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 $\frac{3}{6}$

q1 =

q2 =

q3 =

Answer:_______________

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

$\frac{2}{4}$ 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 $\frac{5}{7}$

q1 =

q2 =

q3 =

Answer:_______________

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 / )

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

q1 =

q2 =

q3 =

Answer:_______________

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

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

q1 =

q2 =

q3 =

Answer:_______________

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

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

q1 =

q2 =

q3 =

Answer:_______________

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

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

q1 =

q2 =

q3 =

Answer:_______________

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

$\frac{3}{5}$ and $\frac{4}{9}$

q1 =

q2 =

q3 =

Answer:_______________

10)

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 / )

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

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

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

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

SOLUTION 1 :

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

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

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

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

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

[LCM of 7 and 6 is 42]

1	x	18	+	21	=	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	7x39	+	3x84	=	1	x	273+252	=	1	x	525
2		7		84		2		7x84		7x84		2		588		2		588

1	x	525	=	$\frac{25}{56}$
1		1176

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

q3 = (a+q2)

1	x	3	+	525	=	1	x	7x525	3x1176	=	1	x	3675+3528	=
2		7		1176		2		7x1176	7x1176		2		8232

1	x	7203	=	7203	=	$\frac{7}{16}$
2		8232		16464

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

Hence, $\frac{13}{28}$ , $\frac{25}{56}$ , $\frac{7}{16}$ is a rational number between $\frac{3}{7}$ and $\frac{3}{6}$

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

$\frac{2}{4}$ and $\frac{5}{6}$

q1 = Answer: $\frac{2}{3}$

q2 = Answer: $\frac{7}{12}$

q3 = Answer: $\frac{13}{24}$

SOLUTION 1 :

$\frac{2}{4}$ and $\frac{5}{6}$

a = $\frac{2}{4}$ , b = $\frac{5}{6}$

Let q1 be the rational number between $\frac{2}{4}$ and $\frac{5}{6}$

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

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

[LCM of 4 and 6 is 24]

1	x	12	+	20	=	1	x	32	=	32	=	$\frac{2}{3}$
2		24		24		2		24		48

q1 = $\frac{2}{3}$

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

1	x	2	+	32	=	1	x	4x32	+	2x48	=	1	x	128+96	=	1	x	224
2		4		48		2		4x48		4x48		2		192		2		192

1	x	224	=	$\frac{7}{12}$
1		384

q2 = $\frac{7}{12}$

q3 = (a+q2)

1	x	2	+	224	=	1	x	4x224	2x384	=	1	x	896+768	=
2		4		384		2		4x384	4x384		2		1536

1	x	1664	=	1664	=	$\frac{13}{24}$
2		1536		3072

q3 = $\frac{13}{24}$

Hence, $\frac{2}{3}$ , $\frac{7}{12}$ , $\frac{13}{24}$ is a rational number between $\frac{2}{4}$ and $\frac{5}{6}$

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

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

q1 = Answer: $\frac{27}{56}$

q2 = Answer: $\frac{41}{112}$

q3 = Answer: $\frac{69}{224}$

SOLUTION 1 :

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

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

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

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

1	x	1x7	+	5x4
2	x	4x7	+	7x4

[LCM of 4 and 7 is 28]

1	x	7	+	20	=	1	x	27	=	27	=	$\frac{27}{56}$
2		28		28		2		28		56

q1 = $\frac{27}{56}$

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

1	x	1	+	27	=	1	x	4x27	+	1x56	=	1	x	108+56	=	1	x	164
2		4		56		2		4x56		4x56		2		224		2		224

1	x	164	=	$\frac{41}{112}$
1		448

q2 = $\frac{41}{112}$

q3 = (a+q2)

1	x	1	+	164	=	1	x	4x164	1x448	=	1	x	656+448	=
2		4		448		2		4x448	4x448		2		1792

1	x	1104	=	1104	=	$\frac{69}{224}$
2		1792		3584

q3 = $\frac{69}{224}$

Hence, $\frac{27}{56}$ , $\frac{41}{112}$ , $\frac{69}{224}$ is a rational number between $\frac{1}{4}$ and $\frac{5}{7}$

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 $\frac{3}{7}$

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

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

q1 = Answer: $\frac{13}{30}$

q2 = Answer: $\frac{19}{60}$

q3 = Answer: $\frac{31}{120}$

SOLUTION 1 :

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

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

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

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

1	x	1x6	+	4x5
2	x	5x6	+	6x5

[LCM of 5 and 6 is 30]

1	x	6	+	20	=	1	x	26	=	26	=	$\frac{13}{30}$
2		30		30		2		30		60

q1 = $\frac{13}{30}$

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

1	x	1	+	26	=	1	x	5x26	+	1x60	=	1	x	130+60	=	1	x	190
2		5		60		2		5x60		5x60		2		300		2		300

1	x	190	=	$\frac{19}{60}$
1		600

q2 = $\frac{19}{60}$

q3 = (a+q2)

1	x	1	+	190	=	1	x	5x190	1x600	=	1	x	950+600	=
2		5		600		2		5x600	5x600		2		3000

1	x	1550	=	1550	=	$\frac{31}{120}$
2		3000		6000

q3 = $\frac{31}{120}$

Hence, $\frac{13}{30}$ , $\frac{19}{60}$ , $\frac{31}{120}$ is a rational number between $\frac{1}{5}$ and $\frac{4}{6}$

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

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

q1 = Answer: $\frac{5}{8}$

q2 = Answer: $\frac{11}{16}$

q3 = Answer: $\frac{23}{32}$

SOLUTION 1 :

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

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

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

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

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

[LCM of 4 and 8 is 32]

1	x	24	+	16	=	1	x	40	=	40	=	$\frac{5}{8}$
2		32		32		2		32		64

q1 = $\frac{5}{8}$

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

1	x	3	+	40	=	1	x	4x40	+	3x64	=	1	x	160+192	=	1	x	352
2		4		64		2		4x64		4x64		2		256		2		256

1	x	352	=	$\frac{11}{16}$
1		512

q2 = $\frac{11}{16}$

q3 = (a+q2)

1	x	3	+	352	=	1	x	4x352	3x512	=	1	x	1408+1536	=
2		4		512		2		4x512	4x512		2		2048

1	x	2944	=	2944	=	$\frac{23}{32}$
2		2048		4096

q3 = $\frac{23}{32}$

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

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

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

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

q2 = Answer: $\frac{1}{3}$

q3 = Answer: $\frac{1}{4}$

SOLUTION 1 :

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

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

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

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

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

[LCM of 6 and 6 is 36]

1	x	6	+	30	=	1	x	36	=	36	=	$\frac{1}{2}$
2		36		36		2		36		72

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

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

1	x	1	+	36	=	1	x	6x36	+	1x72	=	1	x	216+72	=	1	x	288
2		6		72		2		6x72		6x72		2		432		2		432

1	x	288	=	$\frac{1}{3}$
1		864

q2 = $\frac{1}{3}$

q3 = (a+q2)

1	x	1	+	288	=	1	x	6x288	1x864	=	1	x	1728+864	=
2		6		864		2		6x864	6x864		2		5184

1	x	2592	=	2592	=	$\frac{1}{4}$
2		5184		10368

q3 = $\frac{1}{4}$

Hence, $\frac{1}{2}$ , $\frac{1}{3}$ , $\frac{1}{4}$ is a rational number between $\frac{1}{6}$ and $\frac{5}{6}$

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

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

q1 = Answer: $\frac{16}{35}$

q2 = Answer: $\frac{23}{70}$

q3 = Answer: $\frac{37}{140}$

SOLUTION 1 :

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

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

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

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

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

[LCM of 5 and 7 is 35]

1	x	7	+	25	=	1	x	32	=	32	=	$\frac{16}{35}$
2		35		35		2		35		70

q1 = $\frac{16}{35}$

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

1	x	1	+	32	=	1	x	5x32	+	1x70	=	1	x	160+70	=	1	x	230
2		5		70		2		5x70		5x70		2		350		2		350

1	x	230	=	$\frac{23}{70}$
1		700

q2 = $\frac{23}{70}$

q3 = (a+q2)

1	x	1	+	230	=	1	x	5x230	1x700	=	1	x	1150+700	=
2		5		700		2		5x700	5x700		2		3500

1	x	1850	=	1850	=	$\frac{37}{140}$
2		3500		7000

q3 = $\frac{37}{140}$

Hence, $\frac{16}{35}$ , $\frac{23}{70}$ , $\frac{37}{140}$ is a rational number between $\frac{1}{5}$ and $\frac{5}{7}$

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

$\frac{3}{5}$ and $\frac{4}{9}$

q1 = Answer: $\frac{47}{90}$

q2 = Answer: $\frac{101}{180}$

q3 = Answer: $\frac{209}{360}$

SOLUTION 1 :

$\frac{3}{5}$ and $\frac{4}{9}$

a = $\frac{3}{5}$ , b = $\frac{4}{9}$

Let q1 be the rational number between $\frac{3}{5}$ and $\frac{4}{9}$

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

1	x	3x9	+	4x5
2	x	5x9	+	9x5

[LCM of 5 and 9 is 45]

1	x	27	+	20	=	1	x	47	=	47	=	$\frac{47}{90}$
2		45		45		2		45		90

q1 = $\frac{47}{90}$

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

1	x	3	+	47	=	1	x	5x47	+	3x90	=	1	x	235+270	=	1	x	505
2		5		90		2		5x90		5x90		2		450		2		450

1	x	505	=	$\frac{101}{180}$
1		900

q2 = $\frac{101}{180}$

q3 = (a+q2)

1	x	3	+	505	=	1	x	5x505	3x900	=	1	x	2525+2700	=
2		5		900		2		5x900	5x900		2		4500

1	x	5225	=	5225	=	$\frac{209}{360}$
2		4500		9000

q3 = $\frac{209}{360}$

Hence, $\frac{47}{90}$ , $\frac{101}{180}$ , $\frac{209}{360}$ is a rational number between $\frac{3}{5}$ and $\frac{4}{9}$

10)

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 $\frac{4}{7}$