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 / )

$\frac{1}{7}$ and $\frac{5}{9}$

q1 =

q2 =

q3 =

Answer:_______________

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

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

q1 =

q2 =

q3 =

Answer:_______________

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

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

q1 =

q2 =

q3 =

Answer:_______________

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

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

q1 =

q2 =

q3 =

Answer:_______________

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

$\frac{1}{4}$ and $\frac{5}{6}$

q1 =

q2 =

q3 =

Answer:_______________

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

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

q1 =

q2 =

q3 =

Answer:_______________

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

$\frac{1}{7}$ 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 $\frac{5}{8}$

q1 =

q2 =

q3 =

Answer:_______________

10)

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

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

q1 =

q2 =

q3 =

Answer:_______________

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

$\frac{1}{7}$ and $\frac{5}{9}$

q1 = Answer: $\frac{22}{63}$

q2 = Answer: $\frac{31}{126}$

q3 = Answer: $\frac{7}{36}$

SOLUTION 1 :

$\frac{1}{7}$ and $\frac{5}{9}$

a = $\frac{1}{7}$ , b = $\frac{5}{9}$

Let q1 be the rational number between $\frac{1}{7}$ and $\frac{5}{9}$

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

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

[LCM of 7 and 9 is 63]

1	x	9	+	35	=	1	x	44	=	44	=	$\frac{22}{63}$
2		63		63		2		63		126

q1 = $\frac{22}{63}$

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

1	x	1	+	44	=	1	x	7x44	+	1x126	=	1	x	308+126	=	1	x	434
2		7		126		2		7x126		7x126		2		882		2		882

1	x	434	=	$\frac{31}{126}$
1		1764

q2 = $\frac{31}{126}$

q3 = (a+q2)

1	x	1	+	434	=	1	x	7x434	1x1764	=	1	x	3038+1764	=
2		7		1764		2		7x1764	7x1764		2		12348

1	x	4802	=	4802	=	$\frac{7}{36}$
2		12348		24696

q3 = $\frac{7}{36}$

Hence, $\frac{22}{63}$ , $\frac{31}{126}$ , $\frac{7}{36}$ is a rational number between $\frac{1}{7}$ and $\frac{5}{9}$

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

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

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

q2 = Answer: $\frac{11}{24}$

q3 = Answer: $\frac{19}{48}$

SOLUTION 1 :

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

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

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

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

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

[LCM of 6 and 6 is 36]

1	x	12	+	30	=	1	x	42	=	42	=	$\frac{7}{12}$
2		36		36		2		36		72

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

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

1	x	2	+	42	=	1	x	6x42	+	2x72	=	1	x	252+144	=	1	x	396
2		6		72		2		6x72		6x72		2		432		2		432

1	x	396	=	$\frac{11}{24}$
1		864

q2 = $\frac{11}{24}$

q3 = (a+q2)

1	x	2	+	396	=	1	x	6x396	2x864	=	1	x	2376+1728	=
2		6		864		2		6x864	6x864		2		5184

1	x	4104	=	4104	=	$\frac{19}{48}$
2		5184		10368

q3 = $\frac{19}{48}$

Hence, $\frac{7}{12}$ , $\frac{11}{24}$ , $\frac{19}{48}$ is a rational number between $\frac{2}{6}$ and $\frac{5}{6}$

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

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

q1 = Answer: $\frac{11}{20}$

q2 = Answer: $\frac{23}{40}$

q3 = Answer: $\frac{47}{80}$

SOLUTION 1 :

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

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

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

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

1	x	3x8	+	4x5
2	x	5x8	+	8x5

[LCM of 5 and 8 is 40]

1	x	24	+	20	=	1	x	44	=	44	=	$\frac{11}{20}$
2		40		40		2		40		80

q1 = $\frac{11}{20}$

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

1	x	3	+	44	=	1	x	5x44	+	3x80	=	1	x	220+240	=	1	x	460
2		5		80		2		5x80		5x80		2		400		2		400

1	x	460	=	$\frac{23}{40}$
1		800

q2 = $\frac{23}{40}$

q3 = (a+q2)

1	x	3	+	460	=	1	x	5x460	3x800	=	1	x	2300+2400	=
2		5		800		2		5x800	5x800		2		4000

1	x	4700	=	4700	=	$\frac{47}{80}$
2		4000		8000

q3 = $\frac{47}{80}$

Hence, $\frac{11}{20}$ , $\frac{23}{40}$ , $\frac{47}{80}$ is a rational number between $\frac{3}{5}$ and $\frac{4}{8}$

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

$\frac{3}{4}$ and $\frac{5}{6}$

q1 = Answer: $\frac{19}{24}$

q2 = Answer: $\frac{37}{48}$

q3 = Answer: $\frac{73}{96}$

SOLUTION 1 :

$\frac{3}{4}$ and $\frac{5}{6}$

a = $\frac{3}{4}$ , b = $\frac{5}{6}$

Let q1 be the rational number between $\frac{3}{4}$ and $\frac{5}{6}$

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

1	x	3x6	+	5x4
2	x	4x6	+	6x4

[LCM of 4 and 6 is 24]

1	x	18	+	20	=	1	x	38	=	38	=	$\frac{19}{24}$
2		24		24		2		24		48

q1 = $\frac{19}{24}$

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

1	x	3	+	38	=	1	x	4x38	+	3x48	=	1	x	152+144	=	1	x	296
2		4		48		2		4x48		4x48		2		192		2		192

1	x	296	=	$\frac{37}{48}$
1		384

q2 = $\frac{37}{48}$

q3 = (a+q2)

1	x	3	+	296	=	1	x	4x296	3x384	=	1	x	1184+1152	=
2		4		384		2		4x384	4x384		2		1536

1	x	2336	=	2336	=	$\frac{73}{96}$
2		1536		3072

q3 = $\frac{73}{96}$

Hence, $\frac{19}{24}$ , $\frac{37}{48}$ , $\frac{73}{96}$ is a rational number between $\frac{3}{4}$ and $\frac{5}{6}$

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

$\frac{2}{5}$ and $\frac{3}{6}$

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

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

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

SOLUTION 1 :

$\frac{2}{5}$ and $\frac{3}{6}$

a = $\frac{2}{5}$ , b = $\frac{3}{6}$

Let q1 be the rational number between $\frac{2}{5}$ and $\frac{3}{6}$

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

1	x	2x6	+	3x5
2	x	5x6	+	6x5

[LCM of 5 and 6 is 30]

1	x	12	+	15	=	1	x	27	=	27	=	$\frac{9}{20}$
2		30		30		2		30		60

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

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

1	x	2	+	27	=	1	x	5x27	+	2x60	=	1	x	135+120	=	1	x	255
2		5		60		2		5x60		5x60		2		300		2		300

1	x	255	=	$\frac{17}{40}$
1		600

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

q3 = (a+q2)

1	x	2	+	255	=	1	x	5x255	2x600	=	1	x	1275+1200	=
2		5		600		2		5x600	5x600		2		3000

1	x	2475	=	2475	=	$\frac{33}{80}$
2		3000		6000

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

Hence, $\frac{9}{20}$ , $\frac{17}{40}$ , $\frac{33}{80}$ is a rational number between $\frac{2}{5}$ and $\frac{3}{6}$

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

$\frac{1}{4}$ and $\frac{5}{6}$

q1 = Answer: $\frac{13}{24}$

q2 = Answer: $\frac{19}{48}$

q3 = Answer: $\frac{31}{96}$

SOLUTION 1 :

$\frac{1}{4}$ and $\frac{5}{6}$

a = $\frac{1}{4}$ , b = $\frac{5}{6}$

Let q1 be the rational number between $\frac{1}{4}$ and $\frac{5}{6}$

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

1	x	1x6	+	5x4
2	x	4x6	+	6x4

[LCM of 4 and 6 is 24]

1	x	6	+	20	=	1	x	26	=	26	=	$\frac{13}{24}$
2		24		24		2		24		48

q1 = $\frac{13}{24}$

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

1	x	1	+	26	=	1	x	4x26	+	1x48	=	1	x	104+48	=	1	x	152
2		4		48		2		4x48		4x48		2		192		2		192

1	x	152	=	$\frac{19}{48}$
1		384

q2 = $\frac{19}{48}$

q3 = (a+q2)

1	x	1	+	152	=	1	x	4x152	1x384	=	1	x	608+384	=
2		4		384		2		4x384	4x384		2		1536

1	x	992	=	992	=	$\frac{31}{96}$
2		1536		3072

q3 = $\frac{31}{96}$

Hence, $\frac{13}{24}$ , $\frac{19}{48}$ , $\frac{31}{96}$ is a rational number between $\frac{1}{4}$ and $\frac{5}{6}$

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

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

q1 = Answer: $\frac{5}{12}$

q2 = Answer: $\frac{3}{8}$

q3 = Answer: $\frac{17}{48}$

SOLUTION 1 :

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

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

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

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

1	x	2x6	+	3x6
2	x	6x6	+	6x6

[LCM of 6 and 6 is 36]

1	x	12	+	18	=	1	x	30	=	30	=	$\frac{5}{12}$
2		36		36		2		36		72

q1 = $\frac{5}{12}$

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

1	x	2	+	30	=	1	x	6x30	+	2x72	=	1	x	180+144	=	1	x	324
2		6		72		2		6x72		6x72		2		432		2		432

1	x	324	=	$\frac{3}{8}$
1		864

q2 = $\frac{3}{8}$

q3 = (a+q2)

1	x	2	+	324	=	1	x	6x324	2x864	=	1	x	1944+1728	=
2		6		864		2		6x864	6x864		2		5184

1	x	3672	=	3672	=	$\frac{17}{48}$
2		5184		10368

q3 = $\frac{17}{48}$

Hence, $\frac{5}{12}$ , $\frac{3}{8}$ , $\frac{17}{48}$ is a rational number between $\frac{2}{6}$ and $\frac{3}{6}$

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

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

q1 = Answer: $\frac{2}{7}$

q2 = Answer: $\frac{3}{14}$

q3 = Answer: $\frac{5}{28}$

SOLUTION 1 :

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

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

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

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

1	x	1x7	+	3x7
2	x	7x7	+	7x7

[LCM of 7 and 7 is 49]

1	x	7	+	21	=	1	x	28	=	28	=	$\frac{2}{7}$
2		49		49		2		49		98

q1 = $\frac{2}{7}$

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

1	x	1	+	28	=	1	x	7x28	+	1x98	=	1	x	196+98	=	1	x	294
2		7		98		2		7x98		7x98		2		686		2		686

1	x	294	=	$\frac{3}{14}$
1		1372

q2 = $\frac{3}{14}$

q3 = (a+q2)

1	x	1	+	294	=	1	x	7x294	1x1372	=	1	x	2058+1372	=
2		7		1372		2		7x1372	7x1372		2		9604

1	x	3430	=	3430	=	$\frac{5}{28}$
2		9604		19208

q3 = $\frac{5}{28}$

Hence, $\frac{2}{7}$ , $\frac{3}{14}$ , $\frac{5}{28}$ is a rational number between $\frac{1}{7}$ and $\frac{3}{7}$

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

$\frac{3}{6}$ and $\frac{5}{8}$

q1 = Answer: $\frac{9}{16}$

q2 = Answer: $\frac{17}{32}$

q3 = Answer: 3 $\frac{3}{6}$ 4

SOLUTION 1 :

$\frac{3}{6}$ and $\frac{5}{8}$

a = $\frac{3}{6}$ , b = $\frac{5}{8}$

Let q1 be the rational number between $\frac{3}{6}$ and $\frac{5}{8}$

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

1	x	3x8	+	5x6
2	x	6x8	+	8x6

[LCM of 6 and 8 is 48]

1	x	24	+	30	=	1	x	54	=	54	=	$\frac{9}{16}$
2		48		48		2		48		96

q1 = $\frac{9}{16}$

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

1	x	3	+	54	=	1	x	6x54	+	3x96	=	1	x	324+288	=	1	x	612
2		6		96		2		6x96		6x96		2		576		2		576

1	x	612	=	$\frac{17}{32}$
1		1152

q2 = $\frac{17}{32}$

q3 = (a+q2)

1	x	3	+	612	=	1	x	6x612	3x1152	=	1	x	3672+3456	=
2		6		1152		2		6x1152	6x1152		2		6912

1	x	7128	=	7128	=	3 $\frac{3}{6}$ 4
2		6912		13824

q3 = 3 $\frac{3}{6}$ 4

Hence, $\frac{9}{16}$ , $\frac{17}{32}$ ,3 $\frac{3}{6}$ 4 is a rational number between $\frac{3}{6}$ and $\frac{5}{8}$

10)

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

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

q1 = Answer: $\frac{13}{28}$

q2 = Answer: $\frac{27}{56}$

q3 = Answer: $\frac{55}{112}$

SOLUTION 1 :

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

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

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

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

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

[LCM of 6 and 7 is 42]

1	x	21	+	18	=	1	x	39	=	39	=	$\frac{13}{28}$
2		42		42		2		42		84

q1 = $\frac{13}{28}$

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

1	x	3	+	39	=	1	x	6x39	+	3x84	=	1	x	234+252	=	1	x	486
2		6		84		2		6x84		6x84		2		504		2		504

1	x	486	=	$\frac{27}{56}$
1		1008

q2 = $\frac{27}{56}$

q3 = (a+q2)

1	x	3	+	486	=	1	x	6x486	3x1008	=	1	x	2916+3024	=
2		6		1008		2		6x1008	6x1008		2		6048

1	x	5940	=	5940	=	$\frac{55}{112}$
2		6048		12096

q3 = $\frac{55}{112}$

Hence, $\frac{13}{28}$ , $\frac{27}{56}$ , $\frac{55}{112}$ is a rational number between $\frac{3}{6}$ and $\frac{3}{7}$