Sasi Math (Revised for 1024)

Scroll:Real Number System >> Rational ( Exercise1.2) >> saq (4379)

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

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

q1 =

q2 =

Answer:_______________

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

$\frac{3}{5}$ and $\frac{4}{7}$

q1 =

q2 =

Answer:_______________

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

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

q1 =

q2 =

Answer:_______________

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

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

q1 =

q2 =

Answer:_______________

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

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

q1 =

q2 =

Answer:_______________

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

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

q1 =

q2 =

Answer:_______________

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

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

q1 =

q2 =

Answer:_______________

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

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

q1 =

q2 =

Answer:_______________

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

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

q1 =

q2 =

Answer:_______________

10)

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

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

q1 =

q2 =

Answer:_______________

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

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

q1 = Answer: $\frac{5}{9}$

q2 = Answer: $\frac{11}{9}$

SOLUTION 1 :

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

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

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

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

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

[LCM of 6 and 9 is 54]

1	x	36	+	24	=	1	x	60	=	60	=	$\frac{5}{9}$
2		54		54		2		54		108

q1 = $\frac{60}{108}$ = $\frac{5}{9}$

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

1	x	4	+	60	=	1	x	6x60	+	4x108	=	1	x	360+432	=	1	x	792
2		6		108		2		6x108		6x108		2		648		2		648

1	x	792	=	$\frac{11}{9}$
1		1296

q2 = $\frac{11}{9}$

Hence, $\frac{5}{9}$ , $\frac{11}{9}$ is a rational number between $\frac{4}{6}$ and $\frac{4}{9}$

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

$\frac{3}{5}$ and $\frac{4}{7}$

q1 = Answer: $\frac{41}{70}$

q2 = Answer: $\frac{83}{70}$

SOLUTION 1 :

$\frac{3}{5}$ and $\frac{4}{7}$

a = $\frac{3}{5}$ , b = $\frac{4}{7}$

Let q1 be the rational number between $\frac{3}{5}$ and $\frac{4}{7}$

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

1	x	3x7	+	4x5
2	x	5x7	+	7x5

[LCM of 5 and 7 is 35]

1	x	21	+	20	=	1	x	41	=	41	=	$\frac{41}{70}$
2		35		35		2		35		70

q1 = $\frac{41}{70}$ = $\frac{41}{70}$

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

1	x	3	+	41	=	1	x	5x41	+	3x70	=	1	x	205+210	=	1	x	415
2		5		70		2		5x70		5x70		2		350		2		350

1	x	415	=	$\frac{83}{70}$
1		700

q2 = $\frac{83}{70}$

Hence, $\frac{41}{70}$ , $\frac{83}{70}$ is a rational number between $\frac{3}{5}$ and $\frac{4}{7}$

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

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

q1 = Answer: $\frac{61}{90}$

q2 = Answer: $\frac{133}{90}$

SOLUTION 1 :

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

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

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

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

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

[LCM of 5 and 9 is 45]

1	x	36	+	25	=	1	x	61	=	61	=	$\frac{61}{90}$
2		45		45		2		45		90

q1 = $\frac{61}{90}$ = $\frac{61}{90}$

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

1	x	4	+	61	=	1	x	5x61	+	4x90	=	1	x	305+360	=	1	x	665
2		5		90		2		5x90		5x90		2		450		2		450

1	x	665	=	$\frac{133}{90}$
1		900

q2 = $\frac{133}{90}$

Hence, $\frac{61}{90}$ , $\frac{133}{90}$ is a rational number between $\frac{4}{5}$ and $\frac{5}{9}$

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

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

q1 = Answer: $\frac{37}{90}$

q2 = Answer: $\frac{91}{90}$

SOLUTION 1 :

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

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

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

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

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

[LCM of 5 and 9 is 45]

1	x	27	+	10	=	1	x	37	=	37	=	$\frac{37}{90}$
2		45		45		2		45		90

q1 = $\frac{37}{90}$ = $\frac{37}{90}$

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

1	x	3	+	37	=	1	x	5x37	+	3x90	=	1	x	185+270	=	1	x	455
2		5		90		2		5x90		5x90		2		450		2		450

1	x	455	=	$\frac{91}{90}$
1		900

q2 = $\frac{91}{90}$

Hence, $\frac{37}{90}$ , $\frac{91}{90}$ is a rational number between $\frac{3}{5}$ and $\frac{2}{9}$

Find two 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: $\frac{17}{20}$

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 = $\frac{27}{60}$ = $\frac{9}{20}$

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	=	$\frac{17}{20}$
1		600

q2 = $\frac{17}{20}$

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

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

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

q1 = Answer: $\frac{49}{80}$

q2 = Answer: $\frac{97}{80}$

SOLUTION 1 :

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

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

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

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

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

[LCM of 5 and 8 is 40]

1	x	24	+	25	=	1	x	49	=	49	=	$\frac{49}{80}$
2		40		40		2		40		80

q1 = $\frac{49}{80}$ = $\frac{49}{80}$

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

1	x	3	+	49	=	1	x	5x49	+	3x80	=	1	x	245+240	=	1	x	485
2		5		80		2		5x80		5x80		2		400		2		400

1	x	485	=	$\frac{97}{80}$
1		800

q2 = $\frac{97}{80}$

Hence, $\frac{49}{80}$ , $\frac{97}{80}$ is a rational number between $\frac{3}{5}$ and $\frac{5}{8}$

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

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

q1 = Answer: $\frac{7}{15}$

q2 = Answer: $\frac{16}{15}$

SOLUTION 1 :

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

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

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

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

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

[LCM of 5 and 6 is 30]

1	x	18	+	10	=	1	x	28	=	28	=	$\frac{7}{15}$
2		30		30		2		30		60

q1 = $\frac{28}{60}$ = $\frac{7}{15}$

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

1	x	3	+	28	=	1	x	5x28	+	3x60	=	1	x	140+180	=	1	x	320
2		5		60		2		5x60		5x60		2		300		2		300

1	x	320	=	$\frac{16}{15}$
1		600

q2 = $\frac{16}{15}$

Hence, $\frac{7}{15}$ , $\frac{16}{15}$ is a rational number between $\frac{3}{5}$ and $\frac{2}{6}$

Find two 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: $\frac{11}{12}$

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 = $\frac{45}{108}$ = $\frac{5}{12}$

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	=	$\frac{11}{12}$
1		1296

q2 = $\frac{11}{12}$

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

Find two 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: $\frac{3}{4}$

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 = $\frac{30}{72}$ = $\frac{5}{12}$

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	=	$\frac{3}{4}$
1		864

q2 = $\frac{3}{4}$

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

10)

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

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

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

q2 = Answer: $\frac{5}{6}$

SOLUTION 1 :

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

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

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

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

1	x	2x6	+	4x6
2	x	6x6	+	6x6

[LCM of 6 and 6 is 36]

1	x	12	+	24	=	1	x	36	=	36	=	$\frac{1}{2}$
2		36		36		2		36		72

q1 = $\frac{36}{72}$ = $\frac{1}{2}$

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

1	x	2	+	36	=	1	x	6x36	+	2x72	=	1	x	216+144	=	1	x	360
2		6		72		2		6x72		6x72		2		432		2		432

1	x	360	=	$\frac{5}{6}$
1		864

q2 = $\frac{5}{6}$

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