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 /)

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

LHS =

RHS =

Answer:_______________

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

$\frac{1}{3}$ , $\frac{4}{6}$ and $\frac{-5}{8}$

LHS =

RHS =

Answer:_______________

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

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

LHS =

RHS =

Answer:_______________

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

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

LHS =

RHS =

Answer:_______________

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

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

LHS =

RHS =

Answer:_______________

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

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

LHS =

RHS =

Answer:_______________

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

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

LHS =

RHS =

Answer:_______________

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

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

LHS =

RHS =

Answer:_______________

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

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

LHS =

RHS =

Answer:_______________

10)

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

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

LHS =

RHS =

Answer:_______________

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

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

LHS = Answer: $\frac{5}{12}$

RHS = Answer: $\frac{13}{12}$

SOLUTION 1 :

To verify,

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

LHS =

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

[ LCM of 4 and 6 is 24]

3	-	18	+	8
2	-	24	+	24

3	-	18+8	=	3	-	26	=	3x24	-	26x2
2	-	24	=	2	-	24	=	2x24	-	24x2

[LCM of 2 ans 24 is 48]

3x24	-	26x2	=	72	-	52	=	72- 52	=	20	=	$\frac{5}{12}$
24x2		24x2		48		48		48		48

LHS = $\frac{5}{12}$

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

3x4	-	3x2	+	3
2x4	-	4x2	+	6

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

12	-	-6	+	3	=	12-6	+	3	=	6	+	3
8		8		6		8		6		8		6

[LCM of 8 and 6 is 48]

6x6

6x2

36+(16)

\frac{13}{12}

8x6

8x2

RHS = $\frac{13}{12}$

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 /)

$\frac{1}{3}$ , $\frac{4}{6}$ and $\frac{-5}{8}$

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

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

SOLUTION 1 :

To verify,

( $\frac{1}{3}$ - ( $\frac{4}{6}$ - ( $\frac{-5}{8}$ )) = ( $\frac{1}{3}$ - $\frac{4}{6}$ ) - ( $\frac{-5}{8}$ )

LHS =

1	-	4	-	5	=	4x8	+	3x6
3	-	6	-	8	=	6x8	+	6x8

[ LCM of 6 and 8 is 48]

1	-	32	+	18
3	-	48	+	48

1	-	32+18	=	1	-	50	=	1x48	-	50x3
3	-	48	=	3	-	48	=	3x48	-	48x3

[LCM of 3 ans 48 is 144]

1x48

50x3

150

48- 150

-102

\frac{-17}{24}

48x3

144

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

RHS = ( $\frac{1}{3}$ - $\frac{4}{6}$ ) - ( $\frac{-5}{8}$ ) = ( $\frac{1}{3}$ - ( $\frac{4}{6}$ ) $\frac{+5}{8)}$

1x6	-	4x3	+	5
3x6	-	6x3	+	8

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

6	-	-12	+	5	=	6-12	+	5	=	-6	+	5
18		18		8		18		8		18		8

[LCM of 18 and 8 is 144]

-6x8

-6x3

-48

-48+(54)

\frac{1}{24}

18x8

18x3

144

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 /)

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

LHS = Answer: $\frac{101}{-140}$

RHS = Answer: $\frac{59}{140}$

SOLUTION 1 :

To verify,

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

LHS =

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

[ LCM of 5 and 7 is 35]

1	-	14	+	20
4	-	35	+	35

1	-	14+20	=	1	-	34	=	1x35	-	34x4
4	-	35	=	4	-	35	=	4x35	-	35x4

[LCM of 4 ans 35 is 140]

1x35

34x4

136

35- 136

-101

\frac{101}{-140}

35x4

140

LHS = $\frac{101}{-140}$

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

1x5	-	2x4	+	5
4x5	-	5x4	+	7

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

5	-	-8	+	5	=	5-8	+	5	=	-3	+	5
20		20		7		20		7		20		7

[LCM of 20 and 7 is 140]

-3x7

-3x4

-21

-21+(80)

\frac{59}{140}

20x7

20x4

140

RHS = $\frac{59}{140}$

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 /)

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

LHS = Answer: $\frac{-31}{140}$

RHS = Answer: $\frac{129}{140}$

SOLUTION 1 :

To verify,

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

LHS =

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

[ LCM of 5 and 7 is 35]

3	-	14	+	20
4	-	35	+	35

3	-	14+20	=	3	-	34	=	3x35	-	34x4
4	-	35	=	4	-	35	=	4x35	-	35x4

[LCM of 4 ans 35 is 140]

3x35

34x4

105

136

105- 136

-31

\frac{-31}{140}

35x4

140

LHS = $\frac{-31}{140}$

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

3x5	-	2x4	+	3
4x5	-	5x4	+	7

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

15	-	-8	+	3	=	15-8	+	3	=	7	+	3
20		20		7		20		7		20		7

[LCM of 20 and 7 is 140]

7x7

7x4

49+(80)

129

\frac{129}{140}

20x7

20x4

140

RHS = $\frac{129}{140}$

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 /)

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

LHS = Answer: $\frac{37}{-120}$

RHS = Answer: $\frac{53}{120}$

SOLUTION 1 :

To verify,

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

LHS =

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

[ LCM of 5 and 8 is 40]

2	-	24	+	15
3	-	40	+	40

2	-	24+15	=	2	-	39	=	2x40	-	39x3
3	-	40	=	3	-	40	=	3x40	-	40x3

[LCM of 3 ans 40 is 120]

2x40

39x3

117

80- 117

-37

\frac{37}{-120}

40x3

120

LHS = $\frac{37}{-120}$

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

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

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

10	-	-9	+	4	=	10-9	+	4	=	1	+	4
15		15		8		15		8		15		8

[LCM of 15 and 8 is 120]

1x8

1x3

8+(45)

\frac{53}{120}

15x8

15x3

120

RHS = $\frac{53}{120}$

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 /)

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

LHS = Answer: $\frac{1}{5}$

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

SOLUTION 1 :

To verify,

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

LHS =

2	-	2	-	3	=	2x5	+	2x5
2	-	5	-	5	=	5x5	+	5x5

[ LCM of 5 and 5 is 25]

2	-	10	+	10
2	-	25	+	25

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

[LCM of 2 ans 25 is 50]

2x25	-	20x2	=	50	-	40	=	50- 40	=	10	=	$\frac{1}{5}$
25x2		25x2		50		50		50		50

LHS = $\frac{1}{5}$

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

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

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

10	-	-4	+	3	=	10-4	+	3	=	6	+	3
10		10		5		10		5		10		5

[LCM of 10 and 5 is 50]

6x5

6x2

30+(20)

\frac{1}{1}

10x5

10x2

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

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 /)

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

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

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

SOLUTION 1 :

To verify,

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

LHS =

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

[ LCM of 4 and 6 is 24]

1	-	12	+	8
2	-	24	+	24

1	-	12+8	=	1	-	20	=	1x24	-	20x2
2	-	24	=	2	-	24	=	2x24	-	24x2

[LCM of 2 ans 24 is 48]

1x24	-	20x2	=	24	-	40	=	24- 40	=	-16	=	$\frac{1}{-3}$
24x2		24x2		48		48		48		48

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

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

1x4	-	2x2	+	2
2x4	-	4x2	+	6

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

4	-	-4	+	2	=	4-4	+	2	=	0	+	2
8		8		6		8		6		8		6

[LCM of 8 and 6 is 48]

0x6

0x2

0+(16)

\frac{1}{3}

8x6

8x2

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

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 /)

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

LHS = Answer: $\frac{-8}{35}$

RHS = Answer: $\frac{22}{35}$

SOLUTION 1 :

To verify,

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

LHS =

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

[ LCM of 5 and 7 is 35]

3	-	28	+	15
3	-	35	+	35

3	-	28+15	=	3	-	43	=	3x35	-	43x3
3	-	35	=	3	-	35	=	3x35	-	35x3

[LCM of 3 ans 35 is 105]

3x35

43x3

105

129

105- 129

-24

\frac{-8}{35}

35x3

105

LHS = $\frac{-8}{35}$

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

3x5	-	4x3	+	4
3x5	-	5x3	+	7

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

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

[LCM of 15 and 7 is 105]

3x7

3x3

21+(45)

\frac{22}{35}

15x7

15x3

105

RHS = $\frac{22}{35}$

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 $\frac{-5}{8}$

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

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

SOLUTION 1 :

To verify,

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

LHS =

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

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

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

12	-	-15	+	5	=	12-15	+	5	=	-3	+	5
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.

10)

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

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

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

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

SOLUTION 1 :

To verify,

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

LHS =

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

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

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

8	-	-9	+	4	=	8-9	+	4	=	-1	+	4
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.