Sasi Math (Revised for 1024)

Scroll:Real Number System >> Rational Numbers ( Exercise 1.1) >> saq (4363)

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 addition of the following pairs of rational numbers.(ples use /)

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

RHS =

Answer:_______________

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

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

RHS =

Answer:_______________

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

$\frac{1}{4}$ , $\frac{3}{6}$ and $\frac{-2}{8}$

RHS =

Answer:_______________

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

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

RHS =

Answer:_______________

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

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

RHS =

Answer:_______________

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

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

RHS =

Answer:_______________

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

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

RHS =

Answer:_______________

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

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

RHS =

Answer:_______________

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

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

RHS =

Answer:_______________

10)

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

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

RHS =

Answer:_______________

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

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

RHS = Answer: $\frac{9}{10}$

SOLUTION 1 :

To verify,

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

LHS =

3	+	2	+	-3	=	3x5	+	2x3	+	-3
3	+	5	+	6	=	3x5	+	5x3	+	6

[ LCM of 3 and 5 is 15]

15	+	6	+	-3
15	+	15	+	6

15+6	+	-3	=	21	+	-3	=	21	-	3
15	+	6	=	15	+	6	=	15	-	6

[LCM of 15 ans 6 is 90]

21x6	-	3x15	=	126	-	45	=	126- 45	=	81	=	$\frac{9}{10}$
15x6		6x15		90		90		90		90

LHS = $\frac{9}{10}$

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

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

[LCM of 5 and 6 is 30]

3	+	12	-	15	=	3	+	12-15	=	3	+	-3
3		30		30		3		30		3		30

[LCM of 3 and 30 is 90]

3x30

-3x3

-9

90+(-9)

\frac{9}{10}

3x30

30x3

RHS = $\frac{9}{10}$

LHS = RHS

Hence, associative property is true for addition.

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

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

RHS = Answer: $\frac{73}{42}$

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

[ LCM of 2 and 6 is 12]

18	+	8	+	-3
12	+	12	+	7

18+8	+	-3	=	26	+	-3	=	26	-	3
12	+	7	=	12	+	7	=	12	-	7

[LCM of 12 ans 7 is 84]

26x7

3x12

182

182- 36

146

\frac{73}{42}

12x7

7x12

LHS = $\frac{73}{42}$

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

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

[LCM of 6 and 7 is 42]

3	+	28	-	18	=	3	+	28-18	=	3	+	10
2		42		42		2		42		2		42

[LCM of 2 and 42 is 84]

3x42

10x2

126

126+(20)

146

\frac{73}{42}

2x42

42x2

RHS = $\frac{73}{42}$

LHS = RHS

Hence, associative property is true for addition.

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

$\frac{1}{4}$ , $\frac{3}{6}$ and $\frac{-2}{8}$

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

SOLUTION 1 :

To verify,

( $\frac{1}{4}$ + $\frac{3}{6}$ ) + ( $\frac{-2}{8}$ ) = $\frac{1}{4}$ + ( $\frac{3}{6}$ + ( $\frac{-2}{8}$ )

LHS =

1	+	3	+	-2	=	1x6	+	3x4	+	-2
4	+	6	+	8	=	4x6	+	6x4	+	8

[ LCM of 4 and 6 is 24]

6	+	12	+	-2
24	+	24	+	8

6+12	+	-2	=	18	+	-2	=	18	-	2
24	+	8	=	24	+	8	=	24	-	8

[LCM of 24 ans 8 is 192]

18x8

2x24

144

144- 48

\frac{1}{2}

24x8

8x24

192

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

RHS = $\frac{1}{4}$ + ( $\frac{3}{6}$ + ( $\frac{-2}{8}$ ) = $\frac{1}{4}$ + ( $\frac{3}{6}$ $\frac{-2}{8}$ )

1	+	3x8	-	2x6
4	+	6x8	-	8x6

[LCM of 6 and 8 is 48]

1	+	24	-	12	=	1	+	24-12	=	1	+	12
4		48		48		4		48		4		48

[LCM of 4 and 48 is 192]

1x48

12x4

48+(48)

\frac{1}{2}

4x48

48x4

192

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

LHS = RHS

Hence, associative property is true for addition.

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

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

RHS = Answer: $\frac{9}{10}$

SOLUTION 1 :

To verify,

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

LHS =

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

[ LCM of 4 and 4 is 16]

8	+	16	+	-3
16	+	16	+	5

8+16	+	-3	=	24	+	-3	=	24	-	3
16	+	5	=	16	+	5	=	16	-	5

[LCM of 16 ans 5 is 80]

24x5	-	3x16	=	120	-	48	=	120- 48	=	72	=	$\frac{9}{10}$
16x5		5x16		80		80		80		80

LHS = $\frac{9}{10}$

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

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

[LCM of 4 and 5 is 20]

2	+	20	-	12	=	2	+	20-12	=	2	+	8
4		20		20		4		20		4		20

[LCM of 4 and 20 is 80]

2x20

8x4

40+(32)

\frac{9}{10}

4x20

20x4

RHS = $\frac{9}{10}$

LHS = RHS

Hence, associative property is true for addition.

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

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

RHS = Answer: $\frac{7}{6}$

SOLUTION 1 :

To verify,

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

LHS =

2	+	4	+	-4	=	2x6	+	4x2	+	-4
2	+	6	+	8	=	2x6	+	6x2	+	8

[ LCM of 2 and 6 is 12]

12	+	8	+	-4
12	+	12	+	8

12+8	+	-4	=	20	+	-4	=	20	-	4
12	+	8	=	12	+	8	=	12	-	8

[LCM of 12 ans 8 is 96]

20x8

4x12

160

160- 48

112

\frac{7}{6}

12x8

8x12

LHS = $\frac{7}{6}$

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

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

[LCM of 6 and 8 is 48]

2	+	32	-	24	=	2	+	32-24	=	2	+	8
2		48		48		2		48		2		48

[LCM of 2 and 48 is 96]

2x48

8x2

96+(16)

112

\frac{7}{6}

2x48

48x2

RHS = $\frac{7}{6}$

LHS = RHS

Hence, associative property is true for addition.

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

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

RHS = Answer: $\frac{17}{60}$

SOLUTION 1 :

To verify,

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

LHS =

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

[ LCM of 3 and 4 is 12]

4	+	9	+	-4
12	+	12	+	5

4+9	+	-4	=	13	+	-4	=	13	-	4
12	+	5	=	12	+	5	=	12	-	5

[LCM of 12 ans 5 is 60]

13x5	-	4x12	=	65	-	48	=	65- 48	=	17	=	$\frac{17}{60}$
12x5		5x12		60		60		60		60

LHS = $\frac{17}{60}$

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

1	+	3x5	-	4x4
3	+	4x5	-	5x4

[LCM of 4 and 5 is 20]

1	+	15	-	16	=	1	+	15-16	=	1	+	-1
3		20		20		3		20		3		20

[LCM of 3 and 20 is 60]

1x20

-1x3

-3

20+(-3)

\frac{17}{60}

3x20

20x3

RHS = $\frac{17}{60}$

LHS = RHS

Hence, associative property is true for addition.

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

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

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

SOLUTION 1 :

To verify,

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

LHS =

3	+	2	+	-4	=	3x5	+	2x4	+	-4
4	+	5	+	8	=	4x5	+	5x4	+	8

[ LCM of 4 and 5 is 20]

15	+	8	+	-4
20	+	20	+	8

15+8	+	-4	=	23	+	-4	=	23	-	4
20	+	8	=	20	+	8	=	20	-	8

[LCM of 20 ans 8 is 160]

23x8

4x20

184

184- 80

104

\frac{13}{20}

20x8

8x20

160

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

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

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

[LCM of 5 and 8 is 40]

3	+	16	-	20	=	3	+	16-20	=	3	+	-4
4		40		40		4		40		4		40

[LCM of 4 and 40 is 160]

3x40

-4x4

120

-16

120+(-16)

104

\frac{13}{20}

4x40

40x4

160

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

LHS = RHS

Hence, associative property is true for addition.

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

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

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

SOLUTION 1 :

To verify,

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

LHS =

1	+	2	+	-4	=	1x6	+	2x3	+	-4
3	+	6	+	6	=	3x6	+	6x3	+	6

[ LCM of 3 and 6 is 18]

6	+	6	+	-4
18	+	18	+	6

6+6	+	-4	=	12	+	-4	=	12	-	4
18	+	6	=	18	+	6	=	18	-	6

[LCM of 18 ans 6 is 108]

12x6

4x18

72- 72

\frac{0}{1}

18x6

6x18

108

LHS = $\frac{0}{1}$

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

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

[LCM of 6 and 6 is 36]

1	+	12	-	24	=	1	+	12-24	=	1	+	-12
3		36		36		3		36		3		36

[LCM of 3 and 36 is 108]

1x36

-12x3

-36

36+(-36)

\frac{0}{1}

3x36

36x3

108

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

LHS = RHS

Hence, associative property is true for addition.

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

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

RHS = Answer: $\frac{131}{70}$

SOLUTION 1 :

To verify,

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

LHS =

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

[ LCM of 2 and 5 is 10]

15	+	8	+	-3
10	+	10	+	7

15+8	+	-3	=	23	+	-3	=	23	-	3
10	+	7	=	10	+	7	=	10	-	7

[LCM of 10 ans 7 is 70]

23x7

3x10

161

161- 30

131

\frac{131}{70}

10x7

7x10

LHS = $\frac{131}{70}$

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

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

[LCM of 5 and 7 is 35]

3	+	28	-	15	=	3	+	28-15	=	3	+	13
2		35		35		2		35		2		35

[LCM of 2 and 35 is 70]

3x35

13x2

105

105+(26)

131

\frac{131}{70}

2x35

35x2

RHS = $\frac{131}{70}$

LHS = RHS

Hence, associative property is true for addition.

10)

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

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

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

SOLUTION 1 :

To verify,

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

LHS =

2	+	5	+	-3	=	2x5	+	5x4	+	-3
4	+	5	+	6	=	4x5	+	5x4	+	6

[ LCM of 4 and 5 is 20]

10	+	20	+	-3
20	+	20	+	6

10+20	+	-3	=	30	+	-3	=	30	-	3
20	+	6	=	20	+	6	=	20	-	6

[LCM of 20 ans 6 is 120]

30x6

3x20

180

180- 60

120

\frac{1}{1}

20x6

6x20

120

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

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

2	+	5x6	-	3x5
4	+	5x6	-	6x5

[LCM of 5 and 6 is 30]

2	+	30	-	15	=	2	+	30-15	=	2	+	15
4		30		30		4		30		4		30

[LCM of 4 and 30 is 120]

2x30

15x4

60+(60)

120

\frac{1}{1}

4x30

30x4

120

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

LHS = RHS

Hence, associative property is true for addition.