Sasi Math (Revised for 1024)

Scroll:Real Number System >> Rational Numbers ( Exercise 1.1) >> saq (4369)

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.

Verify whether associative property is satisfied for subtraction of the following pairs of rational numbers.(ples use /)

$\frac{2}{3}$ , $\frac{5}{6}$ and $\frac{-4}{7}$

LHS =

RHS =

Answer:_______________

Verify whether associative property is satisfied for subtraction of the following pairs of rational numbers.(ples use /)

$\frac{2}{4}$ , $\frac{4}{5}$ and $\frac{-5}{5}$

LHS =

RHS =

Answer:_______________

Verify whether associative property is satisfied for subtraction of the following pairs of rational numbers.(ples use /)

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

LHS =

RHS =

Answer:_______________

Verify whether associative property is satisfied for subtraction of the following pairs of rational numbers.(ples use /)

$\frac{3}{4}$ , $\frac{3}{5}$ and $\frac{-4}{5}$

LHS =

RHS =

Answer:_______________

Verify whether associative property is satisfied for subtraction of the following pairs of rational numbers.(ples use /)

$\frac{1}{4}$ , $\frac{5}{5}$ and $\frac{-4}{8}$

LHS =

RHS =

Answer:_______________

Verify whether associative property is satisfied for subtraction of the following pairs of rational numbers.(ples use /)

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

LHS =

RHS =

Answer:_______________

Verify whether associative property is satisfied for subtraction of the following pairs of rational numbers.(ples use /)

$\frac{2}{3}$ , $\frac{2}{5}$ and $\frac{-4}{6}$

LHS =

RHS =

Answer:_______________

Verify whether associative property is satisfied for subtraction of the following pairs of rational numbers.(ples use /)

$\frac{3}{2}$ , $\frac{4}{4}$ and $\frac{-3}{8}$

LHS =

RHS =

Answer:_______________

Verify whether associative property is satisfied for subtraction of the following pairs of rational numbers.(ples use /)

$\frac{2}{3}$ , $\frac{2}{4}$ and $\frac{-5}{7}$

LHS =

RHS =

Answer:_______________

10)

Verify whether associative property is satisfied for subtraction of the following pairs of rational numbers.(ples use /)

$\frac{1}{3}$ , $\frac{4}{4}$ and $\frac{-3}{8}$

LHS =

RHS =

Answer:_______________

Verify whether associative property is satisfied for subtraction of the following pairs of rational numbers.(ples use /)

$\frac{2}{3}$ , $\frac{5}{6}$ and $\frac{-4}{7}$

LHS = Answer: $\frac{-25}{42}$

RHS = Answer: $\frac{11}{42}$

SOLUTION 1 :

To verify,

( $\frac{2}{3}$ - ( $\frac{5}{6}$ - ( $\frac{-4}{7}$ )) = ( $\frac{2}{3}$ - $\frac{5}{6}$ ) - ( $\frac{-4}{7}$ )

LHS =

2	-	5	-	4	=	5x7	+	3x6
3	-	6	-	7	=	6x7	+	6x7

[ LCM of 6 and 7 is 42]

2	-	35	+	18
3	-	42	+	42

2	-	35+18	=	2	-	53	=	2x42	-	53x3
3	-	42	=	3	-	42	=	3x42	-	42x3

[LCM of 3 ans 42 is 126]

2x42

53x3

159

84- 159

-75

\frac{-25}{42}

42x3

126

LHS = $\frac{-25}{42}$

RHS = ( $\frac{2}{3}$ - $\frac{5}{6}$ ) - ( $\frac{-4}{7}$ ) = ( $\frac{2}{3}$ - ( $\frac{5}{6}$ ) $\frac{+4}{7)}$

2x6	-	5x3	+	4
3x6	-	6x3	+	7

[LCM of 6 and 3 is 18] .....

12	-	-15	+	4	=	12-15	+	4	=	-3	+	4
18		18		7		18		7		18		7

[LCM of 18 and 7 is 126]

-3x7

-3x3

-21

-21+(54)

\frac{11}{42}

18x7

18x3

126

RHS = $\frac{11}{42}$

LHS ≠ RHS

Hence, associative property is not true for subtraction.

Verify whether associative property is satisfied for subtraction of the following pairs of rational numbers.(ples use /)

$\frac{2}{4}$ , $\frac{4}{5}$ and $\frac{-5}{5}$

LHS = Answer: $\frac{11}{-10}$

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

SOLUTION 1 :

To verify,

( $\frac{2}{4}$ - ( $\frac{4}{5}$ - ( $\frac{-5}{5}$ )) = ( $\frac{2}{4}$ - $\frac{4}{5}$ ) - ( $\frac{-5}{5}$ )

LHS =

2	-	4	-	5	=	4x5	+	4x5
4	-	5	-	5	=	5x5	+	5x5

[ LCM of 5 and 5 is 25]

2	-	20	+	20
4	-	25	+	25

2	-	20+20	=	2	-	40	=	2x25	-	40x4
4	-	25	=	4	-	25	=	4x25	-	25x4

[LCM of 4 ans 25 is 100]

2x25

40x4

160

50- 160

-110

\frac{11}{-10}

25x4

100

LHS = $\frac{11}{-10}$

RHS = ( $\frac{2}{4}$ - $\frac{4}{5}$ ) - ( $\frac{-5}{5}$ ) = ( $\frac{2}{4}$ - ( $\frac{4}{5}$ ) $\frac{+5}{5)}$

2x5	-	4x4	+	5
4x5	-	5x4	+	5

[LCM of 5 and 4 is 20] .....

10	-	-16	+	5	=	10-16	+	5	=	-6	+	5
20		20		5		20		5		20		5

[LCM of 20 and 5 is 100]

-6x5

-6x4

-30

-30+(80)

\frac{1}{2}

20x5

20x4

100

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

LHS ≠ RHS

Hence, associative property is not true for subtraction.

Verify whether associative property is satisfied for subtraction of the following pairs of rational numbers.(ples use /)

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

LHS = Answer: $\frac{1}{-3}$

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

SOLUTION 1 :

To verify,

( $\frac{2}{3}$ - ( $\frac{3}{6}$ - (- $\frac{3}{6}$ )) = ( $\frac{2}{3}$ - $\frac{3}{6}$ ) - (- $\frac{3}{6}$ )

LHS =

2	-	3	-	3	=	3x6	+	3x6
3	-	6	-	6	=	6x6	+	6x6

[ LCM of 6 and 6 is 36]

2	-	18	+	18
3	-	36	+	36

2	-	18+18	=	2	-	36	=	2x36	-	36x3
3	-	36	=	3	-	36	=	3x36	-	36x3

[LCM of 3 ans 36 is 108]

2x36

36x3

108

72- 108

-36

\frac{1}{-3}

36x3

108

LHS = $\frac{1}{-3}$

RHS = ( $\frac{2}{3}$ - $\frac{3}{6}$ ) - (- $\frac{3}{6}$ ) = ( $\frac{2}{3}$ - ( $\frac{3}{6}$ ) + $\frac{3}{6}$ )

2x6	-	3x3	+	3
3x6	-	6x3	+	6

[LCM of 6 and 3 is 18] .....

12	-	-9	+	3	=	12-9	+	3	=	3	+	3
18		18		6		18		6		18		6

[LCM of 18 and 6 is 108]

3x6

3x3

18+(54)

\frac{2}{3}

18x6

18x3

108

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

LHS ≠ RHS

Hence, associative property is not true for subtraction.

Verify whether associative property is satisfied for subtraction of the following pairs of rational numbers.(ples use /)

$\frac{3}{4}$ , $\frac{3}{5}$ and $\frac{-4}{5}$

LHS = Answer: $\frac{-13}{20}$

RHS = Answer: $\frac{19}{20}$

SOLUTION 1 :

To verify,

( $\frac{3}{4}$ - ( $\frac{3}{5}$ - ( $\frac{-4}{5}$ )) = ( $\frac{3}{4}$ - $\frac{3}{5}$ ) - ( $\frac{-4}{5}$ )

LHS =

3	-	3	-	4	=	3x5	+	4x5
4	-	5	-	5	=	5x5	+	5x5

[ LCM of 5 and 5 is 25]

3	-	15	+	20
4	-	25	+	25

3	-	15+20	=	3	-	35	=	3x25	-	35x4
4	-	25	=	4	-	25	=	4x25	-	25x4

[LCM of 4 ans 25 is 100]

3x25

35x4

140

75- 140

-65

\frac{-13}{20}

25x4

100

LHS = $\frac{-13}{20}$

RHS = ( $\frac{3}{4}$ - $\frac{3}{5}$ ) - ( $\frac{-4}{5}$ ) = ( $\frac{3}{4}$ - ( $\frac{3}{5}$ ) $\frac{+4}{5)}$

3x5	-	3x4	+	4
4x5	-	5x4	+	5

[LCM of 5 and 4 is 20] .....

15	-	-12	+	4	=	15-12	+	4	=	3	+	4
20		20		5		20		5		20		5

[LCM of 20 and 5 is 100]

3x5

3x4

15+(80)

\frac{19}{20}

20x5

20x4

100

RHS = $\frac{19}{20}$

LHS ≠ RHS

Hence, associative property is not true for subtraction.

Verify whether associative property is satisfied for subtraction of the following pairs of rational numbers.(ples use /)

$\frac{1}{4}$ , $\frac{5}{5}$ and $\frac{-4}{8}$

LHS = Answer: $\frac{5}{-4}$

RHS = Answer: $\frac{1}{-4}$

SOLUTION 1 :

To verify,

( $\frac{1}{4}$ - ( $\frac{5}{5}$ - ( $\frac{-4}{8}$ )) = ( $\frac{1}{4}$ - $\frac{5}{5}$ ) - ( $\frac{-4}{8}$ )

LHS =

1	-	5	-	4	=	5x8	+	4x5
4	-	5	-	8	=	5x8	+	5x8

[ LCM of 5 and 8 is 40]

1	-	40	+	20
4	-	40	+	40

1	-	40+20	=	1	-	60	=	1x40	-	60x4
4	-	40	=	4	-	40	=	4x40	-	40x4

[LCM of 4 ans 40 is 160]

1x40

60x4

240

40- 240

-200

\frac{5}{-4}

40x4

160

LHS = $\frac{5}{-4}$

RHS = ( $\frac{1}{4}$ - $\frac{5}{5}$ ) - ( $\frac{-4}{8}$ ) = ( $\frac{1}{4}$ - ( $\frac{5}{5}$ ) $\frac{+4}{8)}$

1x5	-	5x4	+	4
4x5	-	5x4	+	8

[LCM of 5 and 4 is 20] .....

5	-	-20	+	4	=	5-20	+	4	=	-15	+	4
20		20		8		20		8		20		8

[LCM of 20 and 8 is 160]

-15x8

-15x4

-120

-120+(80)

-40

\frac{1}{-4}

20x8

20x4

160

RHS = $\frac{1}{-4}$

LHS ≠ RHS

Hence, associative property is not true for subtraction.

Verify whether associative property is satisfied for subtraction of the following pairs of rational numbers.(ples use /)

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

LHS = Answer: $\frac{-2}{21}$

RHS = Answer: $\frac{16}{21}$

SOLUTION 1 :

To verify,

( $\frac{3}{3}$ - ( $\frac{4}{6}$ - ( $\frac{-3}{7}$ )) = ( $\frac{3}{3}$ - $\frac{4}{6}$ ) - ( $\frac{-3}{7}$ )

LHS =

3	-	4	-	3	=	4x7	+	3x6
3	-	6	-	7	=	6x7	+	6x7

[ LCM of 6 and 7 is 42]

3	-	28	+	18
3	-	42	+	42

3	-	28+18	=	3	-	46	=	3x42	-	46x3
3	-	42	=	3	-	42	=	3x42	-	42x3

[LCM of 3 ans 42 is 126]

3x42

46x3

126

138

126- 138

-12

\frac{-2}{21}

42x3

126

LHS = $\frac{-2}{21}$

RHS = ( $\frac{3}{3}$ - $\frac{4}{6}$ ) - ( $\frac{-3}{7}$ ) = ( $\frac{3}{3}$ - ( $\frac{4}{6}$ ) $\frac{+3}{7)}$

3x6	-	4x3	+	3
3x6	-	6x3	+	7

[LCM of 6 and 3 is 18] .....

18	-	-12	+	3	=	18-12	+	3	=	6	+	3
18		18		7		18		7		18		7

[LCM of 18 and 7 is 126]

6x7

6x3

42+(54)

\frac{16}{21}

18x7

18x3

126

RHS = $\frac{16}{21}$

LHS ≠ RHS

Hence, associative property is not true for subtraction.

Verify whether associative property is satisfied for subtraction of the following pairs of rational numbers.(ples use /)

$\frac{2}{3}$ , $\frac{2}{5}$ and $\frac{-4}{6}$

LHS = Answer: $\frac{7}{-30}$

RHS = Answer: $\frac{23}{30}$

SOLUTION 1 :

To verify,

( $\frac{2}{3}$ - ( $\frac{2}{5}$ - ( $\frac{-4}{6}$ )) = ( $\frac{2}{3}$ - $\frac{2}{5}$ ) - ( $\frac{-4}{6}$ )

LHS =

2	-	2	-	4	=	2x6	+	3x5
3	-	5	-	6	=	5x6	+	5x6

[ LCM of 5 and 6 is 30]

2	-	12	+	15
3	-	30	+	30

2	-	12+15	=	2	-	27	=	2x30	-	27x3
3	-	30	=	3	-	30	=	3x30	-	30x3

[LCM of 3 ans 30 is 90]

2x30	-	27x3	=	60	-	81	=	60- 81	=	-21	=	$\frac{7}{-30}$
30x3		30x3		90		90		90		90

LHS = $\frac{7}{-30}$

RHS = ( $\frac{2}{3}$ - $\frac{2}{5}$ ) - ( $\frac{-4}{6}$ ) = ( $\frac{2}{3}$ - ( $\frac{2}{5}$ ) $\frac{+4}{6)}$

2x5	-	2x3	+	4
3x5	-	5x3	+	6

[LCM of 5 and 3 is 15] .....

10	-	-6	+	4	=	10-6	+	4	=	4	+	4
15		15		6		15		6		15		6

[LCM of 15 and 6 is 90]

4x6

4x3

24+(45)

\frac{23}{30}

15x6

15x3

RHS = $\frac{23}{30}$

LHS ≠ RHS

Hence, associative property is not true for subtraction.

Verify whether associative property is satisfied for subtraction of the following pairs of rational numbers.(ples use /)

$\frac{3}{2}$ , $\frac{4}{4}$ and $\frac{-3}{8}$

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

RHS = Answer: $\frac{3}{4}$

SOLUTION 1 :

To verify,

( $\frac{3}{2}$ - ( $\frac{4}{4}$ - ( $\frac{-3}{8}$ )) = ( $\frac{3}{2}$ - $\frac{4}{4}$ ) - ( $\frac{-3}{8}$ )

LHS =

3	-	4	-	3	=	4x8	+	2x4
2	-	4	-	8	=	4x8	+	4x8

[ LCM of 4 and 8 is 32]

3	-	32	+	8
2	-	32	+	32

3	-	32+8	=	3	-	40	=	3x32	-	40x2
2	-	32	=	2	-	32	=	2x32	-	32x2

[LCM of 2 ans 32 is 64]

3x32	-	40x2	=	96	-	80	=	96- 80	=	16	=	$\frac{1}{4}$
32x2		32x2		64		64		64		64

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

RHS = ( $\frac{3}{2}$ - $\frac{4}{4}$ ) - ( $\frac{-3}{8}$ ) = ( $\frac{3}{2}$ - ( $\frac{4}{4}$ ) $\frac{+3}{8)}$

3x4	-	4x2	+	3
2x4	-	4x2	+	8

[LCM of 4 and 2 is 8] .....

12	-	-8	+	3	=	12-8	+	3	=	4	+	3
8		8		8		8		8		8		8

[LCM of 8 and 8 is 64]

4x8

4x2

32+(16)

\frac{3}{4}

8x8

8x2

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

LHS ≠ RHS

Hence, associative property is not true for subtraction.

Verify whether associative property is satisfied for subtraction of the following pairs of rational numbers.(ples use /)

$\frac{2}{3}$ , $\frac{2}{4}$ and $\frac{-5}{7}$

LHS = Answer: $\frac{-11}{42}$

RHS = Answer: $\frac{25}{42}$

SOLUTION 1 :

To verify,

( $\frac{2}{3}$ - ( $\frac{2}{4}$ - ( $\frac{-5}{7}$ )) = ( $\frac{2}{3}$ - $\frac{2}{4}$ ) - ( $\frac{-5}{7}$ )

LHS =

2	-	2	-	5	=	2x7	+	3x4
3	-	4	-	7	=	4x7	+	4x7

[ LCM of 4 and 7 is 28]

2	-	14	+	12
3	-	28	+	28

2	-	14+12	=	2	-	26	=	2x28	-	26x3
3	-	28	=	3	-	28	=	3x28	-	28x3

[LCM of 3 ans 28 is 84]

2x28	-	26x3	=	56	-	78	=	56- 78	=	-22	=	$\frac{-11}{42}$
28x3		28x3		84		84		84		84

LHS = $\frac{-11}{42}$

RHS = ( $\frac{2}{3}$ - $\frac{2}{4}$ ) - ( $\frac{-5}{7}$ ) = ( $\frac{2}{3}$ - ( $\frac{2}{4}$ ) $\frac{+5}{7)}$

2x4	-	2x3	+	5
3x4	-	4x3	+	7

[LCM of 4 and 3 is 12] .....

8	-	-6	+	5	=	8-6	+	5	=	2	+	5
12		12		7		12		7		12		7

[LCM of 12 and 7 is 84]

2x7

2x3

14+(36)

\frac{25}{42}

12x7

12x3

RHS = $\frac{25}{42}$

LHS ≠ RHS

Hence, associative property is not true for subtraction.

10)

Verify whether associative property is satisfied for subtraction of the following pairs of rational numbers.(ples use /)

$\frac{1}{3}$ , $\frac{4}{4}$ and $\frac{-3}{8}$

LHS = Answer: $\frac{25}{-24}$

RHS = Answer: $\frac{7}{-24}$

SOLUTION 1 :

To verify,

( $\frac{1}{3}$ - ( $\frac{4}{4}$ - ( $\frac{-3}{8}$ )) = ( $\frac{1}{3}$ - $\frac{4}{4}$ ) - ( $\frac{-3}{8}$ )

LHS =

1	-	4	-	3	=	4x8	+	3x4
3	-	4	-	8	=	4x8	+	4x8

[ LCM of 4 and 8 is 32]

1	-	32	+	12
3	-	32	+	32

1	-	32+12	=	1	-	44	=	1x32	-	44x3
3	-	32	=	3	-	32	=	3x32	-	32x3

[LCM of 3 ans 32 is 96]

1x32

44x3

132

32- 132

-100

\frac{25}{-24}

32x3

LHS = $\frac{25}{-24}$

RHS = ( $\frac{1}{3}$ - $\frac{4}{4}$ ) - ( $\frac{-3}{8}$ ) = ( $\frac{1}{3}$ - ( $\frac{4}{4}$ ) $\frac{+3}{8)}$

1x4	-	4x3	+	3
3x4	-	4x3	+	8

[LCM of 4 and 3 is 12] .....

4	-	-12	+	3	=	4-12	+	3	=	-8	+	3
12		12		8		12		8		12		8

[LCM of 12 and 8 is 96]

-8x8

-8x3

-64

-64+(36)

-28

\frac{7}{-24}

12x8

12x3

RHS = $\frac{7}{-24}$

LHS ≠ RHS

Hence, associative property is not true for subtraction.