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 /)

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

LHS =

RHS =

Answer:_______________

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

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

LHS =

RHS =

Answer:_______________

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

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

LHS =

RHS =

Answer:_______________

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

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

LHS =

RHS =

Answer:_______________

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

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

LHS =

RHS =

Answer:_______________

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

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

LHS =

RHS =

Answer:_______________

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

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

LHS =

RHS =

Answer:_______________

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

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

LHS =

RHS =

Answer:_______________

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

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

LHS =

RHS =

Answer:_______________

10)

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

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

LHS =

RHS =

Answer:_______________

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

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

LHS = Answer: $\frac{-17}{20}$

RHS = Answer: $\frac{7}{20}$

SOLUTION 1 :

To verify,

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

LHS =

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

[ LCM of 4 and 5 is 20]

3	-	25	+	12
3	-	20	+	20

3	-	25+12	=	3	-	37	=	3x20	-	37x3
3	-	20	=	3	-	20	=	3x20	-	20x3

[LCM of 3 ans 20 is 60]

3x20

37x3

111

60- 111

-51

\frac{-17}{20}

20x3

LHS = $\frac{-17}{20}$

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

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

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

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

[LCM of 12 and 5 is 60]

-3x5

-3x3

-15

-15+(36)

\frac{7}{20}

12x5

12x3

RHS = $\frac{7}{20}$

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 /)

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

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

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

SOLUTION 1 :

To verify,

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

LHS =

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

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

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

10	-	-15	+	3	=	10-15	+	3	=	-5	+	3
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 /)

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

LHS = Answer: $\frac{29}{70}$

RHS = Answer: $\frac{69}{70}$

SOLUTION 1 :

To verify,

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

LHS =

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

[ LCM of 5 and 7 is 35]

3	-	28	+	10
2	-	35	+	35

3	-	28+10	=	3	-	38	=	3x35	-	38x2
2	-	35	=	2	-	35	=	2x35	-	35x2

[LCM of 2 ans 35 is 70]

3x35	-	38x2	=	105	-	76	=	105- 76	=	29	=	$\frac{29}{70}$
35x2		35x2		70		70		70		70

LHS = $\frac{29}{70}$

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

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

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

15	-	-8	+	2	=	15-8	+	2	=	7	+	2
10		10		7		10		7		10		7

[LCM of 10 and 7 is 70]

7x7

7x2

49+(20)

\frac{69}{70}

10x7

10x2

RHS = $\frac{69}{70}$

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 /)

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

LHS = Answer: $\frac{7}{-10}$

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

SOLUTION 1 :

To verify,

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

LHS =

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

[ LCM of 5 and 5 is 25]

1	-	20	+	10
2	-	25	+	25

1	-	20+10	=	1	-	30	=	1x25	-	30x2
2	-	25	=	2	-	25	=	2x25	-	25x2

[LCM of 2 ans 25 is 50]

1x25	-	30x2	=	25	-	60	=	25- 60	=	-35	=	$\frac{7}{-10}$
25x2		25x2		50		50		50		50

LHS = $\frac{7}{-10}$

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

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

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

5	-	-8	+	3	=	5-8	+	3	=	-3	+	3
10		10		5		10		5		10		5

[LCM of 10 and 5 is 50]

-3x5

-3x2

-15

-15+(20)

\frac{1}{10}

10x5

10x2

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

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 /)

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

LHS = Answer: $\frac{43}{-60}$

RHS = Answer: $\frac{53}{60}$

SOLUTION 1 :

To verify,

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

LHS =

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

[ LCM of 6 and 5 is 30]

3	-	20	+	24
4	-	30	+	30

3	-	20+24	=	3	-	44	=	3x30	-	44x4
4	-	30	=	4	-	30	=	4x30	-	30x4

[LCM of 4 ans 30 is 120]

3x30

44x4

176

90- 176

-86

\frac{43}{-60}

30x4

120

LHS = $\frac{43}{-60}$

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

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

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

18	-	-16	+	3	=	18-16	+	3	=	2	+	3
24		24		5		24		5		24		5

[LCM of 24 and 5 is 120]

2x5

2x4

10+(96)

106

\frac{53}{60}

24x5

24x4

120

RHS = $\frac{53}{60}$

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 $\frac{-3}{8}$

LHS = Answer: $\frac{3}{20}$

RHS = Answer: 1 $\frac{3}{20}$

SOLUTION 1 :

To verify,

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

LHS =

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

[ LCM of 5 and 8 is 40]

2	-	24	+	10
2	-	40	+	40

2	-	24+10	=	2	-	34	=	2x40	-	34x2
2	-	40	=	2	-	40	=	2x40	-	40x2

[LCM of 2 ans 40 is 80]

2x40	-	34x2	=	80	-	68	=	80- 68	=	12	=	$\frac{3}{20}$
40x2		40x2		80		80		80		80

LHS = $\frac{3}{20}$

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

2x5	-	3x2	+	3
2x5	-	5x2	+	8

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

10	-	-6	+	3	=	10-6	+	3	=	4	+	3
10		10		8		10		8		10		8

[LCM of 10 and 8 is 80]

4x8

4x2

32+(20)

\frac{3}{20}

10x8

10x2

RHS = 1 $\frac{3}{20}$

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 /)

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

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

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

SOLUTION 1 :

To verify,

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

LHS =

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

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

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

12	-	-16	+	4	=	12-16	+	4	=	-4	+	4
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 /)

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

LHS = Answer: $\frac{8}{21}$

RHS = Answer: $\frac{20}{21}$

SOLUTION 1 :

To verify,

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

LHS =

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

[ LCM of 6 and 7 is 42]

3	-	35	+	12
2	-	42	+	42

3	-	35+12	=	3	-	47	=	3x42	-	47x2
2	-	42	=	2	-	42	=	2x42	-	42x2

[LCM of 2 ans 42 is 84]

3x42	-	47x2	=	126	-	94	=	126- 94	=	32	=	$\frac{8}{21}$
42x2		42x2		84		84		84		84

LHS = $\frac{8}{21}$

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

3x6	-	5x2	+	4
2x6	-	6x2	+	7

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

18	-	-10	+	4	=	18-10	+	4	=	8	+	4
12		12		7		12		7		12		7

[LCM of 12 and 7 is 84]

8x7

8x2

56+(24)

\frac{20}{21}

12x7

12x2

RHS = $\frac{20}{21}$

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 /)

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

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

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

SOLUTION 1 :

To verify,

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

LHS =

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

[ LCM of 5 and 8 is 40]

3	-	40	+	10
2	-	40	+	40

3	-	40+10	=	3	-	50	=	3x40	-	50x2
2	-	40	=	2	-	40	=	2x40	-	40x2

[LCM of 2 ans 40 is 80]

3x40

50x2

120

100

120- 100

\frac{1}{4}

40x2

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

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

3x5	-	5x2	+	3
2x5	-	5x2	+	8

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

15	-	-10	+	3	=	15-10	+	3	=	5	+	3
10		10		8		10		8		10		8

[LCM of 10 and 8 is 80]

5x8

5x2

40+(20)

\frac{3}{4}

10x8

10x2

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

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 /)

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

LHS = Answer: $\frac{17}{-12}$

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

SOLUTION 1 :

To verify,

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

LHS =

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

[ LCM of 4 and 6 is 24]

2	-	30	+	16
4	-	24	+	24

2	-	30+16	=	2	-	46	=	2x24	-	46x4
4	-	24	=	4	-	24	=	4x24	-	24x4

[LCM of 4 ans 24 is 96]

2x24

46x4

184

48- 184

-136

\frac{17}{-12}

24x4

LHS = $\frac{17}{-12}$

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

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

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

8	-	-20	+	2	=	8-20	+	2	=	-12	+	2
16		16		6		16		6		16		6

[LCM of 16 and 6 is 96]

-12x6

-12x4

-72

-72+(64)

-8

\frac{1}{-12}

16x6

16x4

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

LHS ≠ RHS

Hence, associative property is not true for subtraction.