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 /)

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

LHS =

RHS =

Answer:_______________

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

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

LHS =

RHS =

Answer:_______________

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

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

LHS =

RHS =

Answer:_______________

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

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

LHS =

RHS =

Answer:_______________

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

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

LHS =

RHS =

Answer:_______________

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

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

LHS =

RHS =

Answer:_______________

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

$\frac{1}{2}$ , $\frac{3}{4}$ and $\frac{-2}{6}$

LHS =

RHS =

Answer:_______________

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

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

LHS =

RHS =

Answer:_______________

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

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

LHS =

RHS =

Answer:_______________

10)

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

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

LHS =

RHS =

Answer:_______________

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

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

LHS = Answer: $\frac{-15}{28}$

RHS = Answer: $\frac{1}{2}$ 8

SOLUTION 1 :

To verify,

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

LHS =

1	-	3	-	3	=	3x7	+	2x4
2	-	4	-	7	=	4x7	+	4x7

[ LCM of 4 and 7 is 28]

1	-	21	+	8
2	-	28	+	28

1	-	21+8	=	1	-	29	=	1x28	-	29x2
2	-	28	=	2	-	28	=	2x28	-	28x2

[LCM of 2 ans 28 is 56]

1x28	-	29x2	=	28	-	58	=	28- 58	=	-30	=	$\frac{-15}{28}$
28x2		28x2		56		56		56		56

LHS = $\frac{-15}{28}$

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

1x4	-	3x2	+	3
2x4	-	4x2	+	7

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

4	-	-6	+	3	=	4-6	+	3	=	-2	+	3
8		8		7		8		7		8		7

[LCM of 8 and 7 is 56]

-2x7

-2x2

-14

-14+(16)

\frac{1}{2}

8x7

8x2

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

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

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

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

SOLUTION 1 :

To verify,

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

LHS =

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

[ LCM of 6 and 6 is 36]

2	-	30	+	18
3	-	36	+	36

2	-	30+18	=	2	-	48	=	2x36	-	48x3
3	-	36	=	3	-	36	=	3x36	-	36x3

[LCM of 3 ans 36 is 108]

2x36

48x3

144

72- 144

-72

\frac{2}{3}

36x3

108

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

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

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

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

12	-	-15	+	3	=	12-15	+	3	=	-3	+	3
18		18		6		18		6		18		6

[LCM of 18 and 6 is 108]

-3x6

-3x3

-18

-18+(54)

\frac{1}{3}

18x6

18x3

108

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 /)

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

LHS = Answer: $\frac{59}{-140}$

RHS = Answer: $\frac{101}{140}$

SOLUTION 1 :

To verify,

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

LHS =

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

[ LCM of 5 and 7 is 35]

3	-	21	+	20
4	-	35	+	35

3	-	21+20	=	3	-	41	=	3x35	-	41x4
4	-	35	=	4	-	35	=	4x35	-	35x4

[LCM of 4 ans 35 is 140]

3x35

41x4

105

164

105- 164

-59

\frac{59}{-140}

35x4

140

LHS = $\frac{59}{-140}$

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

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

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

15	-	-12	+	5	=	15-12	+	5	=	3	+	5
20		20		7		20		7		20		7

[LCM of 20 and 7 is 140]

3x7

3x4

21+(80)

101

\frac{101}{140}

20x7

20x4

140

RHS = $\frac{101}{140}$

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 /)

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

LHS = Answer: $\frac{113}{-84}$

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

SOLUTION 1 :

To verify,

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

LHS =

1	-	5	-	4	=	5x7	+	3x4
3	-	4	-	7	=	4x7	+	4x7

[ LCM of 4 and 7 is 28]

1	-	35	+	12
3	-	28	+	28

1	-	35+12	=	1	-	47	=	1x28	-	47x3
3	-	28	=	3	-	28	=	3x28	-	28x3

[LCM of 3 ans 28 is 84]

1x28

47x3

141

28- 141

-113

\frac{113}{-84}

28x3

LHS = $\frac{113}{-84}$

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

1x4	-	5x3	+	4
3x4	-	4x3	+	7

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

4	-	-15	+	4	=	4-15	+	4	=	-11	+	4
12		12		7		12		7		12		7

[LCM of 12 and 7 is 84]

-11x7

-11x3

-77

-77+(36)

-41

\frac{41}{-84}

12x7

12x3

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 /)

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

LHS = Answer: $\frac{4}{15}$

RHS = Answer: 1 $\frac{4}{15}$

SOLUTION 1 :

To verify,

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

LHS =

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

[ LCM of 5 and 6 is 30]

2	-	12	+	10
2	-	30	+	30

2	-	12+10	=	2	-	22	=	2x30	-	22x2
2	-	30	=	2	-	30	=	2x30	-	30x2

[LCM of 2 ans 30 is 60]

2x30	-	22x2	=	60	-	44	=	60- 44	=	16	=	$\frac{4}{15}$
30x2		30x2		60		60		60		60

LHS = $\frac{4}{15}$

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

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

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

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

[LCM of 10 and 6 is 60]

6x6

6x2

36+(20)

\frac{4}{15}

10x6

10x2

RHS = 1 $\frac{4}{15}$

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 /)

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

LHS = Answer: $\frac{23}{-28}$

RHS = Answer: $\frac{9}{28}$

SOLUTION 1 :

To verify,

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

LHS =

1	-	2	-	3	=	2x7	+	4x4
4	-	4	-	7	=	4x7	+	4x7

[ LCM of 4 and 7 is 28]

1	-	14	+	16
4	-	28	+	28

1	-	14+16	=	1	-	30	=	1x28	-	30x4
4	-	28	=	4	-	28	=	4x28	-	28x4

[LCM of 4 ans 28 is 112]

1x28

30x4

120

28- 120

-92

\frac{23}{-28}

28x4

112

LHS = $\frac{23}{-28}$

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

1x4	-	2x4	+	3
4x4	-	4x4	+	7

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

4	-	-8	+	3	=	4-8	+	3	=	-4	+	3
16		16		7		16		7		16		7

[LCM of 16 and 7 is 112]

-4x7

-4x4

-28

-28+(64)

\frac{9}{28}

16x7

16x4

112

RHS = $\frac{9}{28}$

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 /)

$\frac{1}{2}$ , $\frac{3}{4}$ and $\frac{-2}{6}$

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

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

SOLUTION 1 :

To verify,

( $\frac{1}{2}$ - ( $\frac{3}{4}$ - ( $\frac{-2}{6}$ )) = ( $\frac{1}{2}$ - $\frac{3}{4}$ ) - ( $\frac{-2}{6}$ )

LHS =

1	-	3	-	2	=	3x6	+	2x4
2	-	4	-	6	=	4x6	+	4x6

[ LCM of 4 and 6 is 24]

1	-	18	+	8
2	-	24	+	24

1	-	18+8	=	1	-	26	=	1x24	-	26x2
2	-	24	=	2	-	24	=	2x24	-	24x2

[LCM of 2 ans 24 is 48]

1x24	-	26x2	=	24	-	52	=	24- 52	=	-28	=	$\frac{-7}{12}$
24x2		24x2		48		48		48		48

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

RHS = ( $\frac{1}{2}$ - $\frac{3}{4}$ ) - ( $\frac{-2}{6}$ ) = ( $\frac{1}{2}$ - ( $\frac{3}{4}$ ) $\frac{+2}{6)}$

1x4	-	3x2	+	2
2x4	-	4x2	+	6

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

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

[LCM of 8 and 6 is 48]

-2x6

-2x2

-12

-12+(16)

\frac{1}{12}

8x6

8x2

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

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 /)

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

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

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

SOLUTION 1 :

To verify,

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

LHS =

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

[ LCM of 6 and 6 is 36]

2	-	12	+	12
2	-	36	+	36

2	-	12+12	=	2	-	24	=	2x36	-	24x2
2	-	36	=	2	-	36	=	2x36	-	36x2

[LCM of 2 ans 36 is 72]

2x36	-	24x2	=	72	-	48	=	72- 48	=	24	=	$\frac{1}{3}$
36x2		36x2		72		72		72		72

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

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

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

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

12	-	-4	+	5	=	12-4	+	5	=	8	+	5
12		12		6		12		6		12		6

[LCM of 12 and 6 is 72]

8x6

8x2

48+(24)

\frac{1}{1}

12x6

12x2

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 /)

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

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

RHS = Answer: $\frac{7}{12}$

SOLUTION 1 :

To verify,

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

LHS =

3	-	5	-	2	=	5x6	+	2x4
2	-	4	-	6	=	4x6	+	4x6

[ LCM of 4 and 6 is 24]

3	-	30	+	8
2	-	24	+	24

3	-	30+8	=	3	-	38	=	3x24	-	38x2
2	-	24	=	2	-	24	=	2x24	-	24x2

[LCM of 2 ans 24 is 48]

3x24	-	38x2	=	72	-	76	=	72- 76	=	-4	=	$\frac{1}{-12}$
24x2		24x2		48		48		48		48

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

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

3x4	-	5x2	+	2
2x4	-	4x2	+	6

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

12	-	-10	+	2	=	12-10	+	2	=	2	+	2
8		8		6		8		6		8		6

[LCM of 8 and 6 is 48]

2x6

2x2

12+(16)

\frac{7}{12}

8x6

8x2

RHS = $\frac{7}{12}$

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 /)

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

LHS = Answer: $\frac{23}{42}$

RHS = Answer: $\frac{47}{42}$

SOLUTION 1 :

To verify,

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

LHS =

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

[ LCM of 6 and 7 is 42]

3	-	28	+	12
2	-	42	+	42

3	-	28+12	=	3	-	40	=	3x42	-	40x2
2	-	42	=	2	-	42	=	2x42	-	42x2

[LCM of 2 ans 42 is 84]

3x42	-	40x2	=	126	-	80	=	126- 80	=	46	=	$\frac{23}{42}$
42x2		42x2		84		84		84		84

LHS = $\frac{23}{42}$

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

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

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

18	-	-8	+	3	=	18-8	+	3	=	10	+	3
12		12		7		12		7		12		7

[LCM of 12 and 7 is 84]

10x7

10x2

70+(24)

\frac{47}{42}

12x7

12x2

RHS = $\frac{47}{42}$

LHS ≠ RHS

Hence, associative property is not true for subtraction.