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 /)

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

LHS =

RHS =

Answer:_______________

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

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

LHS =

RHS =

Answer:_______________

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

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

LHS =

RHS =

Answer:_______________

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

$\frac{1}{3}$ , $\frac{5}{6}$ and $\frac{-2}{7}$

LHS =

RHS =

Answer:_______________

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

$\frac{1}{4}$ , $\frac{5}{4}$ and $\frac{-2}{8}$

LHS =

RHS =

Answer:_______________

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

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

LHS =

RHS =

Answer:_______________

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

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

LHS =

RHS =

Answer:_______________

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

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

LHS =

RHS =

Answer:_______________

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

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

LHS =

RHS =

Answer:_______________

10)

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

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

LHS =

RHS =

Answer:_______________

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

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

LHS = Answer: $\frac{7}{-20}$

RHS = Answer: $\frac{13}{20}$

SOLUTION 1 :

To verify,

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

LHS =

3	-	3	-	4	=	3x8	+	4x5
4	-	5	-	8	=	5x8	+	5x8

[ LCM of 5 and 8 is 40]

3	-	24	+	20
4	-	40	+	40

3	-	24+20	=	3	-	44	=	3x40	-	44x4
4	-	40	=	4	-	40	=	4x40	-	40x4

[LCM of 4 ans 40 is 160]

3x40

44x4

120

176

120- 176

-56

\frac{7}{-20}

40x4

160

LHS = $\frac{7}{-20}$

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

3x5	-	3x4	+	4
4x5	-	5x4	+	8

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

15	-	-12	+	4	=	15-12	+	4	=	3	+	4
20		20		8		20		8		20		8

[LCM of 20 and 8 is 160]

3x8

3x4

24+(80)

104

\frac{13}{20}

20x8

20x4

160

RHS = $\frac{13}{20}$

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 /)

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

LHS = Answer: $\frac{1}{-12}$

RHS = Answer: $\frac{11}{12}$

SOLUTION 1 :

To verify,

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

LHS =

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

[ LCM of 6 and 8 is 48]

3	-	16	+	24
4	-	48	+	48

3	-	16+24	=	3	-	40	=	3x48	-	40x4
4	-	48	=	4	-	48	=	4x48	-	48x4

[LCM of 4 ans 48 is 192]

3x48

40x4

144

160

144- 160

-16

\frac{1}{-12}

48x4

192

LHS = $\frac{1}{-12}$

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

3x6	-	2x4	+	2
4x6	-	6x4	+	8

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

18	-	-8	+	2	=	18-8	+	2	=	10	+	2
24		24		8		24		8		24		8

[LCM of 24 and 8 is 192]

10x8

10x4

80+(96)

176

\frac{11}{12}

24x8

24x4

192

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

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 $\frac{-2}{8}$

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

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

SOLUTION 1 :

To verify,

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

LHS =

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

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

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

12	-	-15	+	2	=	12-15	+	2	=	-3	+	2
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 /)

$\frac{1}{3}$ , $\frac{5}{6}$ and $\frac{-2}{7}$

LHS = Answer: $\frac{-13}{14}$

RHS = Answer: $\frac{1}{-14}$

SOLUTION 1 :

To verify,

( $\frac{1}{3}$ - ( $\frac{5}{6}$ - ( $\frac{-2}{7}$ )) = ( $\frac{1}{3}$ - $\frac{5}{6}$ ) - ( $\frac{-2}{7}$ )

LHS =

1	-	5	-	2	=	5x7	+	3x6
3	-	6	-	7	=	6x7	+	6x7

[ LCM of 6 and 7 is 42]

1	-	35	+	18
3	-	42	+	42

1	-	35+18	=	1	-	53	=	1x42	-	53x3
3	-	42	=	3	-	42	=	3x42	-	42x3

[LCM of 3 ans 42 is 126]

1x42

53x3

159

42- 159

-117

\frac{-13}{14}

42x3

126

LHS = $\frac{-13}{14}$

RHS = ( $\frac{1}{3}$ - $\frac{5}{6}$ ) - ( $\frac{-2}{7}$ ) = ( $\frac{1}{3}$ - ( $\frac{5}{6}$ ) $\frac{+2}{7)}$

1x6	-	5x3	+	2
3x6	-	6x3	+	7

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

6	-	-15	+	2	=	6-15	+	2	=	-9	+	2
18		18		7		18		7		18		7

[LCM of 18 and 7 is 126]

-9x7

-9x3

-63

-63+(54)

-9

\frac{1}{-14}

18x7

18x3

126

RHS = $\frac{1}{-14}$

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 /)

$\frac{1}{4}$ , $\frac{5}{4}$ and $\frac{-2}{8}$

LHS = Answer: $\frac{3}{-2}$

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

SOLUTION 1 :

To verify,

( $\frac{1}{4}$ - ( $\frac{5}{4}$ - ( $\frac{-2}{8}$ )) = ( $\frac{1}{4}$ - $\frac{5}{4}$ ) - ( $\frac{-2}{8}$ )

LHS =

1	-	5	-	2	=	5x8	+	4x4
4	-	4	-	8	=	4x8	+	4x8

[ LCM of 4 and 8 is 32]

1	-	40	+	16
4	-	32	+	32

1	-	40+16	=	1	-	56	=	1x32	-	56x4
4	-	32	=	4	-	32	=	4x32	-	32x4

[LCM of 4 ans 32 is 128]

1x32

56x4

224

32- 224

-192

\frac{3}{-2}

32x4

128

LHS = $\frac{3}{-2}$

RHS = ( $\frac{1}{4}$ - $\frac{5}{4}$ ) - ( $\frac{-2}{8}$ ) = ( $\frac{1}{4}$ - ( $\frac{5}{4}$ ) $\frac{+2}{8)}$

1x4	-	5x4	+	2
4x4	-	4x4	+	8

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

4	-	-20	+	2	=	4-20	+	2	=	-16	+	2
16		16		8		16		8		16		8

[LCM of 16 and 8 is 128]

-16x8

-16x4

-128

-128+(64)

-64

\frac{1}{-2}

16x8

16x4

128

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 /)

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

LHS = Answer: $\frac{1}{15}$

RHS = Answer: 1 $\frac{1}{15}$

SOLUTION 1 :

To verify,

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

LHS =

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

[ LCM of 5 and 6 is 30]

2	-	18	+	10
2	-	30	+	30

2	-	18+10	=	2	-	28	=	2x30	-	28x2
2	-	30	=	2	-	30	=	2x30	-	30x2

[LCM of 2 ans 30 is 60]

2x30	-	28x2	=	60	-	56	=	60- 56	=	4	=	$\frac{1}{15}$
30x2		30x2		60		60		60		60

LHS = $\frac{1}{15}$

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

2x5	-	3x2	+	2
2x5	-	5x2	+	6

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

10	-	-6	+	2	=	10-6	+	2	=	4	+	2
10		10		6		10		6		10		6

[LCM of 10 and 6 is 60]

4x6

4x2

24+(20)

\frac{1}{15}

10x6

10x2

RHS = 1 $\frac{1}{15}$

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 /)

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

LHS = Answer: $\frac{-61}{120}$

RHS = Answer: $\frac{29}{120}$

SOLUTION 1 :

To verify,

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

LHS =

2	-	4	-	3	=	4x8	+	3x5
3	-	5	-	8	=	5x8	+	5x8

[ LCM of 5 and 8 is 40]

2	-	32	+	15
3	-	40	+	40

2	-	32+15	=	2	-	47	=	2x40	-	47x3
3	-	40	=	3	-	40	=	3x40	-	40x3

[LCM of 3 ans 40 is 120]

2x40

47x3

141

80- 141

-61

\frac{-61}{120}

40x3

120

LHS = $\frac{-61}{120}$

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

2x5	-	4x3	+	3
3x5	-	5x3	+	8

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

10	-	-12	+	3	=	10-12	+	3	=	-2	+	3
15		15		8		15		8		15		8

[LCM of 15 and 8 is 120]

-2x8

-2x3

-16

-16+(45)

\frac{29}{120}

15x8

15x3

120

RHS = $\frac{29}{120}$

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 /)

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

LHS = Answer: $\frac{-5}{8}$

RHS = Answer: $\frac{1}{8}$

SOLUTION 1 :

To verify,

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

LHS =

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

[ LCM of 4 and 8 is 32]

3	-	40	+	12
3	-	32	+	32

3	-	40+12	=	3	-	52	=	3x32	-	52x3
3	-	32	=	3	-	32	=	3x32	-	32x3

[LCM of 3 ans 32 is 96]

3x32

52x3

156

96- 156

-60

\frac{-5}{8}

32x3

LHS = $\frac{-5}{8}$

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

3x4	-	5x3	+	3
3x4	-	4x3	+	8

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

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

[LCM of 12 and 8 is 96]

-3x8

-3x3

-24

-24+(36)

\frac{1}{8}

12x8

12x3

RHS = $\frac{1}{8}$

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 $\frac{-3}{7}$

LHS = Answer: $\frac{37}{42}$

RHS = Answer: $\frac{61}{42}$

SOLUTION 1 :

To verify,

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

LHS =

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

[ LCM of 6 and 7 is 42]

3	-	14	+	12
2	-	42	+	42

3	-	14+12	=	3	-	26	=	3x42	-	26x2
2	-	42	=	2	-	42	=	2x42	-	42x2

[LCM of 2 ans 42 is 84]

3x42	-	26x2	=	126	-	52	=	126- 52	=	74	=	$\frac{37}{42}$
42x2		42x2		84		84		84		84

LHS = $\frac{37}{42}$

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

3x6	-	2x2	+	3
2x6	-	6x2	+	7

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

18	-	-4	+	3	=	18-4	+	3	=	14	+	3
12		12		7		12		7		12		7

[LCM of 12 and 7 is 84]

14x7

14x2

98+(24)

122

\frac{61}{42}

12x7

12x2

RHS = $\frac{61}{42}$

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 /)

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

LHS = Answer: - $\frac{2}{5}$

RHS = Answer: $\frac{3}{5}$

SOLUTION 1 :

To verify,

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

LHS =

2	-	2	-	5	=	2x8	+	4x5
4	-	5	-	8	=	5x8	+	5x8

[ LCM of 5 and 8 is 40]

2	-	16	+	20
4	-	40	+	40

2	-	16+20	=	2	-	36	=	2x40	-	36x4
4	-	40	=	4	-	40	=	4x40	-	40x4

[LCM of 4 ans 40 is 160]

2x40

36x4

144

80- 144

-64

\frac{2}{5}

40x4

160

LHS = - $\frac{2}{5}$

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

2x5	-	2x4	+	5
4x5	-	5x4	+	8

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

10	-	-8	+	5	=	10-8	+	5	=	2	+	5
20		20		8		20		8		20		8

[LCM of 20 and 8 is 160]

2x8

2x4

16+(80)

\frac{3}{5}

20x8

20x4

160

RHS = $\frac{3}{5}$

LHS ≠ RHS

Hence, associative property is not true for subtraction.