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 / )

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

q1 =

q2 =

q3 =

Answer:_______________

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

$\frac{3}{7}$ 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 $\frac{5}{6}$

q1 =

q2 =

q3 =

Answer:_______________

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

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

q1 =

q2 =

q3 =

Answer:_______________

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

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

q1 =

q2 =

q3 =

Answer:_______________

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

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

q1 =

q2 =

q3 =

Answer:_______________

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

$\frac{2}{4}$ and $\frac{3}{9}$

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:_______________

10)

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 / )

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

q1 = Answer: $\frac{25}{72}$

q2 = Answer: $\frac{43}{144}$

q3 = Answer: $\frac{79}{288}$

SOLUTION 1 :

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

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

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

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

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

[LCM of 4 and 9 is 36]

1	x	9	+	16	=	1	x	25	=	25	=	$\frac{25}{72}$
2		36		36		2		36		72

q1 = $\frac{25}{72}$

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

1	x	1	+	25	=	1	x	4x25	+	1x72	=	1	x	100+72	=	1	x	172
2		4		72		2		4x72		4x72		2		288		2		288

1	x	172	=	$\frac{43}{144}$
1		576

q2 = $\frac{43}{144}$

q3 = (a+q2)

1	x	1	+	172	=	1	x	4x172	1x576	=	1	x	688+576	=
2		4		576		2		4x576	4x576		2		2304

1	x	1264	=	1264	=	$\frac{79}{288}$
2		2304		4608

q3 = $\frac{79}{288}$

Hence, $\frac{25}{72}$ , $\frac{43}{144}$ , $\frac{79}{288}$ is a rational number between $\frac{1}{4}$ and $\frac{4}{9}$

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

$\frac{3}{7}$ and $\frac{4}{8}$

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

q2 = Answer: $\frac{25}{56}$

q3 = Answer: $\frac{7}{16}$

SOLUTION 1 :

$\frac{3}{7}$ and $\frac{4}{8}$

a = $\frac{3}{7}$ , b = $\frac{4}{8}$

Let q1 be the rational number between $\frac{3}{7}$ and $\frac{4}{8}$

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

1	x	3x8	+	4x7
2	x	7x8	+	8x7

[LCM of 7 and 8 is 56]

1	x	24	+	28	=	1	x	52	=	52	=	$\frac{13}{28}$
2		56		56		2		56		112

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

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

1	x	3	+	52	=	1	x	7x52	+	3x112	=	1	x	364+336	=	1	x	700
2		7		112		2		7x112		7x112		2		784		2		784

1	x	700	=	$\frac{25}{56}$
1		1568

q2 = $\frac{25}{56}$

q3 = (a+q2)

1	x	3	+	700	=	1	x	7x700	3x1568	=	1	x	4900+4704	=
2		7		1568		2		7x1568	7x1568		2		10976

1	x	9604	=	9604	=	$\frac{7}{16}$
2		10976		21952

q3 = $\frac{7}{16}$

Hence, $\frac{13}{28}$ , $\frac{25}{56}$ , $\frac{7}{16}$ is a rational number between $\frac{3}{7}$ and $\frac{4}{8}$

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

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

q1 = Answer: $\frac{37}{60}$

q2 = Answer: $\frac{61}{120}$

q3 = Answer: $\frac{109}{240}$

SOLUTION 1 :

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

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

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

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

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

[LCM of 5 and 6 is 30]

1	x	12	+	25	=	1	x	37	=	37	=	$\frac{37}{60}$
2		30		30		2		30		60

q1 = $\frac{37}{60}$

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

1	x	2	+	37	=	1	x	5x37	+	2x60	=	1	x	185+120	=	1	x	305
2		5		60		2		5x60		5x60		2		300		2		300

1	x	305	=	$\frac{61}{120}$
1		600

q2 = $\frac{61}{120}$

q3 = (a+q2)

1	x	2	+	305	=	1	x	5x305	2x600	=	1	x	1525+1200	=
2		5		600		2		5x600	5x600		2		3000

1	x	2725	=	2725	=	$\frac{109}{240}$
2		3000		6000

q3 = $\frac{109}{240}$

Hence, $\frac{37}{60}$ , $\frac{61}{120}$ , $\frac{109}{240}$ is a rational number between $\frac{2}{5}$ and $\frac{5}{6}$

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

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

q1 = Answer: $\frac{23}{56}$

q2 = Answer: $\frac{37}{112}$

q3 = Answer: $\frac{65}{224}$

SOLUTION 1 :

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

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

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

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

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

[LCM of 4 and 7 is 28]

1	x	7	+	16	=	1	x	23	=	23	=	$\frac{23}{56}$
2		28		28		2		28		56

q1 = $\frac{23}{56}$

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

1	x	1	+	23	=	1	x	4x23	+	1x56	=	1	x	92+56	=	1	x	148
2		4		56		2		4x56		4x56		2		224		2		224

1	x	148	=	$\frac{37}{112}$
1		448

q2 = $\frac{37}{112}$

q3 = (a+q2)

1	x	1	+	148	=	1	x	4x148	1x448	=	1	x	592+448	=
2		4		448		2		4x448	4x448		2		1792

1	x	1040	=	1040	=	$\frac{65}{224}$
2		1792		3584

q3 = $\frac{65}{224}$

Hence, $\frac{23}{56}$ , $\frac{37}{112}$ , $\frac{65}{224}$ is a rational number between $\frac{1}{4}$ and $\frac{4}{7}$

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

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

q1 = Answer: $\frac{3}{7}$

q2 = Answer: $\frac{3}{7}$

q3 = Answer: $\frac{3}{7}$

SOLUTION 1 :

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

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

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

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

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

[LCM of 7 and 7 is 49]

1	x	21	+	21	=	1	x	42	=	42	=	$\frac{3}{7}$
2		49		49		2		49		98

q1 = $\frac{3}{7}$

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

1	x	3	+	42	=	1	x	7x42	+	3x98	=	1	x	294+294	=	1	x	588
2		7		98		2		7x98		7x98		2		686		2		686

1	x	588	=	$\frac{3}{7}$
1		1372

q2 = $\frac{3}{7}$

q3 = (a+q2)

1	x	3	+	588	=	1	x	7x588	3x1372	=	1	x	4116+4116	=
2		7		1372		2		7x1372	7x1372		2		9604

1	x	8232	=	8232	=	$\frac{3}{7}$
2		9604		19208

q3 = $\frac{3}{7}$

Hence, $\frac{3}{7}$ , $\frac{3}{7}$ , $\frac{3}{7}$ is a rational number between $\frac{3}{7}$ and $\frac{3}{7}$

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

$\frac{2}{6}$ and $\frac{5}{9}$

q1 = Answer: $\frac{4}{9}$

q2 = Answer: $\frac{7}{18}$

q3 = Answer: $\frac{13}{36}$

SOLUTION 1 :

$\frac{2}{6}$ and $\frac{5}{9}$

a = $\frac{2}{6}$ , b = $\frac{5}{9}$

Let q1 be the rational number between $\frac{2}{6}$ and $\frac{5}{9}$

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

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

[LCM of 6 and 9 is 54]

1	x	18	+	30	=	1	x	48	=	48	=	$\frac{4}{9}$
2		54		54		2		54		108

q1 = $\frac{4}{9}$

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

1	x	2	+	48	=	1	x	6x48	+	2x108	=	1	x	288+216	=	1	x	504
2		6		108		2		6x108		6x108		2		648		2		648

1	x	504	=	$\frac{7}{18}$
1		1296

q2 = $\frac{7}{18}$

q3 = (a+q2)

1	x	2	+	504	=	1	x	6x504	2x1296	=	1	x	3024+2592	=
2		6		1296		2		6x1296	6x1296		2		7776

1	x	5616	=	5616	=	$\frac{13}{36}$
2		7776		15552

q3 = $\frac{13}{36}$

Hence, $\frac{4}{9}$ , $\frac{7}{18}$ , $\frac{13}{36}$ is a rational number between $\frac{2}{6}$ and $\frac{5}{9}$

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

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

q1 = Answer: $\frac{7}{18}$

q2 = Answer: $\frac{13}{36}$

q3 = Answer: $\frac{25}{72}$

SOLUTION 1 :

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

a = $\frac{2}{6}$ , b = $\frac{4}{9}$

Let q1 be the rational number between $\frac{2}{6}$ and $\frac{4}{9}$

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

1	x	2x9	+	4x6
2	x	6x9	+	9x6

[LCM of 6 and 9 is 54]

1	x	18	+	24	=	1	x	42	=	42	=	$\frac{7}{18}$
2		54		54		2		54		108

q1 = $\frac{7}{18}$

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

1	x	2	+	42	=	1	x	6x42	+	2x108	=	1	x	252+216	=	1	x	468
2		6		108		2		6x108		6x108		2		648		2		648

1	x	468	=	$\frac{13}{36}$
1		1296

q2 = $\frac{13}{36}$

q3 = (a+q2)

1	x	2	+	468	=	1	x	6x468	2x1296	=	1	x	2808+2592	=
2		6		1296		2		6x1296	6x1296		2		7776

1	x	5400	=	5400	=	$\frac{25}{72}$
2		7776		15552

q3 = $\frac{25}{72}$

Hence, $\frac{7}{18}$ , $\frac{13}{36}$ , $\frac{25}{72}$ is a rational number between $\frac{2}{6}$ and $\frac{4}{9}$

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

$\frac{2}{4}$ and $\frac{3}{9}$

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

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

q3 = Answer: $\frac{23}{48}$

SOLUTION 1 :

$\frac{2}{4}$ and $\frac{3}{9}$

a = $\frac{2}{4}$ , b = $\frac{3}{9}$

Let q1 be the rational number between $\frac{2}{4}$ and $\frac{3}{9}$

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

1	x	2x9	+	3x4
2	x	4x9	+	9x4

[LCM of 4 and 9 is 36]

1	x	18	+	12	=	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	4x30	+	2x72	=	1	x	120+144	=	1	x	264
2		4		72		2		4x72		4x72		2		288		2		288

1	x	264	=	$\frac{11}{24}$
1		576

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

q3 = (a+q2)

1	x	2	+	264	=	1	x	4x264	2x576	=	1	x	1056+1152	=
2		4		576		2		4x576	4x576		2		2304

1	x	2208	=	2208	=	$\frac{23}{48}$
2		2304		4608

q3 = $\frac{23}{48}$

Hence, $\frac{5}{12}$ , $\frac{11}{24}$ , $\frac{23}{48}$ is a rational number between $\frac{2}{4}$ and $\frac{3}{9}$

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 $\frac{3}{8}$

10)

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 $\frac{5}{8}$