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 /)

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

RHS =

Answer:_______________

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

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

RHS =

Answer:_______________

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

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

RHS =

Answer:_______________

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

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

RHS =

Answer:_______________

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

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

RHS =

Answer:_______________

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

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

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 $\frac{-3}{7}$

RHS =

Answer:_______________

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

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

RHS =

Answer:_______________

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

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

RHS =

Answer:_______________

10)

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

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

RHS =

Answer:_______________

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

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

RHS = Answer: $\frac{21}{40}$

SOLUTION 1 :

To verify,

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

LHS =

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

[ LCM of 4 and 5 is 20]

10	+	8	+	-3
20	+	20	+	8

10+8	+	-3	=	18	+	-3	=	18	-	3
20	+	8	=	20	+	8	=	20	-	8

[LCM of 20 ans 8 is 160]

18x8

3x20

144

144- 60

\frac{21}{40}

20x8

8x20

160

LHS = $\frac{21}{40}$

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

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

[LCM of 5 and 8 is 40]

2	+	16	-	15	=	2	+	16-15	=	2	+	1
4		40		40		4		40		4		40

[LCM of 4 and 40 is 160]

2x40

1x4

80+(4)

\frac{21}{40}

4x40

40x4

160

RHS = $\frac{21}{40}$

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 /)

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

RHS = Answer: $\frac{1}{6}$

SOLUTION 1 :

To verify,

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

LHS =

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

[ LCM of 4 and 6 is 24]

12	+	8	+	-4
24	+	24	+	6

12+8	+	-4	=	20	+	-4	=	20	-	4
24	+	6	=	24	+	6	=	24	-	6

[LCM of 24 ans 6 is 144]

20x6

4x24

120

120- 96

\frac{1}{6}

24x6

6x24

144

LHS = $\frac{1}{6}$

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

2	+	2x6	-	4x6
4	+	6x6	-	6x6

[LCM of 6 and 6 is 36]

2	+	12	-	24	=	2	+	12-24	=	2	+	-12
4		36		36		4		36		4		36

[LCM of 4 and 36 is 144]

2x36

-12x4

-48

72+(-48)

\frac{1}{6}

4x36

36x4

144

RHS = $\frac{1}{6}$

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 /)

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

RHS = Answer: $\frac{19}{28}$

SOLUTION 1 :

To verify,

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

LHS =

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

[ LCM of 2 and 4 is 8]

4	+	6	+	-4
8	+	8	+	7

4+6	+	-4	=	10	+	-4	=	10	-	4
8	+	7	=	8	+	7	=	8	-	7

[LCM of 8 ans 7 is 56]

10x7	-	4x8	=	70	-	32	=	70- 32	=	38	=	$\frac{19}{28}$
8x7		7x8		56		56		56		56

LHS = $\frac{19}{28}$

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

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

[LCM of 4 and 7 is 28]

1	+	21	-	16	=	1	+	21-16	=	1	+	5
2		28		28		2		28		2		28

[LCM of 2 and 28 is 56]

1x28

5x2

28+(10)

\frac{19}{28}

2x28

28x2

RHS = $\frac{19}{28}$

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 /)

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

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

SOLUTION 1 :

To verify,

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

LHS =

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

[ LCM of 3 and 6 is 18]

12	+	6	+	-3
18	+	18	+	6

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

[LCM of 18 ans 6 is 108]

18x6

3x18

108

108- 54

\frac{1}{2}

18x6

6x18

108

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

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

2	+	2x6	-	3x6
3	+	6x6	-	6x6

[LCM of 6 and 6 is 36]

2	+	12	-	18	=	2	+	12-18	=	2	+	-6
3		36		36		3		36		3		36

[LCM of 3 and 36 is 108]

2x36

-6x3

-18

72+(-18)

\frac{1}{2}

3x36

36x3

108

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 /)

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

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

SOLUTION 1 :

To verify,

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

LHS =

1	+	3	+	-3	=	1x4	+	3x2	+	-3
2	+	4	+	8	=	2x4	+	4x2	+	8

[ LCM of 2 and 4 is 8]

4	+	6	+	-3
8	+	8	+	8

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

[LCM of 8 ans 8 is 64]

10x8	-	3x8	=	80	-	24	=	80- 24	=	56	=	$\frac{7}{8}$
8x8		8x8		64		64		64		64

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

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

1	+	3x8	-	3x4
2	+	4x8	-	8x4

[LCM of 4 and 8 is 32]

1	+	24	-	12	=	1	+	24-12	=	1	+	12
2		32		32		2		32		2		32

[LCM of 2 and 32 is 64]

1x32

12x2

32+(24)

\frac{7}{8}

2x32

32x2

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

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 /)

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

RHS = Answer: $\frac{9}{8}$

SOLUTION 1 :

To verify,

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

LHS =

3	+	3	+	-3	=	3x6	+	3x3	+	-3
3	+	6	+	8	=	3x6	+	6x3	+	8

[ LCM of 3 and 6 is 18]

18	+	9	+	-3
18	+	18	+	8

18+9	+	-3	=	27	+	-3	=	27	-	3
18	+	8	=	18	+	8	=	18	-	8

[LCM of 18 ans 8 is 144]

27x8

3x18

216

216- 54

162

\frac{9}{8}

18x8

8x18

144

LHS = $\frac{9}{8}$

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

3	+	3x8	-	3x6
3	+	6x8	-	8x6

[LCM of 6 and 8 is 48]

3	+	24	-	18	=	3	+	24-18	=	3	+	6
3		48		48		3		48		3		48

[LCM of 3 and 48 is 144]

3x48

6x3

144

144+(18)

162

\frac{9}{8}

3x48

48x3

144

RHS = $\frac{9}{8}$

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 $\frac{-3}{7}$

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

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

[ LCM of 4 and 5 is 20]

15	+	8	+	-3
20	+	20	+	7

15+8	+	-3	=	23	+	-3	=	23	-	3
20	+	7	=	20	+	7	=	20	-	7

[LCM of 20 ans 7 is 140]

23x7

3x20

161

161- 60

101

\frac{101}{140}

20x7

7x20

140

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

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

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

[LCM of 5 and 7 is 35]

3	+	14	-	15	=	3	+	14-15	=	3	+	-1
4		35		35		4		35		4		35

[LCM of 4 and 35 is 140]

3x35

-1x4

105

-4

105+(-4)

101

\frac{101}{140}

4x35

35x4

140

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

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 /)

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

RHS = Answer: $\frac{11}{10}$

SOLUTION 1 :

To verify,

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

LHS =

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

[ LCM of 3 and 6 is 18]

12	+	15	+	-2
18	+	18	+	5

12+15	+	-2	=	27	+	-2	=	27	-	2
18	+	5	=	18	+	5	=	18	-	5

[LCM of 18 ans 5 is 90]

27x5	-	2x18	=	135	-	36	=	135- 36	=	99	=	$\frac{11}{10}$
18x5		5x18		90		90		90		90

LHS = $\frac{11}{10}$

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

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

[LCM of 6 and 5 is 30]

2	+	25	-	12	=	2	+	25-12	=	2	+	13
3		30		30		3		30		3		30

[LCM of 3 and 30 is 90]

2x30

13x3

60+(39)

\frac{11}{10}

3x30

30x3

RHS = $\frac{11}{10}$

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 /)

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

RHS = Answer: $\frac{15}{14}$

SOLUTION 1 :

To verify,

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

LHS =

3	+	2	+	-3	=	3x4	+	2x3	+	-3
3	+	4	+	7	=	3x4	+	4x3	+	7

[ LCM of 3 and 4 is 12]

12	+	6	+	-3
12	+	12	+	7

12+6	+	-3	=	18	+	-3	=	18	-	3
12	+	7	=	12	+	7	=	12	-	7

[LCM of 12 ans 7 is 84]

18x7	-	3x12	=	126	-	36	=	126- 36	=	90	=	$\frac{15}{14}$
12x7		7x12		84		84		84		84

LHS = $\frac{15}{14}$

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

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

[LCM of 4 and 7 is 28]

3	+	14	-	12	=	3	+	14-12	=	3	+	2
3		28		28		3		28		3		28

[LCM of 3 and 28 is 84]

3x28

2x3

84+(6)

\frac{15}{14}

3x28

28x3

RHS = $\frac{15}{14}$

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 /)

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

RHS = Answer: $\frac{52}{105}$

SOLUTION 1 :

To verify,

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

LHS =

2	+	2	+	-4	=	2x5	+	2x3	+	-4
3	+	5	+	7	=	3x5	+	5x3	+	7

[ LCM of 3 and 5 is 15]

10	+	6	+	-4
15	+	15	+	7

10+6	+	-4	=	16	+	-4	=	16	-	4
15	+	7	=	15	+	7	=	15	-	7

[LCM of 15 ans 7 is 105]

16x7

4x15

112

112- 60

\frac{52}{105}

15x7

7x15

105

LHS = $\frac{52}{105}$

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

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

[LCM of 5 and 7 is 35]

2	+	14	-	20	=	2	+	14-20	=	2	+	-6
3		35		35		3		35		3		35

[LCM of 3 and 35 is 105]

2x35

-6x3

-18

70+(-18)

\frac{52}{105}

3x35

35x3

105

RHS = $\frac{52}{105}$

LHS = RHS

Hence, associative property is true for addition.