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 /)

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

RHS =

Answer:_______________

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

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

RHS =

Answer:_______________

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

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

RHS =

Answer:_______________

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

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

RHS =

Answer:_______________

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

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

RHS =

Answer:_______________

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

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

RHS =

Answer:_______________

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

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

RHS =

Answer:_______________

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

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

RHS =

Answer:_______________

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

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

RHS =

Answer:_______________

10)

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

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

RHS =

Answer:_______________

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

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

RHS = Answer: $\frac{74}{105}$

SOLUTION 1 :

To verify,

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

LHS =

1	+	4	+	-3	=	1x5	+	4x3	+	-3
3	+	5	+	7	=	3x5	+	5x3	+	7

[ LCM of 3 and 5 is 15]

5	+	12	+	-3
15	+	15	+	7

5+12	+	-3	=	17	+	-3	=	17	-	3
15	+	7	=	15	+	7	=	15	-	7

[LCM of 15 ans 7 is 105]

17x7

3x15

119

119- 45

\frac{74}{105}

15x7

7x15

105

LHS = $\frac{74}{105}$

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

1	+	4x7	-	3x5
3	+	5x7	-	7x5

[LCM of 5 and 7 is 35]

1	+	28	-	15	=	1	+	28-15	=	1	+	13
3		35		35		3		35		3		35

[LCM of 3 and 35 is 105]

1x35

13x3

35+(39)

\frac{74}{105}

3x35

35x3

105

RHS = $\frac{74}{105}$

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 $\frac{-4}{5}$

RHS = Answer: $\frac{7}{10}$

SOLUTION 1 :

To verify,

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

LHS =

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

[ LCM of 3 and 6 is 18]

18	+	9	+	-4
18	+	18	+	5

18+9	+	-4	=	27	+	-4	=	27	-	4
18	+	5	=	18	+	5	=	18	-	5

[LCM of 18 ans 5 is 90]

27x5	-	4x18	=	135	-	72	=	135- 72	=	63	=	$\frac{7}{10}$
18x5		5x18		90		90		90		90

LHS = $\frac{7}{10}$

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

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

[LCM of 6 and 5 is 30]

3	+	15	-	24	=	3	+	15-24	=	3	+	-9
3		30		30		3		30		3		30

[LCM of 3 and 30 is 90]

3x30

-9x3

-27

90+(-27)

\frac{7}{10}

3x30

30x3

RHS = $\frac{7}{10}$

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 /)

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

RHS = Answer: $\frac{11}{20}$

SOLUTION 1 :

To verify,

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

LHS =

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

[ LCM of 4 and 5 is 20]

15	+	8	+	-3
20	+	20	+	5

15+8	+	-3	=	23	+	-3	=	23	-	3
20	+	5	=	20	+	5	=	20	-	5

[LCM of 20 ans 5 is 100]

23x5

3x20

115

115- 60

\frac{11}{20}

20x5

5x20

100

LHS = $\frac{11}{20}$

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

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

[LCM of 5 and 5 is 25]

3	+	10	-	15	=	3	+	10-15	=	3	+	-5
4		25		25		4		25		4		25

[LCM of 4 and 25 is 100]

3x25

-5x4

-20

75+(-20)

\frac{11}{20}

4x25

25x4

100

RHS = $\frac{11}{20}$

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 /)

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

RHS = Answer: $\frac{17}{24}$

SOLUTION 1 :

To verify,

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

LHS =

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

[ LCM of 4 and 6 is 24]

18	+	8	+	-3
24	+	24	+	8

18+8	+	-3	=	26	+	-3	=	26	-	3
24	+	8	=	24	+	8	=	24	-	8

[LCM of 24 ans 8 is 192]

26x8

3x24

208

208- 72

136

\frac{17}{24}

24x8

8x24

192

LHS = $\frac{17}{24}$

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

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

[LCM of 6 and 8 is 48]

3	+	16	-	18	=	3	+	16-18	=	3	+	-2
4		48		48		4		48		4		48

[LCM of 4 and 48 is 192]

3x48

-2x4

144

-8

144+(-8)

136

\frac{17}{24}

4x48

48x4

192

RHS = $\frac{17}{24}$

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 /)

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

RHS = Answer: $\frac{37}{28}$

SOLUTION 1 :

To verify,

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

LHS =

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

[ LCM of 3 and 4 is 12]

12	+	9	+	-3
12	+	12	+	7

12+9	+	-3	=	21	+	-3	=	21	-	3
12	+	7	=	12	+	7	=	12	-	7

[LCM of 12 ans 7 is 84]

21x7

3x12

147

147- 36

111

\frac{37}{28}

12x7

7x12

LHS = $\frac{37}{28}$

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

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

[LCM of 4 and 7 is 28]

3	+	21	-	12	=	3	+	21-12	=	3	+	9
3		28		28		3		28		3		28

[LCM of 3 and 28 is 84]

3x28

9x3

84+(27)

111

\frac{37}{28}

3x28

28x3

RHS = $\frac{37}{28}$

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 /)

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

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

SOLUTION 1 :

To verify,

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

LHS =

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

[ LCM of 4 and 6 is 24]

18	+	8	+	-2
24	+	24	+	6

18+8	+	-2	=	26	+	-2	=	26	-	2
24	+	6	=	24	+	6	=	24	-	6

[LCM of 24 ans 6 is 144]

26x6

2x24

156

156- 48

108

\frac{3}{4}

24x6

6x24

144

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

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

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

[LCM of 6 and 6 is 36]

3	+	12	-	12	=	3	+	12-12	=	3	+	0
4		36		36		4		36		4		36

[LCM of 4 and 36 is 144]

3x36

0x4

108

108+(0)

108

\frac{3}{4}

4x36

36x4

144

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

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 /)

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

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

SOLUTION 1 :

To verify,

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

LHS =

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

[ LCM of 4 and 4 is 16]

8	+	8	+	-2
16	+	16	+	6

8+8	+	-2	=	16	+	-2	=	16	-	2
16	+	6	=	16	+	6	=	16	-	6

[LCM of 16 ans 6 is 96]

16x6	-	2x16	=	96	-	32	=	96- 32	=	64	=	$\frac{2}{3}$
16x6		6x16		96		96		96		96

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

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

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

[LCM of 4 and 6 is 24]

2	+	12	-	8	=	2	+	12-8	=	2	+	4
4		24		24		4		24		4		24

[LCM of 4 and 24 is 96]

2x24

4x4

48+(16)

\frac{2}{3}

4x24

24x4

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

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 /)

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

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

SOLUTION 1 :

To verify,

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

LHS =

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

[ LCM of 4 and 5 is 20]

10	+	20	+	-3
20	+	20	+	8

10+20	+	-3	=	30	+	-3	=	30	-	3
20	+	8	=	20	+	8	=	20	-	8

[LCM of 20 ans 8 is 160]

30x8

3x20

240

240- 60

180

\frac{9}{8}

20x8

8x20

160

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

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

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

[LCM of 5 and 8 is 40]

2	+	40	-	15	=	2	+	40-15	=	2	+	25
4		40		40		4		40		4		40

[LCM of 4 and 40 is 160]

2x40

25x4

100

80+(100)

180

\frac{9}{8}

4x40

40x4

160

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 /)

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

RHS = Answer: $\frac{8}{15}$

SOLUTION 1 :

To verify,

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

LHS =

2	+	4	+	-4	=	2x6	+	4x3	+	-4
3	+	6	+	5	=	3x6	+	6x3	+	5

[ LCM of 3 and 6 is 18]

12	+	12	+	-4
18	+	18	+	5

12+12	+	-4	=	24	+	-4	=	24	-	4
18	+	5	=	18	+	5	=	18	-	5

[LCM of 18 ans 5 is 90]

24x5	-	4x18	=	120	-	72	=	120- 72	=	48	=	$\frac{8}{15}$
18x5		5x18		90		90		90		90

LHS = $\frac{8}{15}$

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

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

[LCM of 6 and 5 is 30]

2	+	20	-	24	=	2	+	20-24	=	2	+	-4
3		30		30		3		30		3		30

[LCM of 3 and 30 is 90]

2x30

-4x3

-12

60+(-12)

\frac{8}{15}

3x30

30x3

RHS = $\frac{8}{15}$

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 /)

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

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

SOLUTION 1 :

To verify,

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

LHS =

3	+	4	+	-2	=	3x4	+	4x3	+	-2
3	+	4	+	5	=	3x4	+	4x3	+	5

[ LCM of 3 and 4 is 12]

12	+	12	+	-2
12	+	12	+	5

12+12	+	-2	=	24	+	-2	=	24	-	2
12	+	5	=	12	+	5	=	12	-	5

[LCM of 12 ans 5 is 60]

24x5	-	2x12	=	120	-	24	=	120- 24	=	96	=	$\frac{8}{5}$
12x5		5x12		60		60		60		60

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

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

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

[LCM of 4 and 5 is 20]

3	+	20	-	8	=	3	+	20-8	=	3	+	12
3		20		20		3		20		3		20

[LCM of 3 and 20 is 60]

3x20

12x3

60+(36)

\frac{8}{5}

3x20

20x3

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

LHS = RHS

Hence, associative property is true for addition.