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 /)

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

LHS =

RHS =

Answer:_______________

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

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

LHS =

RHS =

Answer:_______________

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

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

LHS =

RHS =

Answer:_______________

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

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

LHS =

RHS =

Answer:_______________

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

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

LHS =

RHS =

Answer:_______________

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

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

LHS =

RHS =

Answer:_______________

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

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

LHS =

RHS =

Answer:_______________

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

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

LHS =

RHS =

Answer:_______________

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

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

LHS =

RHS =

Answer:_______________

10)

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

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

LHS =

RHS =

Answer:_______________

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

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

LHS = Answer: $\frac{5}{-24}$

RHS = Answer: $\frac{13}{24}$

SOLUTION 1 :

To verify,

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

LHS =

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

[ LCM of 4 and 8 is 32]

2	-	16	+	12
3	-	32	+	32

2	-	16+12	=	2	-	28	=	2x32	-	28x3
3	-	32	=	3	-	32	=	3x32	-	32x3

[LCM of 3 ans 32 is 96]

2x32	-	28x3	=	64	-	84	=	64- 84	=	-20	=	$\frac{5}{-24}$
32x3		32x3		96		96		96		96

LHS = $\frac{5}{-24}$

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

2x4	-	2x3	+	5
3x4	-	4x3	+	8

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

8	-	-6	+	5	=	8-6	+	5	=	2	+	5
12		12		8		12		8		12		8

[LCM of 12 and 8 is 96]

2x8

2x3

16+(36)

\frac{13}{24}

12x8

12x3

RHS = $\frac{13}{24}$

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 /)

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

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

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

SOLUTION 1 :

To verify,

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

LHS =

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

[ LCM of 4 and 8 is 32]

2	-	40	+	8
2	-	32	+	32

2	-	40+8	=	2	-	48	=	2x32	-	48x2
2	-	32	=	2	-	32	=	2x32	-	32x2

[LCM of 2 ans 32 is 64]

2x32	-	48x2	=	64	-	96	=	64- 96	=	-32	=	$\frac{1}{-2}$
32x2		32x2		64		64		64		64

LHS = $\frac{1}{-2}$

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

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

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

8	-	-10	+	2	=	8-10	+	2	=	-2	+	2
8		8		8		8		8		8		8

[LCM of 8 and 8 is 64]

-2x8

-2x2

-16

-16+(16)

\frac{0}{1}

8x8

8x2

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 /)

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

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

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

SOLUTION 1 :

To verify,

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

LHS =

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

[ LCM of 4 and 8 is 32]

2	-	16	+	16
4	-	32	+	32

2	-	16+16	=	2	-	32	=	2x32	-	32x4
4	-	32	=	4	-	32	=	4x32	-	32x4

[LCM of 4 ans 32 is 128]

2x32

32x4

128

64- 128

-64

\frac{1}{-2}

32x4

128

LHS = $\frac{1}{-2}$

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

2x4	-	2x4	+	4
4x4	-	4x4	+	8

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

8	-	-8	+	4	=	8-8	+	4	=	0	+	4
16		16		8		16		8		16		8

[LCM of 16 and 8 is 128]

0x8

0x4

0+(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 /)

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

LHS = Answer: $\frac{1}{-24}$

RHS = Answer: $\frac{17}{24}$

SOLUTION 1 :

To verify,

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

LHS =

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

[ LCM of 6 and 8 is 48]

3	-	32	+	18
3	-	48	+	48

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

[LCM of 3 ans 48 is 144]

3x48

50x3

144

150

144- 150

-6

\frac{1}{-24}

48x3

144

LHS = $\frac{1}{-24}$

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

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

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

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

[LCM of 18 and 8 is 144]

6x8

6x3

48+(54)

102

\frac{17}{24}

18x8

18x3

144

RHS = $\frac{17}{24}$

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 /)

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

LHS = Answer: $\frac{-7}{12}$

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

SOLUTION 1 :

To verify,

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

LHS =

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

[ LCM of 4 and 6 is 24]

2	-	18	+	12
3	-	24	+	24

2	-	18+12	=	2	-	30	=	2x24	-	30x3
3	-	24	=	3	-	24	=	3x24	-	24x3

[LCM of 3 ans 24 is 72]

2x24	-	30x3	=	48	-	90	=	48- 90	=	-42	=	$\frac{-7}{12}$
24x3		24x3		72		72		72		72

LHS = $\frac{-7}{12}$

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

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

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

8	-	-9	+	4	=	8-9	+	4	=	-1	+	4
12		12		6		12		6		12		6

[LCM of 12 and 6 is 72]

-1x6

-1x3

-6

-6+(36)

\frac{5}{12}

12x6

12x3

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

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 /)

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

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

RHS = Answer: $\frac{7}{8}$

SOLUTION 1 :

To verify,

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

LHS =

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

[ LCM of 4 and 8 is 32]

3	-	16	+	12
3	-	32	+	32

3	-	16+12	=	3	-	28	=	3x32	-	28x3
3	-	32	=	3	-	32	=	3x32	-	32x3

[LCM of 3 ans 32 is 96]

3x32	-	28x3	=	96	-	84	=	96- 84	=	12	=	$\frac{1}{8}$
32x3		32x3		96		96		96		96

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

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

3x4	-	2x3	+	5
3x4	-	4x3	+	8

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

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

[LCM of 12 and 8 is 96]

6x8

6x3

48+(36)

\frac{7}{8}

12x8

12x3

RHS = $\frac{7}{8}$

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 /)

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

LHS = Answer: $\frac{4}{-7}$

RHS = Answer: $\frac{4}{7}$

SOLUTION 1 :

To verify,

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

LHS =

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

[ LCM of 4 and 7 is 28]

3	-	21	+	16
4	-	28	+	28

3	-	21+16	=	3	-	37	=	3x28	-	37x4
4	-	28	=	4	-	28	=	4x28	-	28x4

[LCM of 4 ans 28 is 112]

3x28

37x4

148

84- 148

-64

\frac{4}{-7}

28x4

112

LHS = $\frac{4}{-7}$

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

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

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

12	-	-12	+	3	=	12-12	+	3	=	0	+	3
16		16		7		16		7		16		7

[LCM of 16 and 7 is 112]

0x7

0x4

0+(64)

\frac{4}{7}

16x7

16x4

112

RHS = $\frac{4}{7}$

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 /)

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

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

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

SOLUTION 1 :

To verify,

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

LHS =

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

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

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

5	-	-8	+	2	=	5-8	+	2	=	-3	+	2
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 /)

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

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

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

SOLUTION 1 :

To verify,

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

LHS =

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

[ LCM of 4 and 8 is 32]

3	-	24	+	16
4	-	32	+	32

3	-	24+16	=	3	-	40	=	3x32	-	40x4
4	-	32	=	4	-	32	=	4x32	-	32x4

[LCM of 4 ans 32 is 128]

3x32

40x4

160

96- 160

-64

\frac{1}{-2}

32x4

128

LHS = $\frac{1}{-2}$

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

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

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

12	-	-12	+	4	=	12-12	+	4	=	0	+	4
16		16		8		16		8		16		8

[LCM of 16 and 8 is 128]

0x8

0x4

0+(64)

\frac{1}{2}

16x8

16x4

128

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

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 /)

$\frac{2}{3}$ , $\frac{5}{6}$ 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.