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 /)

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

LHS =

RHS =

Answer:_______________

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

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

LHS =

RHS =

Answer:_______________

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

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

LHS =

RHS =

Answer:_______________

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

$\frac{1}{3}$ , $\frac{2}{6}$ and $\frac{-2}{7}$

LHS =

RHS =

Answer:_______________

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

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

LHS =

RHS =

Answer:_______________

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

$\frac{1}{4}$ , $\frac{2}{6}$ and $\frac{-4}{7}$

LHS =

RHS =

Answer:_______________

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

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

LHS =

RHS =

Answer:_______________

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

$\frac{1}{2}$ , $\frac{3}{5}$ and $\frac{-4}{7}$

LHS =

RHS =

Answer:_______________

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

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

LHS =

RHS =

Answer:_______________

10)

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

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

LHS =

RHS =

Answer:_______________

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

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

LHS = Answer: $\frac{11}{-24}$

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

SOLUTION 1 :

To verify,

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

LHS =

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

[ LCM of 4 and 8 is 32]

2	-	24	+	12
3	-	32	+	32

2	-	24+12	=	2	-	36	=	2x32	-	36x3
3	-	32	=	3	-	32	=	3x32	-	32x3

[LCM of 3 ans 32 is 96]

2x32

36x3

108

64- 108

-44

\frac{11}{-24}

32x3

LHS = $\frac{11}{-24}$

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

2x4	-	3x3	+	2
3x4	-	4x3	+	8

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

8	-	-9	+	2	=	8-9	+	2	=	-1	+	2
12		12		8		12		8		12		8

[LCM of 12 and 8 is 96]

-1x8

-1x3

-8

-8+(36)

\frac{7}{24}

12x8

12x3

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

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 /)

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

LHS = Answer: $\frac{-29}{30}$

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

SOLUTION 1 :

To verify,

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

LHS =

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

[ LCM of 6 and 5 is 30]

2	-	20	+	24
4	-	30	+	30

2	-	20+24	=	2	-	44	=	2x30	-	44x4
4	-	30	=	4	-	30	=	4x30	-	30x4

[LCM of 4 ans 30 is 120]

2x30

44x4

176

60- 176

-116

\frac{-29}{30}

30x4

120

LHS = $\frac{-29}{30}$

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

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

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

12	-	-16	+	5	=	12-16	+	5	=	-4	+	5
24		24		5		24		5		24		5

[LCM of 24 and 5 is 120]

-4x5

-4x4

-20

-20+(96)

\frac{19}{30}

24x5

24x4

120

RHS = $\frac{19}{30}$

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 /)

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

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

RHS = Answer: $\frac{17}{30}$

SOLUTION 1 :

To verify,

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

LHS =

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

[ LCM of 6 and 5 is 30]

2	-	25	+	12
2	-	30	+	30

2	-	25+12	=	2	-	37	=	2x30	-	37x2
2	-	30	=	2	-	30	=	2x30	-	30x2

[LCM of 2 ans 30 is 60]

2x30	-	37x2	=	60	-	74	=	60- 74	=	-14	=	$\frac{7}{-30}$
30x2		30x2		60		60		60		60

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

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

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

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

12	-	-10	+	5	=	12-10	+	5	=	2	+	5
12		12		5		12		5		12		5

[LCM of 12 and 5 is 60]

2x5

2x2

10+(24)

\frac{17}{30}

12x5

12x2

RHS = $\frac{17}{30}$

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 /)

$\frac{1}{3}$ , $\frac{2}{6}$ and $\frac{-2}{7}$

LHS = Answer: $\frac{-3}{7}$

RHS = Answer: $\frac{3}{7}$

SOLUTION 1 :

To verify,

( $\frac{1}{3}$ - ( $\frac{2}{6}$ - ( $\frac{-2}{7}$ )) = ( $\frac{1}{3}$ - $\frac{2}{6}$ ) - ( $\frac{-2}{7}$ )

LHS =

1	-	2	-	2	=	2x7	+	3x6
3	-	6	-	7	=	6x7	+	6x7

[ LCM of 6 and 7 is 42]

1	-	14	+	18
3	-	42	+	42

1	-	14+18	=	1	-	32	=	1x42	-	32x3
3	-	42	=	3	-	42	=	3x42	-	42x3

[LCM of 3 ans 42 is 126]

1x42

32x3

42- 96

-54

\frac{-3}{7}

42x3

126

LHS = $\frac{-3}{7}$

RHS = ( $\frac{1}{3}$ - $\frac{2}{6}$ ) - ( $\frac{-2}{7}$ ) = ( $\frac{1}{3}$ - ( $\frac{2}{6}$ ) $\frac{+2}{7)}$

1x6	-	2x3	+	2
3x6	-	6x3	+	7

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

6	-	-6	+	2	=	6-6	+	2	=	0	+	2
18		18		7		18		7		18		7

[LCM of 18 and 7 is 126]

0x7

0x3

0+(54)

\frac{3}{7}

18x7

18x3

126

RHS = $\frac{3}{7}$

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 /)

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

LHS = Answer: $\frac{85}{-84}$

RHS = Answer: $\frac{13}{-84}$

SOLUTION 1 :

To verify,

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

LHS =

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

[ LCM of 4 and 7 is 28]

2	-	35	+	12
3	-	28	+	28

2	-	35+12	=	2	-	47	=	2x28	-	47x3
3	-	28	=	3	-	28	=	3x28	-	28x3

[LCM of 3 ans 28 is 84]

2x28

47x3

141

56- 141

-85

\frac{85}{-84}

28x3

LHS = $\frac{85}{-84}$

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

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

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

8	-	-15	+	3	=	8-15	+	3	=	-7	+	3
12		12		7		12		7		12		7

[LCM of 12 and 7 is 84]

-7x7

-7x3

-49

-49+(36)

-13

\frac{13}{-84}

12x7

12x3

RHS = $\frac{13}{-84}$

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 /)

$\frac{1}{4}$ , $\frac{2}{6}$ and $\frac{-4}{7}$

LHS = Answer: $\frac{-55}{84}$

RHS = Answer: $\frac{41}{84}$

SOLUTION 1 :

To verify,

( $\frac{1}{4}$ - ( $\frac{2}{6}$ - ( $\frac{-4}{7}$ )) = ( $\frac{1}{4}$ - $\frac{2}{6}$ ) - ( $\frac{-4}{7}$ )

LHS =

1	-	2	-	4	=	2x7	+	4x6
4	-	6	-	7	=	6x7	+	6x7

[ LCM of 6 and 7 is 42]

1	-	14	+	24
4	-	42	+	42

1	-	14+24	=	1	-	38	=	1x42	-	38x4
4	-	42	=	4	-	42	=	4x42	-	42x4

[LCM of 4 ans 42 is 168]

1x42

38x4

152

42- 152

-110

\frac{-55}{84}

42x4

168

LHS = $\frac{-55}{84}$

RHS = ( $\frac{1}{4}$ - $\frac{2}{6}$ ) - ( $\frac{-4}{7}$ ) = ( $\frac{1}{4}$ - ( $\frac{2}{6}$ ) $\frac{+4}{7)}$

1x6	-	2x4	+	4
4x6	-	6x4	+	7

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

6	-	-8	+	4	=	6-8	+	4	=	-2	+	4
24		24		7		24		7		24		7

[LCM of 24 and 7 is 168]

-2x7

-2x4

-14

-14+(96)

\frac{41}{84}

24x7

24x4

168

RHS = $\frac{41}{84}$

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 $\frac{-2}{6}$

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

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

SOLUTION 1 :

To verify,

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

LHS =

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

[ LCM of 5 and 6 is 30]

2	-	30	+	15
3	-	30	+	30

2	-	30+15	=	2	-	45	=	2x30	-	45x3
3	-	30	=	3	-	30	=	3x30	-	30x3

[LCM of 3 ans 30 is 90]

2x30

45x3

135

60- 135

-75

\frac{-5}{6}

30x3

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

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

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

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

10	-	-15	+	2	=	10-15	+	2	=	-5	+	2
15		15		6		15		6		15		6

[LCM of 15 and 6 is 90]

-5x6

-5x3

-30

-30+(45)

\frac{1}{6}

15x6

15x3

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 /)

$\frac{1}{2}$ , $\frac{3}{5}$ and $\frac{-4}{7}$

LHS = Answer: $\frac{27}{-70}$

RHS = Answer: $\frac{13}{70}$

SOLUTION 1 :

To verify,

( $\frac{1}{2}$ - ( $\frac{3}{5}$ - ( $\frac{-4}{7}$ )) = ( $\frac{1}{2}$ - $\frac{3}{5}$ ) - ( $\frac{-4}{7}$ )

LHS =

1	-	3	-	4	=	3x7	+	2x5
2	-	5	-	7	=	5x7	+	5x7

[ LCM of 5 and 7 is 35]

1	-	21	+	10
2	-	35	+	35

1	-	21+10	=	1	-	31	=	1x35	-	31x2
2	-	35	=	2	-	35	=	2x35	-	35x2

[LCM of 2 ans 35 is 70]

1x35	-	31x2	=	35	-	62	=	35- 62	=	-27	=	$\frac{27}{-70}$
35x2		35x2		70		70		70		70

LHS = $\frac{27}{-70}$

RHS = ( $\frac{1}{2}$ - $\frac{3}{5}$ ) - ( $\frac{-4}{7}$ ) = ( $\frac{1}{2}$ - ( $\frac{3}{5}$ ) $\frac{+4}{7)}$

1x5	-	3x2	+	4
2x5	-	5x2	+	7

[LCM of 5 and 2 is 10] .....

5	-	-6	+	4	=	5-6	+	4	=	-1	+	4
10		10		7		10		7		10		7

[LCM of 10 and 7 is 70]

-1x7

-1x2

-7

-7+(20)

\frac{13}{70}

10x7

10x2

RHS = $\frac{13}{70}$

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 /)

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

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

RHS = Answer: $\frac{7}{6}$

SOLUTION 1 :

To verify,

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

LHS =

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

[ LCM of 6 and 6 is 36]

3	-	12	+	18
3	-	36	+	36

3	-	12+18	=	3	-	30	=	3x36	-	30x3
3	-	36	=	3	-	36	=	3x36	-	36x3

[LCM of 3 ans 36 is 108]

3x36

30x3

108

108- 90

\frac{1}{6}

36x3

108

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

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

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

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

18	-	-6	+	5	=	18-6	+	5	=	12	+	5
18		18		6		18		6		18		6

[LCM of 18 and 6 is 108]

12x6

12x3

72+(54)

126

\frac{7}{6}

18x6

18x3

108

RHS = $\frac{7}{6}$

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 /)

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

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

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

SOLUTION 1 :

To verify,

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

LHS =

2	-	2	-	5	=	2x6	+	2x4
2	-	4	-	6	=	4x6	+	4x6

[ LCM of 4 and 6 is 24]

2	-	12	+	8
2	-	24	+	24

2	-	12+8	=	2	-	20	=	2x24	-	20x2
2	-	24	=	2	-	24	=	2x24	-	24x2

[LCM of 2 ans 24 is 48]

2x24	-	20x2	=	48	-	40	=	48- 40	=	8	=	$\frac{1}{6}$
24x2		24x2		48		48		48		48

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

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

2x4	-	2x2	+	5
2x4	-	4x2	+	6

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

8	-	-4	+	5	=	8-4	+	5	=	4	+	5
8		8		6		8		6		8		6

[LCM of 8 and 6 is 48]

4x6

4x2

24+(16)

\frac{5}{6}

8x6

8x2

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

LHS ≠ RHS

Hence, associative property is not true for subtraction.