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 /)

$\frac{1}{3}$ , $\frac{2}{5}$ and $\frac{-2}{8}$

RHS =

Answer:_______________

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

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

RHS =

Answer:_______________

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

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

RHS =

Answer:_______________

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

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

RHS =

Answer:_______________

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

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

RHS =

Answer:_______________

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

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

RHS =

Answer:_______________

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

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

RHS =

Answer:_______________

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

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

RHS =

Answer:_______________

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

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

RHS =

Answer:_______________

10)

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

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

RHS =

Answer:_______________

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

$\frac{1}{3}$ , $\frac{2}{5}$ and $\frac{-2}{8}$

RHS = Answer: $\frac{29}{60}$

SOLUTION 1 :

To verify,

( $\frac{1}{3}$ + $\frac{2}{5}$ ) + ( $\frac{-2}{8}$ ) = $\frac{1}{3}$ + ( $\frac{2}{5}$ + ( $\frac{-2}{8}$ )

LHS =

1	+	2	+	-2	=	1x5	+	2x3	+	-2
3	+	5	+	8	=	3x5	+	5x3	+	8

[ LCM of 3 and 5 is 15]

5	+	6	+	-2
15	+	15	+	8

5+6	+	-2	=	11	+	-2	=	11	-	2
15	+	8	=	15	+	8	=	15	-	8

[LCM of 15 ans 8 is 120]

11x8

2x15

88- 30

\frac{29}{60}

15x8

8x15

120

LHS = $\frac{29}{60}$

RHS = $\frac{1}{3}$ + ( $\frac{2}{5}$ + ( $\frac{-2}{8}$ ) = $\frac{1}{3}$ + ( $\frac{2}{5}$ $\frac{-2}{8}$ )

1	+	2x8	-	2x5
3	+	5x8	-	8x5

[LCM of 5 and 8 is 40]

1	+	16	-	10	=	1	+	16-10	=	1	+	6
3		40		40		3		40		3		40

[LCM of 3 and 40 is 120]

1x40

6x3

40+(18)

\frac{29}{60}

3x40

40x3

120

RHS = $\frac{29}{60}$

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 /)

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

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

SOLUTION 1 :

To verify,

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

LHS =

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

[ LCM of 3 and 5 is 15]

10	+	15	+	-4
15	+	15	+	8

10+15	+	-4	=	25	+	-4	=	25	-	4
15	+	8	=	15	+	8	=	15	-	8

[LCM of 15 ans 8 is 120]

25x8

4x15

200

200- 60

140

\frac{7}{6}

15x8

8x15

120

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

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

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

[LCM of 5 and 8 is 40]

2	+	40	-	20	=	2	+	40-20	=	2	+	20
3		40		40		3		40		3		40

[LCM of 3 and 40 is 120]

2x40

20x3

80+(60)

140

\frac{7}{6}

3x40

40x3

120

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 /)

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

RHS = Answer: $\frac{23}{20}$

SOLUTION 1 :

To verify,

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

LHS =

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

[ LCM of 4 and 5 is 20]

15	+	16	+	-2
20	+	20	+	5

15+16	+	-2	=	31	+	-2	=	31	-	2
20	+	5	=	20	+	5	=	20	-	5

[LCM of 20 ans 5 is 100]

31x5

2x20

155

155- 40

115

\frac{23}{20}

20x5

5x20

100

LHS = $\frac{23}{20}$

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

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

[LCM of 5 and 5 is 25]

3	+	20	-	10	=	3	+	20-10	=	3	+	10
4		25		25		4		25		4		25

[LCM of 4 and 25 is 100]

3x25

10x4

75+(40)

115

\frac{23}{20}

4x25

25x4

100

RHS = $\frac{23}{20}$

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 /)

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

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

SOLUTION 1 :

To verify,

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

LHS =

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

[ LCM of 3 and 6 is 18]

6	+	12	+	-4
18	+	18	+	5

6+12	+	-4	=	18	+	-4	=	18	-	4
18	+	5	=	18	+	5	=	18	-	5

[LCM of 18 ans 5 is 90]

18x5	-	4x18	=	90	-	72	=	90- 72	=	18	=	$\frac{1}{5}$
18x5		5x18		90		90		90		90

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

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

1	+	4x5	-	4x6
3	+	6x5	-	5x6

[LCM of 6 and 5 is 30]

1	+	20	-	24	=	1	+	20-24	=	1	+	-4
3		30		30		3		30		3		30

[LCM of 3 and 30 is 90]

1x30

-4x3

-12

30+(-12)

\frac{1}{5}

3x30

30x3

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

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 /)

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

RHS = Answer: $\frac{11}{12}$

SOLUTION 1 :

To verify,

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

LHS =

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

[ LCM of 3 and 4 is 12]

8	+	9	+	-3
12	+	12	+	6

8+9	+	-3	=	17	+	-3	=	17	-	3
12	+	6	=	12	+	6	=	12	-	6

[LCM of 12 ans 6 is 72]

17x6	-	3x12	=	102	-	36	=	102- 36	=	66	=	$\frac{11}{12}$
12x6		6x12		72		72		72		72

LHS = $\frac{11}{12}$

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

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

[LCM of 4 and 6 is 24]

2	+	18	-	12	=	2	+	18-12	=	2	+	6
3		24		24		3		24		3		24

[LCM of 3 and 24 is 72]

2x24

6x3

48+(18)

\frac{11}{12}

3x24

24x3

RHS = $\frac{11}{12}$

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 /)

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

RHS = Answer: $\frac{57}{40}$

SOLUTION 1 :

To verify,

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

LHS =

2	+	4	+	-3	=	2x5	+	4x2	+	-3
2	+	5	+	8	=	2x5	+	5x2	+	8

[ LCM of 2 and 5 is 10]

10	+	8	+	-3
10	+	10	+	8

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

[LCM of 10 ans 8 is 80]

18x8

3x10

144

144- 30

114

\frac{57}{40}

10x8

8x10

LHS = $\frac{57}{40}$

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

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

[LCM of 5 and 8 is 40]

2	+	32	-	15	=	2	+	32-15	=	2	+	17
2		40		40		2		40		2		40

[LCM of 2 and 40 is 80]

2x40

17x2

80+(34)

114

\frac{57}{40}

2x40

40x2

RHS = $\frac{57}{40}$

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 /)

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

RHS = Answer: $\frac{5}{8}$

SOLUTION 1 :

To verify,

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

LHS =

2	+	2	+	-3	=	2x6	+	2x3	+	-3
3	+	6	+	8	=	3x6	+	6x3	+	8

[ LCM of 3 and 6 is 18]

12	+	6	+	-3
18	+	18	+	8

12+6	+	-3	=	18	+	-3	=	18	-	3
18	+	8	=	18	+	8	=	18	-	8

[LCM of 18 ans 8 is 144]

18x8

3x18

144

144- 54

\frac{5}{8}

18x8

8x18

144

LHS = $\frac{5}{8}$

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

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

[LCM of 6 and 8 is 48]

2	+	16	-	18	=	2	+	16-18	=	2	+	-2
3		48		48		3		48		3		48

[LCM of 3 and 48 is 144]

2x48

-2x3

-6

96+(-6)

\frac{5}{8}

3x48

48x3

144

RHS = $\frac{5}{8}$

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 /)

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

RHS = Answer: $\frac{27}{20}$

SOLUTION 1 :

To verify,

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

LHS =

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

[ LCM of 4 and 4 is 16]

8	+	20	+	-2
16	+	16	+	5

8+20	+	-2	=	28	+	-2	=	28	-	2
16	+	5	=	16	+	5	=	16	-	5

[LCM of 16 ans 5 is 80]

28x5

2x16

140

140- 32

108

\frac{27}{20}

16x5

5x16

LHS = $\frac{27}{20}$

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

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

[LCM of 4 and 5 is 20]

2	+	25	-	8	=	2	+	25-8	=	2	+	17
4		20		20		4		20		4		20

[LCM of 4 and 20 is 80]

2x20

17x4

40+(68)

108

\frac{27}{20}

4x20

20x4

RHS = $\frac{27}{20}$

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 /)

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

RHS = Answer: $\frac{7}{5}$

SOLUTION 1 :

To verify,

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

LHS =

3	+	3	+	-3	=	3x6	+	3x2	+	-3
2	+	6	+	5	=	2x6	+	6x2	+	5

[ LCM of 2 and 6 is 12]

18	+	6	+	-3
12	+	12	+	5

18+6	+	-3	=	24	+	-3	=	24	-	3
12	+	5	=	12	+	5	=	12	-	5

[LCM of 12 ans 5 is 60]

24x5	-	3x12	=	120	-	36	=	120- 36	=	84	=	$\frac{7}{5}$
12x5		5x12		60		60		60		60

LHS = $\frac{7}{5}$

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

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

[LCM of 6 and 5 is 30]

3	+	15	-	18	=	3	+	15-18	=	3	+	-3
2		30		30		2		30		2		30

[LCM of 2 and 30 is 60]

3x30

-3x2

-6

90+(-6)

\frac{7}{5}

2x30

30x2

RHS = $\frac{7}{5}$

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 /)

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

RHS = Answer: $\frac{37}{70}$

SOLUTION 1 :

To verify,

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

LHS =

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

[ LCM of 4 and 5 is 20]

10	+	12	+	-4
20	+	20	+	7

10+12	+	-4	=	22	+	-4	=	22	-	4
20	+	7	=	20	+	7	=	20	-	7

[LCM of 20 ans 7 is 140]

22x7

4x20

154

154- 80

\frac{37}{70}

20x7

7x20

140

LHS = $\frac{37}{70}$

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

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

[LCM of 5 and 7 is 35]

2	+	21	-	20	=	2	+	21-20	=	2	+	1
4		35		35		4		35		4		35

[LCM of 4 and 35 is 140]

2x35

1x4

70+(4)

\frac{37}{70}

4x35

35x4

140

RHS = $\frac{37}{70}$

LHS = RHS

Hence, associative property is true for addition.