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 /)

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

RHS =

Answer:_______________

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

$\frac{1}{3}$ , $\frac{5}{6}$ and $\frac{-3}{7}$

RHS =

Answer:_______________

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

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

RHS =

Answer:_______________

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

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

RHS =

Answer:_______________

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

$\frac{1}{2}$ , $\frac{5}{5}$ and $\frac{-3}{6}$

RHS =

Answer:_______________

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

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

RHS =

Answer:_______________

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

$\frac{1}{2}$ , $\frac{5}{6}$ and $\frac{-2}{6}$

RHS =

Answer:_______________

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

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

RHS =

Answer:_______________

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

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

RHS =

Answer:_______________

10)

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

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

RHS =

Answer:_______________

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

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

RHS = Answer: $\frac{13}{12}$

SOLUTION 1 :

To verify,

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

LHS =

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

[ LCM of 3 and 6 is 18]

18	+	6	+	-2
18	+	18	+	8

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

[LCM of 18 ans 8 is 144]

24x8

2x18

192

192- 36

156

\frac{13}{12}

18x8

8x18

144

LHS = $\frac{13}{12}$

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

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

[LCM of 6 and 8 is 48]

3	+	16	-	12	=	3	+	16-12	=	3	+	4
3		48		48		3		48		3		48

[LCM of 3 and 48 is 144]

3x48

4x3

144

144+(12)

156

\frac{13}{12}

3x48

48x3

144

RHS = $\frac{13}{12}$

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 /)

$\frac{1}{3}$ , $\frac{5}{6}$ and $\frac{-3}{7}$

RHS = Answer: $\frac{31}{42}$

SOLUTION 1 :

To verify,

( $\frac{1}{3}$ + $\frac{5}{6}$ ) + ( $\frac{-3}{7}$ ) = $\frac{1}{3}$ + ( $\frac{5}{6}$ + ( $\frac{-3}{7}$ )

LHS =

1	+	5	+	-3	=	1x6	+	5x3	+	-3
3	+	6	+	7	=	3x6	+	6x3	+	7

[ LCM of 3 and 6 is 18]

6	+	15	+	-3
18	+	18	+	7

6+15	+	-3	=	21	+	-3	=	21	-	3
18	+	7	=	18	+	7	=	18	-	7

[LCM of 18 ans 7 is 126]

21x7

3x18

147

147- 54

\frac{31}{42}

18x7

7x18

126

LHS = $\frac{31}{42}$

RHS = $\frac{1}{3}$ + ( $\frac{5}{6}$ + ( $\frac{-3}{7}$ ) = $\frac{1}{3}$ + ( $\frac{5}{6}$ $\frac{-3}{7}$ )

1	+	5x7	-	3x6
3	+	6x7	-	7x6

[LCM of 6 and 7 is 42]

1	+	35	-	18	=	1	+	35-18	=	1	+	17
3		42		42		3		42		3		42

[LCM of 3 and 42 is 126]

1x42

17x3

42+(51)

\frac{31}{42}

3x42

42x3

126

RHS = $\frac{31}{42}$

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 /)

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

RHS = Answer: $\frac{3}{2}$

SOLUTION 1 :

To verify,

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

LHS =

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

[ LCM of 4 and 4 is 16]

12	+	20	+	-3
16	+	16	+	6

12+20	+	-3	=	32	+	-3	=	32	-	3
16	+	6	=	16	+	6	=	16	-	6

[LCM of 16 ans 6 is 96]

32x6

3x16

192

192- 48

144

\frac{3}{2}

16x6

6x16

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

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

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

[LCM of 4 and 6 is 24]

3	+	30	-	12	=	3	+	30-12	=	3	+	18
4		24		24		4		24		4		24

[LCM of 4 and 24 is 96]

3x24

18x4

72+(72)

144

\frac{3}{2}

4x24

24x4

RHS = $\frac{3}{2}$

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 /)

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

RHS = Answer: $\frac{5}{6}$

SOLUTION 1 :

To verify,

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

LHS =

1	+	4	+	-3	=	1x4	+	4x3	+	-3
3	+	4	+	6	=	3x4	+	4x3	+	6

[ LCM of 3 and 4 is 12]

4	+	12	+	-3
12	+	12	+	6

4+12	+	-3	=	16	+	-3	=	16	-	3
12	+	6	=	12	+	6	=	12	-	6

[LCM of 12 ans 6 is 72]

16x6	-	3x12	=	96	-	36	=	96- 36	=	60	=	$\frac{5}{6}$
12x6		6x12		72		72		72		72

LHS = $\frac{5}{6}$

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

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

[LCM of 4 and 6 is 24]

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

[LCM of 3 and 24 is 72]

1x24

12x3

24+(36)

\frac{5}{6}

3x24

24x3

RHS = $\frac{5}{6}$

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 /)

$\frac{1}{2}$ , $\frac{5}{5}$ and $\frac{-3}{6}$

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

SOLUTION 1 :

To verify,

( $\frac{1}{2}$ + $\frac{5}{5}$ ) + ( $\frac{-3}{6}$ ) = $\frac{1}{2}$ + ( $\frac{5}{5}$ + ( $\frac{-3}{6}$ )

LHS =

1	+	5	+	-3	=	1x5	+	5x2	+	-3
2	+	5	+	6	=	2x5	+	5x2	+	6

[ LCM of 2 and 5 is 10]

5	+	10	+	-3
10	+	10	+	6

5+10	+	-3	=	15	+	-3	=	15	-	3
10	+	6	=	10	+	6	=	10	-	6

[LCM of 10 ans 6 is 60]

15x6	-	3x10	=	90	-	30	=	90- 30	=	60	=	$\frac{1}{1}$
10x6		6x10		60		60		60		60

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

RHS = $\frac{1}{2}$ + ( $\frac{5}{5}$ + ( $\frac{-3}{6}$ ) = $\frac{1}{2}$ + ( $\frac{5}{5}$ $\frac{-3}{6}$ )

1	+	5x6	-	3x5
2	+	5x6	-	6x5

[LCM of 5 and 6 is 30]

1	+	30	-	15	=	1	+	30-15	=	1	+	15
2		30		30		2		30		2		30

[LCM of 2 and 30 is 60]

1x30

15x2

30+(30)

\frac{1}{1}

2x30

30x2

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

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 /)

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

RHS = Answer: $\frac{5}{6}$

SOLUTION 1 :

To verify,

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

LHS =

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

[ LCM of 2 and 6 is 12]

12	+	6	+	-4
12	+	12	+	6

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

[LCM of 12 ans 6 is 72]

18x6	-	4x12	=	108	-	48	=	108- 48	=	60	=	$\frac{5}{6}$
12x6		6x12		72		72		72		72

LHS = $\frac{5}{6}$

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

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

[LCM of 6 and 6 is 36]

2	+	18	-	24	=	2	+	18-24	=	2	+	-6
2		36		36		2		36		2		36

[LCM of 2 and 36 is 72]

2x36

-6x2

-12

72+(-12)

\frac{5}{6}

2x36

36x2

RHS = $\frac{5}{6}$

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 /)

$\frac{1}{2}$ , $\frac{5}{6}$ and $\frac{-2}{6}$

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

SOLUTION 1 :

To verify,

( $\frac{1}{2}$ + $\frac{5}{6}$ ) + ( $\frac{-2}{6}$ ) = $\frac{1}{2}$ + ( $\frac{5}{6}$ + ( $\frac{-2}{6}$ )

LHS =

1	+	5	+	-2	=	1x6	+	5x2	+	-2
2	+	6	+	6	=	2x6	+	6x2	+	6

[ LCM of 2 and 6 is 12]

6	+	10	+	-2
12	+	12	+	6

6+10	+	-2	=	16	+	-2	=	16	-	2
12	+	6	=	12	+	6	=	12	-	6

[LCM of 12 ans 6 is 72]

16x6	-	2x12	=	96	-	24	=	96- 24	=	72	=	$\frac{1}{1}$
12x6		6x12		72		72		72		72

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

RHS = $\frac{1}{2}$ + ( $\frac{5}{6}$ + ( $\frac{-2}{6}$ ) = $\frac{1}{2}$ + ( $\frac{5}{6}$ $\frac{-2}{6}$ )

1	+	5x6	-	2x6
2	+	6x6	-	6x6

[LCM of 6 and 6 is 36]

1	+	30	-	12	=	1	+	30-12	=	1	+	18
2		36		36		2		36		2		36

[LCM of 2 and 36 is 72]

1x36

18x2

36+(36)

\frac{1}{1}

2x36

36x2

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

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 /)

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

RHS = Answer: $\frac{5}{6}$

SOLUTION 1 :

To verify,

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

LHS =

3	+	3	+	-4	=	3x4	+	3x4	+	-4
4	+	4	+	6	=	4x4	+	4x4	+	6

[ LCM of 4 and 4 is 16]

12	+	12	+	-4
16	+	16	+	6

12+12	+	-4	=	24	+	-4	=	24	-	4
16	+	6	=	16	+	6	=	16	-	6

[LCM of 16 ans 6 is 96]

24x6	-	4x16	=	144	-	64	=	144- 64	=	80	=	$\frac{5}{6}$
16x6		6x16		96		96		96		96

LHS = $\frac{5}{6}$

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

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

[LCM of 4 and 6 is 24]

3	+	18	-	16	=	3	+	18-16	=	3	+	2
4		24		24		4		24		4		24

[LCM of 4 and 24 is 96]

3x24

2x4

72+(8)

\frac{5}{6}

4x24

24x4

RHS = $\frac{5}{6}$

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 $\frac{-3}{8}$

RHS = Answer: $\frac{47}{40}$

SOLUTION 1 :

To verify,

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

LHS =

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

[ LCM of 4 and 5 is 20]

15	+	16	+	-3
20	+	20	+	8

15+16	+	-3	=	31	+	-3	=	31	-	3
20	+	8	=	20	+	8	=	20	-	8

[LCM of 20 ans 8 is 160]

31x8

3x20

248

248- 60

188

\frac{47}{40}

20x8

8x20

160

LHS = $\frac{47}{40}$

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

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

[LCM of 5 and 8 is 40]

3	+	32	-	15	=	3	+	32-15	=	3	+	17
4		40		40		4		40		4		40

[LCM of 4 and 40 is 160]

3x40

17x4

120

120+(68)

188

\frac{47}{40}

4x40

40x4

160

RHS = $\frac{47}{40}$

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 /)

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

RHS = Answer: 4 $\frac{3}{3}$ 5

SOLUTION 1 :

To verify,

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

LHS =

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

[ LCM of 3 and 5 is 15]

15	+	12	+	-4
15	+	15	+	7

15+12	+	-4	=	27	+	-4	=	27	-	4
15	+	7	=	15	+	7	=	15	-	7

[LCM of 15 ans 7 is 105]

27x7

4x15

189

189- 60

129

\frac{3}{3}

15x7

7x15

105

LHS = 4 $\frac{3}{3}$ 5

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

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

[LCM of 5 and 7 is 35]

3	+	28	-	20	=	3	+	28-20	=	3	+	8
3		35		35		3		35		3		35

[LCM of 3 and 35 is 105]

3x35

8x3

105

105+(24)

129

\frac{3}{3}

3x35

35x3

105

RHS = 4 $\frac{3}{3}$ 5

LHS = RHS

Hence, associative property is true for addition.