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 / )

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

q1 =

q2 =

q3 =

Answer:_______________

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

$\frac{1}{6}$ and $\frac{4}{7}$

q1 =

q2 =

q3 =

Answer:_______________

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

$\frac{2}{4}$ and $\frac{5}{8}$

q1 =

q2 =

q3 =

Answer:_______________

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

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

q1 =

q2 =

q3 =

Answer:_______________

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

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

q1 =

q2 =

q3 =

Answer:_______________

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 / )

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

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:_______________

10)

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

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

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 / )

$\frac{2}{5}$ 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 / )

$\frac{1}{6}$ and $\frac{4}{7}$

q1 = Answer: $\frac{31}{84}$

q2 = Answer: $\frac{15}{56}$

q3 = Answer: $\frac{73}{336}$

SOLUTION 1 :

$\frac{1}{6}$ and $\frac{4}{7}$

a = $\frac{1}{6}$ , b = $\frac{4}{7}$

Let q1 be the rational number between $\frac{1}{6}$ and $\frac{4}{7}$

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

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

[LCM of 6 and 7 is 42]

1	x	7	+	24	=	1	x	31	=	31	=	$\frac{31}{84}$
2		42		42		2		42		84

q1 = $\frac{31}{84}$

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

1	x	1	+	31	=	1	x	6x31	+	1x84	=	1	x	186+84	=	1	x	270
2		6		84		2		6x84		6x84		2		504		2		504

1	x	270	=	$\frac{15}{56}$
1		1008

q2 = $\frac{15}{56}$

q3 = (a+q2)

1	x	1	+	270	=	1	x	6x270	1x1008	=	1	x	1620+1008	=
2		6		1008		2		6x1008	6x1008		2		6048

1	x	2628	=	2628	=	$\frac{73}{336}$
2		6048		12096

q3 = $\frac{73}{336}$

Hence, $\frac{31}{84}$ , $\frac{15}{56}$ , $\frac{73}{336}$ is a rational number between $\frac{1}{6}$ and $\frac{4}{7}$

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

$\frac{2}{4}$ and $\frac{5}{8}$

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

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

q3 = Answer: $\frac{33}{64}$

SOLUTION 1 :

$\frac{2}{4}$ and $\frac{5}{8}$

a = $\frac{2}{4}$ , b = $\frac{5}{8}$

Let q1 be the rational number between $\frac{2}{4}$ and $\frac{5}{8}$

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

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

[LCM of 4 and 8 is 32]

1	x	16	+	20	=	1	x	36	=	36	=	$\frac{9}{16}$
2		32		32		2		32		64

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

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

1	x	2	+	36	=	1	x	4x36	+	2x64	=	1	x	144+128	=	1	x	272
2		4		64		2		4x64		4x64		2		256		2		256

1	x	272	=	$\frac{17}{32}$
1		512

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

q3 = (a+q2)

1	x	2	+	272	=	1	x	4x272	2x512	=	1	x	1088+1024	=
2		4		512		2		4x512	4x512		2		2048

1	x	2112	=	2112	=	$\frac{33}{64}$
2		2048		4096

q3 = $\frac{33}{64}$

Hence, $\frac{9}{16}$ , $\frac{17}{32}$ , $\frac{33}{64}$ is a rational number between $\frac{2}{4}$ and $\frac{5}{8}$

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

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

q1 = Answer: $\frac{8}{15}$

q2 = Answer: $\frac{7}{15}$

q3 = Answer: $\frac{13}{30}$

SOLUTION 1 :

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

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

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

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

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

[LCM of 5 and 6 is 30]

1	x	12	+	20	=	1	x	32	=	32	=	$\frac{8}{15}$
2		30		30		2		30		60

q1 = $\frac{8}{15}$

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

1	x	2	+	32	=	1	x	5x32	+	2x60	=	1	x	160+120	=	1	x	280
2		5		60		2		5x60		5x60		2		300		2		300

1	x	280	=	$\frac{7}{15}$
1		600

q2 = $\frac{7}{15}$

q3 = (a+q2)

1	x	2	+	280	=	1	x	5x280	2x600	=	1	x	1400+1200	=
2		5		600		2		5x600	5x600		2		3000

1	x	2600	=	2600	=	$\frac{13}{30}$
2		3000		6000

q3 = $\frac{13}{30}$

Hence, $\frac{8}{15}$ , $\frac{7}{15}$ , $\frac{13}{30}$ is a rational number between $\frac{2}{5}$ and $\frac{4}{6}$

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

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

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

q2 = Answer: $\frac{5}{14}$

q3 = Answer: $\frac{9}{28}$

SOLUTION 1 :

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

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

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

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

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

[LCM of 7 and 7 is 49]

1	x	14	+	28	=	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	2	+	42	=	1	x	7x42	+	2x98	=	1	x	294+196	=	1	x	490
2		7		98		2		7x98		7x98		2		686		2		686

1	x	490	=	$\frac{5}{14}$
1		1372

q2 = $\frac{5}{14}$

q3 = (a+q2)

1	x	2	+	490	=	1	x	7x490	2x1372	=	1	x	3430+2744	=
2		7		1372		2		7x1372	7x1372		2		9604

1	x	6174	=	6174	=	$\frac{9}{28}$
2		9604		19208

q3 = $\frac{9}{28}$

Hence, $\frac{3}{7}$ , $\frac{5}{14}$ , $\frac{9}{28}$ is a rational number between $\frac{2}{7}$ and $\frac{4}{7}$

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 $\frac{5}{8}$

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 $\frac{5}{8}$

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 $\frac{4}{7}$

10)

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

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

q1 = Answer: $\frac{47}{72}$

q2 = Answer: $\frac{101}{144}$

q3 = Answer: $\frac{209}{288}$

SOLUTION 1 :

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

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

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

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

1	x	3x9	+	5x4
2	x	4x9	+	9x4

[LCM of 4 and 9 is 36]

1	x	27	+	20	=	1	x	47	=	47	=	$\frac{47}{72}$
2		36		36		2		36		72

q1 = $\frac{47}{72}$

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

1	x	3	+	47	=	1	x	4x47	+	3x72	=	1	x	188+216	=	1	x	404
2		4		72		2		4x72		4x72		2		288		2		288

1	x	404	=	$\frac{101}{144}$
1		576

q2 = $\frac{101}{144}$

q3 = (a+q2)

1	x	3	+	404	=	1	x	4x404	3x576	=	1	x	1616+1728	=
2		4		576		2		4x576	4x576		2		2304

1	x	3344	=	3344	=	$\frac{209}{288}$
2		2304		4608

q3 = $\frac{209}{288}$

Hence, $\frac{47}{72}$ , $\frac{101}{144}$ , $\frac{209}{288}$ is a rational number between $\frac{3}{4}$ and $\frac{5}{9}$