70		5x70		2		350		2		350

1	x	415	=	$\frac{83}{140}$
1		700

q2 = $\frac{83}{140}$

q3 = (a+q2)

1	x	3	+	415	=	1	x	5x415	3x700	=	1	x	2075+2100	=
2		5		700		2		5x700	5x700		2		3500

1	x	4175	=	4175	=	$\frac{167}{280}$
2		3500		7000

q3 = $\frac{167}{280}$

Hence, $\frac{41}{70}$ , $\frac{83}{140}$ , $\frac{167}{280}$ is a rational number between $\frac{3}{5}$ and $\frac{4}{7}$

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

$\frac{2}{7}$ and $\frac{5}{8}$

q1 = Answer: $\frac{51}{112}$

q2 = Answer: $\frac{83}{224}$

q3 = Answer: $\frac{21}{64}$

SOLUTION 1 :

$\frac{2}{7}$ and $\frac{5}{8}$

a = $\frac{2}{7}$ , b = $\frac{5}{8}$

Let q1 be the rational number between $\frac{2}{7}$ and $\frac{5}{8}$

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

1	x	2x8	+	5x7
2	x	7x8	+	8x7

[LCM of 7 and 8 is 56]

1	x	16	+	35	=	1	x	51	=	51	=	$\frac{51}{112}$
2		56		56		2		56		112

q1 = $\frac{51}{112}$

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

1	x	2	+	51	=	1	x	7x51	+	2x112	=	1	x	357+224	=	1	x	581
2		7		112		2		7x112		7x112		2		784		2		784

1	x	581	=	$\frac{83}{224}$
1		1568

q2 = $\frac{83}{224}$

q3 = (a+q2)

1	x	2	+	581	=	1	x	7x581	2x1568	=	1	x	4067+3136	=
2		7		1568		2		7x1568	7x1568		2		10976

1	x	7203	=	7203	=	$\frac{21}{64}$
2		10976		21952

q3 = $\frac{21}{64}$

Hence, $\frac{51}{112}$ , $\frac{83}{224}$ , $\frac{21}{64}$ is a rational number between $\frac{2}{7}$ and $\frac{5}{8}$

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

$\frac{1}{4}$ and $\frac{5}{8}$

q1 = Answer: $\frac{7}{16}$

q2 = Answer: $\frac{11}{32}$

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

SOLUTION 1 :

$\frac{1}{4}$ and $\frac{5}{8}$

a = $\frac{1}{4}$ , b = $\frac{5}{8}$

Let q1 be the rational number between $\frac{1}{4}$ and $\frac{5}{8}$

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

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

[LCM of 4 and 8 is 32]

1	x	8	+	20	=	1	x	28	=	28	=	$\frac{7}{16}$
2		32		32		2		32		64

q1 = $\frac{7}{16}$

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

1	x	1	+	28	=	1	x	4x28	+	1x64	=	1	x	112+64	=	1	x	176
2		4		64		2		4x64		4x64		2		256		2		256

1	x	176	=	$\frac{11}{32}$
1		512

q2 = $\frac{11}{32}$

q3 = (a+q2)

1	x	1	+	176	=	1	x	4x176	1x512	=	1	x	704+512	=
2		4		512		2		4x512	4x512		2		2048

1	x	1216	=	1216	=	$\frac{19}{64}$
2		2048		4096

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

Hence, $\frac{7}{16}$ , $\frac{11}{32}$ , $\frac{19}{64}$ is a rational number between $\frac{1}{4}$ and $\frac{5}{8}$

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

$\frac{2}{7}$ and $\frac{4}{9}$

q1 = Answer: $\frac{23}{63}$

q2 = Answer: $\frac{41}{126}$

q3 = Answer: $\frac{11}{36}$

SOLUTION 1 :

$\frac{2}{7}$ and $\frac{4}{9}$

a = $\frac{2}{7}$ , b = $\frac{4}{9}$

Let q1 be the rational number between $\frac{2}{7}$ and $\frac{4}{9}$

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

1	x	2x9	+	4x7
2	x	7x9	+	9x7

[LCM of 7 and 9 is 63]

1	x	18	+	28	=	1	x	46	=	46	=	$\frac{23}{63}$
2		63		63		2		63		126

q1 = $\frac{23}{63}$

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

1	x	2	+	46	=	1	x	7x46	+	2x126	=	1	x	322+252	=	1	x	574
2		7		126		2		7x126		7x126		2		882		2		882

1	x	574	=	$\frac{41}{126}$
1		1764

q2 = $\frac{41}{126}$

q3 = (a+q2)

1	x	2	+	574	=	1	x	7x574	2x1764	=	1	x	4018+3528	=
2		7		1764		2		7x1764	7x1764		2		12348

1	x	7546	=	7546	=	$\frac{11}{36}$
2		12348		24696

q3 = $\frac{11}{36}$

Hence, $\frac{23}{63}$ , $\frac{41}{126}$ , $\frac{11}{36}$ is a rational number between $\frac{2}{7}$ and $\frac{4}{9}$

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

$\frac{1}{7}$ and $\frac{5}{6}$

q1 = Answer: $\frac{41}{84}$

q2 = Answer: $\frac{53}{168}$

q3 = Answer: $\frac{11}{48}$

SOLUTION 1 :

$\frac{1}{7}$ and $\frac{5}{6}$

a = $\frac{1}{7}$ , b = $\frac{5}{6}$

Let q1 be the rational number between $\frac{1}{7}$ and $\frac{5}{6}$

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

1	x	1x6	+	5x7
2	x	7x6	+	6x7

[LCM of 7 and 6 is 42]

1	x	6	+	35	=	1	x	41	=	41	=	$\frac{41}{84}$
2		42		42		2		42		84

q1 = $\frac{41}{84}$

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

1	x	1	+	41	=	1	x	7x41	+	1x84	=	1	x	287+84	=	1	x	371
2		7		84		2		7x84		7x84		2		588		2		588

1	x	371	=	$\frac{53}{168}$
1		1176

q2 = $\frac{53}{168}$

q3 = (a+q2)

1	x	1	+	371	=	1	x	7x371	1x1176	=	1	x	2597+1176	=
2		7		1176		2		7x1176	7x1176		2		8232

1	x	3773	=	3773	=	$\frac{11}{48}$
2		8232		16464

q3 = $\frac{11}{48}$

Hence, $\frac{41}{84}$ , $\frac{53}{168}$ , $\frac{11}{48}$ is a rational number between $\frac{1}{7}$ and $\frac{5}{6}$

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

$\frac{2}{5}$ and $\frac{3}{7}$

q1 = Answer: $\frac{29}{70}$

q2 = Answer: $\frac{57}{140}$

q3 = Answer: $\frac{113}{280}$

SOLUTION 1 :

$\frac{2}{5}$ and $\frac{3}{7}$

a = $\frac{2}{5}$ , b = $\frac{3}{7}$

Let q1 be the rational number between $\frac{2}{5}$ and $\frac{3}{7}$

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

1	x	2x7	+	3x5
2	x	5x7	+	7x5

[LCM of 5 and 7 is 35]

1	x	14	+	15	=	1	x	29	=	29	=	$\frac{29}{70}$
2		35		35		2		35		70

q1 = $\frac{29}{70}$

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

1	x	2	+	29	=	1	x	5x29	+	2x70	=	1	x	145+140	=	1	x	285
2		5		70		2		5x70		5x70		2		350		2		350

1	x	285	=	$\frac{57}{140}$
1		700

q2 = $\frac{57}{140}$

q3 = (a+q2)

1	x	2	+	285	=	1	x	5x285	2x700	=	1	x	1425+1400	=
2		5		700		2		5x700	5x700		2		3500

1	x	2825	=	2825	=	$\frac{113}{280}$
2		3500		7000

q3 = $\frac{113}{280}$

Hence, $\frac{29}{70}$ , $\frac{57}{140}$ , $\frac{113}{280}$ is a rational number between $\frac{2}{5}$ and $\frac{3}{7}$

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

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

q1 = Answer: $\frac{1}{2}$

q2 = Answer: $\frac{1}{2}$

q3 = Answer: $\frac{1}{2}$

SOLUTION 1 :

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

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

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

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

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

[LCM of 4 and 8 is 32]

1	x	16	+	16	=	1	x	32	=	32	=	$\frac{1}{2}$
2		32		32		2		32		64

q1 = $\frac{1}{2}$

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

1	x	2	+	32	=	1	x	4x32	+	2x64	=	1	x	128+128	=	1	x	256
2		4		64		2		4x64		4x64		2		256		2		256

1	x	256	=	$\frac{1}{2}$
1		512

q2 = $\frac{1}{2}$

q3 = (a+q2)

1	x	2	+	256	=	1	x	4x256	2x512	=	1	x	1024+1024	=
2		4		512		2		4x512	4x512		2		2048

1	x	2048	=	2048	=	$\frac{1}{2}$
2		2048		4096

q3 = $\frac{1}{2}$

Hence, $\frac{1}{2}$ , $\frac{1}{2}$ , $\frac{1}{2}$ is a rational number between $\frac{2}{4}$ and $\frac{4}{8}$

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

$\frac{2}{4}$ and $\frac{4}{6}$

q1 = Answer: $\frac{7}{12}$

q2 = Answer: $\frac{13}{24}$

q3 = Answer: $\frac{25}{48}$

SOLUTION 1 :

$\frac{2}{4}$ and $\frac{4}{6}$

a = $\frac{2}{4}$ , b = $\frac{4}{6}$

Let q1 be the rational number between $\frac{2}{4}$ and $\frac{4}{6}$

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

1	x	2x6	+	4x4
2	x	4x6	+	6x4

[LCM of 4 and 6 is 24]

1	x	12	+	16	=	1	x	28	=	28	=	$\frac{7}{12}$
2		24		24		2		24		48

q1 = $\frac{7}{12}$

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

1	x	2	+	28	=	1	x	4x28	+	2x48	=	1	x	112+96	=	1	x	208
2		4		48		2		4x48		4x48		2		192		2		192

1	x	208	=	$\frac{13}{24}$
1		384

q2 = $\frac{13}{24}$

q3 = (a+q2)

1	x	2	+	208	=	1	x	4x208	2x384	=	1	x	832+768	=
2		4		384		2		4x384	4x384		2		1536

1	x	1600	=	1600	=	$\frac{25}{48}$
2		1536		3072

q3 = $\frac{25}{48}$

Hence, $\frac{7}{12}$ , $\frac{13}{24}$ , $\frac{25}{48}$ is a rational number between $\frac{2}{4}$ and $\frac{4}{6}$

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

$\frac{3}{5}$ and $\frac{5}{7}$

q1 = Answer: $\frac{23}{35}$

q2 = Answer: $\frac{22}{35}$

q3 = Answer: $\frac{43}{70}$

SOLUTION 1 :

$\frac{3}{5}$ and $\frac{5}{7}$

a = $\frac{3}{5}$ , b = $\frac{5}{7}$

Let q1 be the rational number between $\frac{3}{5}$ and $\frac{5}{7}$

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

1	x	3x7	+	5x5
2	x	5x7	+	7x5

[LCM of 5 and 7 is 35]

1	x	21	+	25	=	1	x	46	=	46	=	$\frac{23}{35}$
2		35		35		2		35		70

q1 = $\frac{23}{35}$

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

1	x	3	+	46	=	1	x	5x46	+	3x70	=	1	x	230+210	=	1	x	440
2		5		70		2		5x70		5x70		2		350		2		350

1	x	440	=	$\frac{22}{35}$
1		700

q2 = $\frac{22}{35}$

q3 = (a+q2)

1	x	3	+	440	=	1	x	5x440	3x700	=	1	x	2200+2100	=
2		5		700		2		5x700	5x700		2		3500

1	x	4300	=	4300	=	$\frac{43}{70}$
2		3500		7000

q3 = $\frac{43}{70}$

Hence, $\frac{23}{35}$ , $\frac{22}{35}$ , $\frac{43}{70}$ is a rational number between $\frac{3}{5}$ and $\frac{5}{7}$

10)

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

$\frac{2}{6}$ and $\frac{3}{8}$

q1 = Answer: $\frac{17}{48}$

q2 = Answer: $\frac{11}{32}$

q3 = Answer: $\frac{65}{192}$

SOLUTION 1 :

$\frac{2}{6}$ and $\frac{3}{8}$

a = $\frac{2}{6}$ , b = $\frac{3}{8}$

Let q1 be the rational number between $\frac{2}{6}$ and $\frac{3}{8}$

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

1	x	2x8	+	3x6
2	x	6x8	+	8x6

[LCM of 6 and 8 is 48]

1	x	16	+	18	=	1	x	34	=	34	=	$\frac{17}{48}$
2		48		48		2		48		96

q1 = $\frac{17}{48}$

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

1	x	2	+	34	=	1	x	6x34	+	2x96	=	1	x	204+192	=	1	x	396
2		6		96		2		6x96		6x96		2		576		2		576

1	x	396	=	$\frac{11}{32}$
1		1152

q2 = $\frac{11}{32}$

q3 = (a+q2)

1	x	2	+	396	=	1	x	6x396	2x1152	=	1	x	2376+2304	=
2		6		1152		2		6x1152	6x1152		2		6912

1	x	4680	=	4680	=	$\frac{65}{192}$
2		6912		13824

q3 = $\frac{65}{192}$

Hence, $\frac{17}{48}$ , $\frac{11}{32}$ , $\frac{65}{192}$ is a rational number between $\frac{2}{6}$ and $\frac{3}{8}$