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 / )

$\frac{3}{7}$ and $\frac{4}{6}$

q1 =

q2 =

q3 =

Answer:_______________

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

$\frac{2}{6}$ 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 $\frac{4}{9}$

q1 =

q2 =

q3 =

Answer:_______________

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

$\frac{1}{5}$ and $\frac{4}{7}$

q1 =

q2 =

q3 =

Answer:_______________

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

$\frac{1}{4}$ and $\frac{5}{9}$

q1 =

q2 =

q3 =

Answer:_______________

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

$\frac{1}{6}$ and $\frac{3}{9}$

q1 =

q2 =

q3 =

Answer:_______________

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

$\frac{1}{4}$ and $\frac{3}{7}$

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:_______________

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

$\frac{1}{4}$ and $\frac{4}{6}$

q1 =

q2 =

q3 =

Answer:_______________

10)

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

$\frac{2}{6}$ and $\frac{5}{8}$

q1 =

q2 =

q3 =

Answer:_______________

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

$\frac{3}{7}$ and $\frac{4}{6}$

q1 = Answer: $\frac{23}{42}$

q2 = Answer: $\frac{41}{84}$

q3 = Answer: $\frac{11}{24}$

SOLUTION 1 :

$\frac{3}{7}$ and $\frac{4}{6}$

a = $\frac{3}{7}$ , b = $\frac{4}{6}$

Let q1 be the rational number between $\frac{3}{7}$ and $\frac{4}{6}$

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

1	x	3x6	+	4x7
2	x	7x6	+	6x7

[LCM of 7 and 6 is 42]

1	x	18	+	28	=	1	x	46	=	46	=	$\frac{23}{42}$
2		42		42		2		42		84

q1 = $\frac{23}{42}$

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

1	x	3	+	46	=	1	x	7x46	+	3x84	=	1	x	322+252	=	1	x	574
2		7		84		2		7x84		7x84		2		588		2		588

1	x	574	=	$\frac{41}{84}$
1		1176

q2 = $\frac{41}{84}$

q3 = (a+q2)

1	x	3	+	574	=	1	x	7x574	3x1176	=	1	x	4018+3528	=
2		7		1176		2		7x1176	7x1176		2		8232

1	x	7546	=	7546	=	$\frac{11}{24}$
2		8232		16464

q3 = $\frac{11}{24}$

Hence, $\frac{23}{42}$ , $\frac{41}{84}$ , $\frac{11}{24}$ is a rational number between $\frac{3}{7}$ and $\frac{4}{6}$

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

$\frac{2}{6}$ and $\frac{4}{7}$

q1 = Answer: $\frac{19}{42}$

q2 = Answer: $\frac{11}{28}$

q3 = Answer: $\frac{61}{168}$

SOLUTION 1 :

$\frac{2}{6}$ and $\frac{4}{7}$

a = $\frac{2}{6}$ , b = $\frac{4}{7}$

Let q1 be the rational number between $\frac{2}{6}$ and $\frac{4}{7}$

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

1	x	2x7	+	4x6
2	x	6x7	+	7x6

[LCM of 6 and 7 is 42]

1	x	14	+	24	=	1	x	38	=	38	=	$\frac{19}{42}$
2		42		42		2		42		84

q1 = $\frac{19}{42}$

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

1	x	2	+	38	=	1	x	6x38	+	2x84	=	1	x	228+168	=	1	x	396
2		6		84		2		6x84		6x84		2		504		2		504

1	x	396	=	$\frac{11}{28}$
1		1008

q2 = $\frac{11}{28}$

q3 = (a+q2)

1	x	2	+	396	=	1	x	6x396	2x1008	=	1	x	2376+2016	=
2		6		1008		2		6x1008	6x1008		2		6048

1	x	4392	=	4392	=	$\frac{61}{168}$
2		6048		12096

q3 = $\frac{61}{168}$

Hence, $\frac{19}{42}$ , $\frac{11}{28}$ , $\frac{61}{168}$ is a rational number between $\frac{2}{6}$ and $\frac{4}{7}$

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 / )

$\frac{1}{5}$ and $\frac{4}{7}$

q1 = Answer: $\frac{27}{70}$

q2 = Answer: $\frac{41}{140}$

q3 = Answer: $\frac{69}{280}$

SOLUTION 1 :

$\frac{1}{5}$ and $\frac{4}{7}$

a = $\frac{1}{5}$ , b = $\frac{4}{7}$

Let q1 be the rational number between $\frac{1}{5}$ and $\frac{4}{7}$

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

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

[LCM of 5 and 7 is 35]

1	x	7	+	20	=	1	x	27	=	27	=	$\frac{27}{70}$
2		35		35		2		35		70

q1 = $\frac{27}{70}$

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

1	x	1	+	27	=	1	x	5x27	+	1x70	=	1	x	135+70	=	1	x	205
2		5		70		2		5x70		5x70		2		350		2		350

1	x	205	=	$\frac{41}{140}$
1		700

q2 = $\frac{41}{140}$

q3 = (a+q2)

1	x	1	+	205	=	1	x	5x205	1x700	=	1	x	1025+700	=
2		5		700		2		5x700	5x700		2		3500

1	x	1725	=	1725	=	$\frac{69}{280}$
2		3500		7000

q3 = $\frac{69}{280}$

Hence, $\frac{27}{70}$ , $\frac{41}{140}$ , $\frac{69}{280}$ is a rational number between $\frac{1}{5}$ and $\frac{4}{7}$

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

$\frac{1}{4}$ and $\frac{5}{9}$

q1 = Answer: $\frac{29}{72}$

q2 = Answer: $\frac{47}{144}$

q3 = Answer: $\frac{83}{288}$

SOLUTION 1 :

$\frac{1}{4}$ and $\frac{5}{9}$

a = $\frac{1}{4}$ , b = $\frac{5}{9}$

Let q1 be the rational number between $\frac{1}{4}$ and $\frac{5}{9}$

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

1	x	1x9	+	5x4
2	x	4x9	+	9x4

[LCM of 4 and 9 is 36]

1	x	9	+	20	=	1	x	29	=	29	=	$\frac{29}{72}$
2		36		36		2		36		72

q1 = $\frac{29}{72}$

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

1	x	1	+	29	=	1	x	4x29	+	1x72	=	1	x	116+72	=	1	x	188
2		4		72		2		4x72		4x72		2		288		2		288

1	x	188	=	$\frac{47}{144}$
1		576

q2 = $\frac{47}{144}$

q3 = (a+q2)

1	x	1	+	188	=	1	x	4x188	1x576	=	1	x	752+576	=
2		4		576		2		4x576	4x576		2		2304

1	x	1328	=	1328	=	$\frac{83}{288}$
2		2304		4608

q3 = $\frac{83}{288}$

Hence, $\frac{29}{72}$ , $\frac{47}{144}$ , $\frac{83}{288}$ is a rational number between $\frac{1}{4}$ and $\frac{5}{9}$

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

$\frac{1}{6}$ and $\frac{3}{9}$

q1 = Answer: $\frac{1}{4}$

q2 = Answer: $\frac{5}{24}$

q3 = Answer: $\frac{3}{16}$

SOLUTION 1 :

$\frac{1}{6}$ and $\frac{3}{9}$

a = $\frac{1}{6}$ , b = $\frac{3}{9}$

Let q1 be the rational number between $\frac{1}{6}$ and $\frac{3}{9}$

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

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

[LCM of 6 and 9 is 54]

1	x	9	+	18	=	1	x	27	=	27	=	$\frac{1}{4}$
2		54		54		2		54		108

q1 = $\frac{1}{4}$

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

1	x	1	+	27	=	1	x	6x27	+	1x108	=	1	x	162+108	=	1	x	270
2		6		108		2		6x108		6x108		2		648		2		648

1	x	270	=	$\frac{5}{24}$
1		1296

q2 = $\frac{5}{24}$

q3 = (a+q2)

1	x	1	+	270	=	1	x	6x270	1x1296	=	1	x	1620+1296	=
2		6		1296		2		6x1296	6x1296		2		7776

1	x	2916	=	2916	=	$\frac{3}{16}$
2		7776		15552

q3 = $\frac{3}{16}$

Hence, $\frac{1}{4}$ , $\frac{5}{24}$ , $\frac{3}{16}$ is a rational number between $\frac{1}{6}$ and $\frac{3}{9}$

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

$\frac{1}{4}$ and $\frac{3}{7}$

q1 = Answer: $\frac{19}{56}$

q2 = Answer: $\frac{33}{112}$

q3 = Answer: $\frac{61}{224}$

SOLUTION 1 :

$\frac{1}{4}$ and $\frac{3}{7}$

a = $\frac{1}{4}$ , b = $\frac{3}{7}$

Let q1 be the rational number between $\frac{1}{4}$ and $\frac{3}{7}$

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

1	x	1x7	+	3x4
2	x	4x7	+	7x4

[LCM of 4 and 7 is 28]

1	x	7	+	12	=	1	x	19	=	19	=	$\frac{19}{56}$
2		28		28		2		28		56

q1 = $\frac{19}{56}$

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

1	x	1	+	19	=	1	x	4x19	+	1x56	=	1	x	76+56	=	1	x	132
2		4		56		2		4x56		4x56		2		224		2		224

1	x	132	=	$\frac{33}{112}$
1		448

q2 = $\frac{33}{112}$

q3 = (a+q2)

1	x	1	+	132	=	1	x	4x132	1x448	=	1	x	528+448	=
2		4		448		2		4x448	4x448		2		1792

1	x	976	=	976	=	$\frac{61}{224}$
2		1792		3584

q3 = $\frac{61}{224}$

Hence, $\frac{19}{56}$ , $\frac{33}{112}$ , $\frac{61}{224}$ is a rational number between $\frac{1}{4}$ and $\frac{3}{7}$

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 $\frac{5}{8}$

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

$\frac{1}{4}$ and $\frac{4}{6}$

q1 = Answer: $\frac{11}{24}$

q2 = Answer: $\frac{17}{48}$

q3 = Answer: $\frac{29}{96}$

SOLUTION 1 :

$\frac{1}{4}$ and $\frac{4}{6}$

a = $\frac{1}{4}$ , b = $\frac{4}{6}$

Let q1 be the rational number between $\frac{1}{4}$ and $\frac{4}{6}$

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

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

[LCM of 4 and 6 is 24]

1	x	6	+	16	=	1	x	22	=	22	=	$\frac{11}{24}$
2		24		24		2		24		48

q1 = $\frac{11}{24}$

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

1	x	1	+	22	=	1	x	4x22	+	1x48	=	1	x	88+48	=	1	x	136
2		4		48		2		4x48		4x48		2		192		2		192

1	x	136	=	$\frac{17}{48}$
1		384

q2 = $\frac{17}{48}$

q3 = (a+q2)

1	x	1	+	136	=	1	x	4x136	1x384	=	1	x	544+384	=
2		4		384		2		4x384	4x384		2		1536

1	x	928	=	928	=	$\frac{29}{96}$
2		1536		3072

q3 = $\frac{29}{96}$

Hence, $\frac{11}{24}$ , $\frac{17}{48}$ , $\frac{29}{96}$ is a rational number between $\frac{1}{4}$ and $\frac{4}{6}$

10)

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

$\frac{2}{6}$ and $\frac{5}{8}$

q1 = Answer: $\frac{23}{48}$

q2 = Answer: $\frac{13}{32}$

q3 = Answer: $\frac{71}{192}$

SOLUTION 1 :

$\frac{2}{6}$ and $\frac{5}{8}$

a = $\frac{2}{6}$ , b = $\frac{5}{8}$

Let q1 be the rational number between $\frac{2}{6}$ and $\frac{5}{8}$

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

1	x	2x8	+	5x6
2	x	6x8	+	8x6

[LCM of 6 and 8 is 48]

1	x	16	+	30	=	1	x	46	=	46	=	$\frac{23}{48}$
2		48		48		2		48		96

q1 = $\frac{23}{48}$

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

1	x	2	+	46	=	1	x	6x46	+	2x96	=	1	x	276+192	=	1	x	468
2		6		96		2		6x96		6x96		2		576		2		576

1	x	468	=	$\frac{13}{32}$
1		1152

q2 = $\frac{13}{32}$

q3 = (a+q2)

1	x	2	+	468	=	1	x	6x468	2x1152	=	1	x	2808+2304	=
2		6		1152		2		6x1152	6x1152		2		6912

1	x	5112	=	5112	=	$\frac{71}{192}$
2		6912		13824

q3 = $\frac{71}{192}$

Hence, $\frac{23}{48}$ , $\frac{13}{32}$ , $\frac{71}{192}$ is a rational number between $\frac{2}{6}$ and $\frac{5}{8}$