Sasi Math (Revised for 1024)

Scroll:Real Number System >> Rational ( Exercise1.2) >> saq (4377)

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

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

Answer:_______________

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

$\frac{3}{5}$ and $\frac{4}{8}$

Answer:_______________

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

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

Answer:_______________

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

$\frac{3}{4}$ and $\frac{6}{7}$

Answer:_______________

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

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

Answer:_______________

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

$\frac{3}{6}$ and $\frac{4}{8}$

Answer:_______________

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

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

Answer:_______________

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

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

Answer:_______________

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

$\frac{3}{5}$ and $\frac{6}{9}$

Answer:_______________

10)

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

$\frac{2}{4}$ and $\frac{6}{7}$

Answer:_______________

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

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

Answer: $\frac{39}{70}$

SOLUTION 1 :

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

a = $\frac{2}{5}$ , b = $\frac{5}{7}$

Let q1 be the rational number between $\frac{2}{5}$ and $\frac{5}{7}$

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

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

[LCM of 5 and 7 is 35]

1	x	14	+	25	=	1	x	39	=	39	=	$\frac{39}{70}$
2		35		35		2		35		70

Hence, $\frac{39}{70}$ is a rational number between $\frac{2}{5}$ and $\frac{5}{7}$

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

$\frac{3}{5}$ and $\frac{4}{8}$

Answer: $\frac{11}{20}$

SOLUTION 1 :

$\frac{3}{5}$ and $\frac{4}{8}$

a = $\frac{3}{5}$ , b = $\frac{4}{8}$

Let q1 be the rational number between $\frac{3}{5}$ and $\frac{4}{8}$

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

1	x	3x8	+	4x5
2	x	5x8	+	8x5

[LCM of 5 and 8 is 40]

1	x	24	+	20	=	1	x	44	=	44	=	$\frac{11}{20}$
2		40		40		2		40		80

Hence, $\frac{11}{20}$ is a rational number between $\frac{3}{5}$ and $\frac{4}{8}$

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

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

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

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

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

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

$\frac{3}{4}$ and $\frac{6}{7}$

Answer: $\frac{45}{56}$

SOLUTION 1 :

$\frac{3}{4}$ and $\frac{6}{7}$

a = $\frac{3}{4}$ , b = $\frac{6}{7}$

Let q1 be the rational number between $\frac{3}{4}$ and $\frac{6}{7}$

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

1	x	3x7	+	6x4
2	x	4x7	+	7x4

[LCM of 4 and 7 is 28]

1	x	21	+	24	=	1	x	45	=	45	=	$\frac{45}{56}$
2		28		28		2		28		56

Hence, $\frac{45}{56}$ is a rational number between $\frac{3}{4}$ and $\frac{6}{7}$

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

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

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

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

Hence, $\frac{9}{16}$ is a rational number between $\frac{3}{6}$ and $\frac{5}{8}$

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

$\frac{3}{6}$ and $\frac{4}{8}$

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

SOLUTION 1 :

$\frac{3}{6}$ and $\frac{4}{8}$

a = $\frac{3}{6}$ , b = $\frac{4}{8}$

Let q1 be the rational number between $\frac{3}{6}$ and $\frac{4}{8}$

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

1	x	3x8	+	4x6
2	x	6x8	+	8x6

[LCM of 6 and 8 is 48]

1	x	24	+	24	=	1	x	48	=	48	=	$\frac{1}{2}$
2		48		48		2		48		96

Hence, $\frac{1}{2}$ is a rational number between $\frac{3}{6}$ and $\frac{4}{8}$

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

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

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

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

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

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

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

Answer: $\frac{17}{36}$

SOLUTION 1 :

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

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

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

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

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

[LCM of 4 and 9 is 36]

1	x	18	+	16	=	1	x	34	=	34	=	$\frac{17}{36}$
2		36		36		2		36		72

Hence, $\frac{17}{36}$ is a rational number between $\frac{2}{4}$ and $\frac{4}{9}$

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

$\frac{3}{5}$ and $\frac{6}{9}$

Answer: $\frac{19}{30}$

SOLUTION 1 :

$\frac{3}{5}$ and $\frac{6}{9}$

a = $\frac{3}{5}$ , b = $\frac{6}{9}$

Let q1 be the rational number between $\frac{3}{5}$ and $\frac{6}{9}$

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

1	x	3x9	+	6x5
2	x	5x9	+	9x5

[LCM of 5 and 9 is 45]

1	x	27	+	30	=	1	x	57	=	57	=	$\frac{19}{30}$
2		45		45		2		45		90

Hence, $\frac{19}{30}$ is a rational number between $\frac{3}{5}$ and $\frac{6}{9}$

10)

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

$\frac{2}{4}$ and $\frac{6}{7}$

Answer: $\frac{19}{28}$

SOLUTION 1 :

$\frac{2}{4}$ and $\frac{6}{7}$

a = $\frac{2}{4}$ , b = $\frac{6}{7}$

Let q1 be the rational number between $\frac{2}{4}$ and $\frac{6}{7}$

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

1	x	2x7	+	6x4
2	x	4x7	+	7x4

[LCM of 4 and 7 is 28]

1	x	14	+	24	=	1	x	38	=	38	=	$\frac{19}{28}$
2		28		28		2		28		56

Hence, $\frac{19}{28}$ is a rational number between $\frac{2}{4}$ and $\frac{6}{7}$