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 / )

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

q1 =

q2 =

q3 =

Answer:_______________

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

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

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 / )

$\frac{2}{7}$ and $\frac{3}{8}$

q1 =

q2 =

q3 =

Answer:_______________

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

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

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 / )

$\frac{2}{5}$ and $\frac{3}{9}$

q1 =

q2 =

q3 =

Answer:_______________

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

$\frac{2}{6}$ and $\frac{3}{8}$

q1 =

q2 =

q3 =

Answer:_______________

10)

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

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

q1 = Answer: $\frac{1}{3}$

q2 = Answer: $\frac{1}{4}$

q3 = Answer: $\frac{5}{24}$

SOLUTION 1 :

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

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

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

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

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

[LCM of 6 and 6 is 36]

1	x	6	+	18	=	1	x	24	=	24	=	$\frac{1}{3}$
2		36		36		2		36		72

q1 = $\frac{1}{3}$

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

1	x	1	+	24	=	1	x	6x24	+	1x72	=	1	x	144+72	=	1	x	216
2		6		72		2		6x72		6x72		2		432		2		432

1	x	216	=	$\frac{1}{4}$
1		864

q2 = $\frac{1}{4}$

q3 = (a+q2)

1	x	1	+	216	=	1	x	6x216	1x864	=	1	x	1296+864	=
2		6		864		2		6x864	6x864		2		5184

1	x	2160	=	2160	=	$\frac{5}{24}$
2		5184		10368

q3 = $\frac{5}{24}$

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

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

$\frac{3}{7}$ and $\frac{5}{9}$

q1 = Answer: $\frac{31}{63}$

q2 = Answer: $\frac{29}{63}$

q3 = Answer: $\frac{4}{9}$

SOLUTION 1 :

$\frac{3}{7}$ and $\frac{5}{9}$

a = $\frac{3}{7}$ , b = $\frac{5}{9}$

Let q1 be the rational number between $\frac{3}{7}$ and $\frac{5}{9}$

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

1	x	3x9	+	5x7
2	x	7x9	+	9x7

[LCM of 7 and 9 is 63]

1	x	27	+	35	=	1	x	62	=	62	=	$\frac{31}{63}$
2		63		63		2		63		126

q1 = $\frac{31}{63}$

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

1	x	3	+	62	=	1	x	7x62	+	3x126	=	1	x	434+378	=	1	x	812
2		7		126		2		7x126		7x126		2		882		2		882

1	x	812	=	$\frac{29}{63}$
1		1764

q2 = $\frac{29}{63}$

q3 = (a+q2)

1	x	3	+	812	=	1	x	7x812	3x1764	=	1	x	5684+5292	=
2		7		1764		2		7x1764	7x1764		2		12348

1	x	10976	=	10976	=	$\frac{4}{9}$
2		12348		24696

q3 = $\frac{4}{9}$

Hence, $\frac{31}{63}$ , $\frac{29}{63}$ , $\frac{4}{9}$ is a rational number between $\frac{3}{7}$ and $\frac{5}{9}$

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

$\frac{1}{7}$ and $\frac{3}{8}$

q1 = Answer: $\frac{29}{112}$

q2 = Answer: $\frac{45}{224}$

q3 = Answer: $\frac{11}{64}$

SOLUTION 1 :

$\frac{1}{7}$ and $\frac{3}{8}$

a = $\frac{1}{7}$ , b = $\frac{3}{8}$

Let q1 be the rational number between $\frac{1}{7}$ and $\frac{3}{8}$

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

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

[LCM of 7 and 8 is 56]

1	x	8	+	21	=	1	x	29	=	29	=	$\frac{29}{112}$
2		56		56		2		56		112

q1 = $\frac{29}{112}$

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

1	x	1	+	29	=	1	x	7x29	+	1x112	=	1	x	203+112	=	1	x	315
2		7		112		2		7x112		7x112		2		784		2		784

1	x	315	=	$\frac{45}{224}$
1		1568

q2 = $\frac{45}{224}$

q3 = (a+q2)

1	x	1	+	315	=	1	x	7x315	1x1568	=	1	x	2205+1568	=
2		7		1568		2		7x1568	7x1568		2		10976

1	x	3773	=	3773	=	$\frac{11}{64}$
2		10976		21952

q3 = $\frac{11}{64}$

Hence, $\frac{29}{112}$ , $\frac{45}{224}$ , $\frac{11}{64}$ is a rational number between $\frac{1}{7}$ and $\frac{3}{8}$

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 / )

$\frac{2}{7}$ 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 $\frac{3}{8}$

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

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

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

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

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

SOLUTION 1 :

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

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

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

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

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

[LCM of 6 and 9 is 54]

1	x	27	+	18	=	1	x	45	=	45	=	$\frac{5}{12}$
2		54		54		2		54		108

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

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

1	x	3	+	45	=	1	x	6x45	+	3x108	=	1	x	270+324	=	1	x	594
2		6		108		2		6x108		6x108		2		648		2		648

1	x	594	=	$\frac{11}{24}$
1		1296

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

q3 = (a+q2)

1	x	3	+	594	=	1	x	6x594	3x1296	=	1	x	3564+3888	=
2		6		1296		2		6x1296	6x1296		2		7776

1	x	7452	=	7452	=	$\frac{23}{48}$
2		7776		15552

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

Hence, $\frac{5}{12}$ , $\frac{11}{24}$ , $\frac{23}{48}$ is a rational number between $\frac{3}{6}$ and $\frac{3}{9}$

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 / )

$\frac{2}{5}$ and $\frac{3}{9}$

q1 = Answer: $\frac{11}{30}$

q2 = Answer: $\frac{23}{60}$

q3 = Answer: $\frac{47}{120}$

SOLUTION 1 :

$\frac{2}{5}$ and $\frac{3}{9}$

a = $\frac{2}{5}$ , b = $\frac{3}{9}$

Let q1 be the rational number between $\frac{2}{5}$ and $\frac{3}{9}$

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

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

[LCM of 5 and 9 is 45]

1	x	18	+	15	=	1	x	33	=	33	=	$\frac{11}{30}$
2		45		45		2		45		90

q1 = $\frac{11}{30}$

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

1	x	2	+	33	=	1	x	5x33	+	2x90	=	1	x	165+180	=	1	x	345
2		5		90		2		5x90		5x90		2		450		2		450

1	x	345	=	$\frac{23}{60}$
1		900

q2 = $\frac{23}{60}$

q3 = (a+q2)

1	x	2	+	345	=	1	x	5x345	2x900	=	1	x	1725+1800	=
2		5		900		2		5x900	5x900		2		4500

1	x	3525	=	3525	=	$\frac{47}{120}$
2		4500		9000

q3 = $\frac{47}{120}$

Hence, $\frac{11}{30}$ , $\frac{23}{60}$ , $\frac{47}{120}$ is a rational number between $\frac{2}{5}$ and $\frac{3}{9}$

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

$\frac{2}{6}$ and $\frac{3}{8}$

q1 = Answer: $\frac{17}{48}$

q2 = Answer: $\frac{11}{32}$

q3 = Answer: $\frac{65}{192}$

SOLUTION 1 :

$\frac{2}{6}$ and $\frac{3}{8}$

a = $\frac{2}{6}$ , b = $\frac{3}{8}$

Let q1 be the rational number between $\frac{2}{6}$ and $\frac{3}{8}$

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

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

[LCM of 6 and 8 is 48]

1	x	16	+	18	=	1	x	34	=	34	=	$\frac{17}{48}$
2		48		48		2		48		96

q1 = $\frac{17}{48}$

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

1	x	2	+	34	=	1	x	6x34	+	2x96	=	1	x	204+192	=	1	x	396
2		6		96		2		6x96		6x96		2		576		2		576

1	x	396	=	$\frac{11}{32}$
1		1152

q2 = $\frac{11}{32}$

q3 = (a+q2)

1	x	2	+	396	=	1	x	6x396	2x1152	=	1	x	2376+2304	=
2		6		1152		2		6x1152	6x1152		2		6912

1	x	4680	=	4680	=	$\frac{65}{192}$
2		6912		13824

q3 = $\frac{65}{192}$

Hence, $\frac{17}{48}$ , $\frac{11}{32}$ , $\frac{65}{192}$ is a rational number between $\frac{2}{6}$ and $\frac{3}{8}$

10)

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

$\frac{1}{6}$ and $\frac{5}{9}$

q1 = Answer: $\frac{13}{36}$

q2 = Answer: $\frac{19}{72}$

q3 = Answer: $\frac{31}{144}$

SOLUTION 1 :

$\frac{1}{6}$ and $\frac{5}{9}$

a = $\frac{1}{6}$ , b = $\frac{5}{9}$

Let q1 be the rational number between $\frac{1}{6}$ and $\frac{5}{9}$

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

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

[LCM of 6 and 9 is 54]

1	x	9	+	30	=	1	x	39	=	39	=	$\frac{13}{36}$
2		54		54		2		54		108

q1 = $\frac{13}{36}$

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

1	x	1	+	39	=	1	x	6x39	+	1x108	=	1	x	234+108	=	1	x	342
2		6		108		2		6x108		6x108		2		648		2		648

1	x	342	=	$\frac{19}{72}$
1		1296

q2 = $\frac{19}{72}$

q3 = (a+q2)

1	x	1	+	342	=	1	x	6x342	1x1296	=	1	x	2052+1296	=
2		6		1296		2		6x1296	6x1296		2		7776

1	x	3348	=	3348	=	$\frac{31}{144}$
2		7776		15552

q3 = $\frac{31}{144}$

Hence, $\frac{13}{36}$ , $\frac{19}{72}$ , $\frac{31}{144}$ is a rational number between $\frac{1}{6}$ and $\frac{5}{9}$