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 /)

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

LHS =

RHS =

Answer:_______________

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

$\frac{2}{2}$ , $\frac{3}{4}$ and $\frac{-5}{8}$

LHS =

RHS =

Answer:_______________

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

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

LHS =

RHS =

Answer:_______________

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

$\frac{2}{3}$ , $\frac{5}{6}$ and $\frac{-4}{8}$

LHS =

RHS =

Answer:_______________

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

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

LHS =

RHS =

Answer:_______________

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

$\frac{2}{3}$ , $\frac{5}{5}$ and $\frac{-5}{8}$

LHS =

RHS =

Answer:_______________

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

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

LHS =

RHS =

Answer:_______________

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

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

LHS =

RHS =

Answer:_______________

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

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

LHS =

RHS =

Answer:_______________

10)

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

$\frac{1}{4}$ , $\frac{3}{6}$ and $\frac{-2}{5}$

LHS =

RHS =

Answer:_______________

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

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

LHS = Answer: $\frac{-17}{105}$

RHS = Answer: $\frac{73}{105}$

SOLUTION 1 :

To verify,

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

LHS =

2	-	2	-	2	=	2x7	+	3x5
3	-	5	-	7	=	5x7	+	5x7

[ LCM of 5 and 7 is 35]

2	-	14	+	15
3	-	35	+	35

2	-	14+15	=	2	-	29	=	2x35	-	29x3
3	-	35	=	3	-	35	=	3x35	-	35x3

[LCM of 3 ans 35 is 105]

2x35

29x3

70- 87

-17

\frac{-17}{105}

35x3

105

LHS = $\frac{-17}{105}$

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

2x5	-	2x3	+	2
3x5	-	5x3	+	7

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

10	-	-6	+	2	=	10-6	+	2	=	4	+	2
15		15		7		15		7		15		7

[LCM of 15 and 7 is 105]

4x7

4x3

28+(45)

\frac{73}{105}

15x7

15x3

105

RHS = $\frac{73}{105}$

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 /)

$\frac{2}{2}$ , $\frac{3}{4}$ and $\frac{-5}{8}$

LHS = Answer: $\frac{0}{1}$

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

SOLUTION 1 :

To verify,

( $\frac{2}{2}$ - ( $\frac{3}{4}$ - ( $\frac{-5}{8}$ )) = ( $\frac{2}{2}$ - $\frac{3}{4}$ ) - ( $\frac{-5}{8}$ )

LHS =

2	-	3	-	5	=	3x8	+	2x4
2	-	4	-	8	=	4x8	+	4x8

[ LCM of 4 and 8 is 32]

2	-	24	+	8
2	-	32	+	32

2	-	24+8	=	2	-	32	=	2x32	-	32x2
2	-	32	=	2	-	32	=	2x32	-	32x2

[LCM of 2 ans 32 is 64]

2x32	-	32x2	=	64	-	64	=	64- 64	=	0	=	$\frac{0}{1}$
32x2		32x2		64		64		64		64

LHS = $\frac{0}{1}$

RHS = ( $\frac{2}{2}$ - $\frac{3}{4}$ ) - ( $\frac{-5}{8}$ ) = ( $\frac{2}{2}$ - ( $\frac{3}{4}$ ) $\frac{+5}{8)}$

2x4	-	3x2	+	5
2x4	-	4x2	+	8

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

8	-	-6	+	5	=	8-6	+	5	=	2	+	5
8		8		8		8		8		8		8

[LCM of 8 and 8 is 64]

2x8

2x2

16+(16)

\frac{1}{2}

8x8

8x2

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 /)

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

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

RHS = Answer: $\frac{0}{1}$

SOLUTION 1 :

To verify,

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

LHS =

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

[ LCM of 4 and 8 is 32]

1	-	24	+	16
4	-	32	+	32

1	-	24+16	=	1	-	40	=	1x32	-	40x4
4	-	32	=	4	-	32	=	4x32	-	32x4

[LCM of 4 ans 32 is 128]

1x32

40x4

160

32- 160

-128

\frac{-1}{1}

32x4

128

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

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

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

[LCM of 4 and 4 is 16] .....

4	-	-12	+	4	=	4-12	+	4	=	-8	+	4
16		16		8		16		8		16		8

[LCM of 16 and 8 is 128]

-8x8

-8x4

-64

-64+(64)

\frac{0}{1}

16x8

16x4

128

RHS = $\frac{0}{1}$

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 /)

$\frac{2}{3}$ , $\frac{5}{6}$ and $\frac{-4}{8}$

LHS = Answer: $\frac{-13}{24}$

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

SOLUTION 1 :

To verify,

( $\frac{2}{3}$ - ( $\frac{5}{6}$ - ( $\frac{-4}{8}$ )) = ( $\frac{2}{3}$ - $\frac{5}{6}$ ) - ( $\frac{-4}{8}$ )

LHS =

2	-	5	-	4	=	5x8	+	3x6
3	-	6	-	8	=	6x8	+	6x8

[ LCM of 6 and 8 is 48]

2	-	40	+	18
3	-	48	+	48

2	-	40+18	=	2	-	58	=	2x48	-	58x3
3	-	48	=	3	-	48	=	3x48	-	48x3

[LCM of 3 ans 48 is 144]

2x48

58x3

174

96- 174

-78

\frac{-13}{24}

48x3

144

LHS = $\frac{-13}{24}$

RHS = ( $\frac{2}{3}$ - $\frac{5}{6}$ ) - ( $\frac{-4}{8}$ ) = ( $\frac{2}{3}$ - ( $\frac{5}{6}$ ) $\frac{+4}{8)}$

2x6	-	5x3	+	4
3x6	-	6x3	+	8

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

12	-	-15	+	4	=	12-15	+	4	=	-3	+	4
18		18		8		18		8		18		8

[LCM of 18 and 8 is 144]

-3x8

-3x3

-24

-24+(54)

\frac{5}{24}

18x8

18x3

144

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

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 /)

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

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

RHS = Answer: $\frac{47}{30}$

SOLUTION 1 :

To verify,

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

LHS =

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

[ LCM of 6 and 5 is 30]

3	-	10	+	12
2	-	30	+	30

3	-	10+12	=	3	-	22	=	3x30	-	22x2
2	-	30	=	2	-	30	=	2x30	-	30x2

[LCM of 2 ans 30 is 60]

3x30	-	22x2	=	90	-	44	=	90- 44	=	46	=	$\frac{23}{30}$
30x2		30x2		60		60		60		60

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

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

3x6	-	2x2	+	5
2x6	-	6x2	+	5

[LCM of 6 and 2 is 12] .....

18	-	-4	+	5	=	18-4	+	5	=	14	+	5
12		12		5		12		5		12		5

[LCM of 12 and 5 is 60]

14x5

14x2

70+(24)

\frac{47}{30}

12x5

12x2

RHS = $\frac{47}{30}$

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 /)

$\frac{2}{3}$ , $\frac{5}{5}$ and $\frac{-5}{8}$

LHS = Answer: $\frac{-17}{24}$

RHS = Answer: $\frac{1}{24}$

SOLUTION 1 :

To verify,

( $\frac{2}{3}$ - ( $\frac{5}{5}$ - ( $\frac{-5}{8}$ )) = ( $\frac{2}{3}$ - $\frac{5}{5}$ ) - ( $\frac{-5}{8}$ )

LHS =

2	-	5	-	5	=	5x8	+	3x5
3	-	5	-	8	=	5x8	+	5x8

[ LCM of 5 and 8 is 40]

2	-	40	+	15
3	-	40	+	40

2	-	40+15	=	2	-	55	=	2x40	-	55x3
3	-	40	=	3	-	40	=	3x40	-	40x3

[LCM of 3 ans 40 is 120]

2x40

55x3

165

80- 165

-85

\frac{-17}{24}

40x3

120

LHS = $\frac{-17}{24}$

RHS = ( $\frac{2}{3}$ - $\frac{5}{5}$ ) - ( $\frac{-5}{8}$ ) = ( $\frac{2}{3}$ - ( $\frac{5}{5}$ ) $\frac{+5}{8)}$

2x5	-	5x3	+	5
3x5	-	5x3	+	8

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

10	-	-15	+	5	=	10-15	+	5	=	-5	+	5
15		15		8		15		8		15		8

[LCM of 15 and 8 is 120]

-5x8

-5x3

-40

-40+(45)

\frac{1}{24}

15x8

15x3

120

RHS = $\frac{1}{24}$

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 /)

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

LHS = Answer: $\frac{-5}{6}$

RHS = Answer: $\frac{1}{6}$

SOLUTION 1 :

To verify,

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

LHS =

2	-	4	-	4	=	4x6	+	3x4
3	-	4	-	6	=	4x6	+	4x6

[ LCM of 4 and 6 is 24]

2	-	24	+	12
3	-	24	+	24

2	-	24+12	=	2	-	36	=	2x24	-	36x3
3	-	24	=	3	-	24	=	3x24	-	24x3

[LCM of 3 ans 24 is 72]

2x24

36x3

108

48- 108

-60

\frac{-5}{6}

24x3

LHS = $\frac{-5}{6}$

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

2x4	-	4x3	+	4
3x4	-	4x3	+	6

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

8	-	-12	+	4	=	8-12	+	4	=	-4	+	4
12		12		6		12		6		12		6

[LCM of 12 and 6 is 72]

-4x6

-4x3

-24

-24+(36)

\frac{1}{6}

12x6

12x3

RHS = $\frac{1}{6}$

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 /)

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

LHS = Answer: $\frac{23}{-28}$

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

SOLUTION 1 :

To verify,

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

LHS =

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

[ LCM of 4 and 7 is 28]

3	-	28	+	16
4	-	28	+	28

3	-	28+16	=	3	-	44	=	3x28	-	44x4
4	-	28	=	4	-	28	=	4x28	-	28x4

[LCM of 4 ans 28 is 112]

3x28

44x4

176

84- 176

-92

\frac{23}{-28}

28x4

112

LHS = $\frac{23}{-28}$

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

3x4	-	4x4	+	2
4x4	-	4x4	+	7

[LCM of 4 and 4 is 16] .....

12	-	-16	+	2	=	12-16	+	2	=	-4	+	2
16		16		7		16		7		16		7

[LCM of 16 and 7 is 112]

-4x7

-4x4

-28

-28+(64)

\frac{9}{28}

16x7

16x4

112

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

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 /)

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

LHS = Answer: $\frac{1}{10}$

RHS = Answer: $\frac{9}{10}$

SOLUTION 1 :

To verify,

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

LHS =

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

[ LCM of 6 and 5 is 30]

2	-	15	+	12
2	-	30	+	30

2	-	15+12	=	2	-	27	=	2x30	-	27x2
2	-	30	=	2	-	30	=	2x30	-	30x2

[LCM of 2 ans 30 is 60]

2x30	-	27x2	=	60	-	54	=	60- 54	=	6	=	$\frac{1}{10}$
30x2		30x2		60		60		60		60

LHS = $\frac{1}{10}$

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

2x6	-	3x2	+	2
2x6	-	6x2	+	5

[LCM of 6 and 2 is 12] .....

12	-	-6	+	2	=	12-6	+	2	=	6	+	2
12		12		5		12		5		12		5

[LCM of 12 and 5 is 60]

6x5

6x2

30+(24)

\frac{9}{10}

12x5

12x2

RHS = $\frac{9}{10}$

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 /)

$\frac{1}{4}$ , $\frac{3}{6}$ and $\frac{-2}{5}$

LHS = Answer: $\frac{21}{-20}$

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

SOLUTION 1 :

To verify,

( $\frac{1}{4}$ - ( $\frac{3}{6}$ - ( $\frac{-2}{5}$ )) = ( $\frac{1}{4}$ - $\frac{3}{6}$ ) - ( $\frac{-2}{5}$ )

LHS =

1	-	3	-	2	=	3x5	+	4x6
4	-	6	-	5	=	6x5	+	6x5

[ LCM of 6 and 5 is 30]

1	-	15	+	24
4	-	30	+	30

1	-	15+24	=	1	-	39	=	1x30	-	39x4
4	-	30	=	4	-	30	=	4x30	-	30x4

[LCM of 4 ans 30 is 120]

1x30

39x4

156

30- 156

-126

\frac{21}{-20}

30x4

120

LHS = $\frac{21}{-20}$

RHS = ( $\frac{1}{4}$ - $\frac{3}{6}$ ) - ( $\frac{-2}{5}$ ) = ( $\frac{1}{4}$ - ( $\frac{3}{6}$ ) $\frac{+2}{5)}$

1x6	-	3x4	+	2
4x6	-	6x4	+	5

[LCM of 6 and 4 is 24] .....

6	-	-12	+	2	=	6-12	+	2	=	-6	+	2
24		24		5		24		5		24		5

[LCM of 24 and 5 is 120]

-6x5

-6x4

-30

-30+(96)

\frac{11}{20}

24x5

24x4

120

RHS = $\frac{11}{20}$

LHS ≠ RHS

Hence, associative property is not true for subtraction.