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 /)

$\frac{1}{4}$ , $\frac{5}{5}$ and $\frac{-2}{7}$

RHS =

Answer:_______________

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

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

RHS =

Answer:_______________

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

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

RHS =

Answer:_______________

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

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

RHS =

Answer:_______________

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

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

RHS =

Answer:_______________

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

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

RHS =

Answer:_______________

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

$\frac{1}{4}$ , $\frac{4}{5}$ and $\frac{-3}{8}$

RHS =

Answer:_______________

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

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

RHS =

Answer:_______________

10)

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

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

RHS =

Answer:_______________

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

$\frac{1}{4}$ , $\frac{5}{5}$ and $\frac{-2}{7}$

RHS = Answer: $\frac{27}{28}$

SOLUTION 1 :

To verify,

( $\frac{1}{4}$ + $\frac{5}{5}$ ) + ( $\frac{-2}{7}$ ) = $\frac{1}{4}$ + ( $\frac{5}{5}$ + ( $\frac{-2}{7}$ )

LHS =

1	+	5	+	-2	=	1x5	+	5x4	+	-2
4	+	5	+	7	=	4x5	+	5x4	+	7

[ LCM of 4 and 5 is 20]

5	+	20	+	-2
20	+	20	+	7

5+20	+	-2	=	25	+	-2	=	25	-	2
20	+	7	=	20	+	7	=	20	-	7

[LCM of 20 ans 7 is 140]

25x7

2x20

175

175- 40

135

\frac{27}{28}

20x7

7x20

140

LHS = $\frac{27}{28}$

RHS = $\frac{1}{4}$ + ( $\frac{5}{5}$ + ( $\frac{-2}{7}$ ) = $\frac{1}{4}$ + ( $\frac{5}{5}$ $\frac{-2}{7}$ )

1	+	5x7	-	2x5
4	+	5x7	-	7x5

[LCM of 5 and 7 is 35]

1	+	35	-	10	=	1	+	35-10	=	1	+	25
4		35		35		4		35		4		35

[LCM of 4 and 35 is 140]

1x35

25x4

100

35+(100)

135

\frac{27}{28}

4x35

35x4

140

RHS = $\frac{27}{28}$

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 /)

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

RHS = Answer: $\frac{7}{15}$

SOLUTION 1 :

To verify,

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

LHS =

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

[ LCM of 3 and 5 is 15]

10	+	9	+	-4
15	+	15	+	5

10+9	+	-4	=	19	+	-4	=	19	-	4
15	+	5	=	15	+	5	=	15	-	5

[LCM of 15 ans 5 is 75]

19x5	-	4x15	=	95	-	60	=	95- 60	=	35	=	$\frac{7}{15}$
15x5		5x15		75		75		75		75

LHS = $\frac{7}{15}$

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

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

[LCM of 5 and 5 is 25]

2	+	15	-	20	=	2	+	15-20	=	2	+	-5
3		25		25		3		25		3		25

[LCM of 3 and 25 is 75]

2x25

-5x3

-15

50+(-15)

\frac{7}{15}

3x25

25x3

RHS = $\frac{7}{15}$

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 /)

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

RHS = Answer: $\frac{17}{12}$

SOLUTION 1 :

To verify,

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

LHS =

2	+	3	+	-2	=	2x4	+	3x2	+	-2
2	+	4	+	6	=	2x4	+	4x2	+	6

[ LCM of 2 and 4 is 8]

8	+	6	+	-2
8	+	8	+	6

8+6	+	-2	=	14	+	-2	=	14	-	2
8	+	6	=	8	+	6	=	8	-	6

[LCM of 8 ans 6 is 48]

14x6	-	2x8	=	84	-	16	=	84- 16	=	68	=	$\frac{17}{12}$
8x6		6x8		48		48		48		48

LHS = $\frac{17}{12}$

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

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

[LCM of 4 and 6 is 24]

2	+	18	-	8	=	2	+	18-8	=	2	+	10
2		24		24		2		24		2		24

[LCM of 2 and 24 is 48]

2x24

10x2

48+(20)

\frac{17}{12}

2x24

24x2

RHS = $\frac{17}{12}$

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 /)

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

RHS = Answer: $\frac{53}{60}$

SOLUTION 1 :

To verify,

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

LHS =

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

[ LCM of 4 and 5 is 20]

15	+	16	+	-4
20	+	20	+	6

15+16	+	-4	=	31	+	-4	=	31	-	4
20	+	6	=	20	+	6	=	20	-	6

[LCM of 20 ans 6 is 120]

31x6

4x20

186

186- 80

106

\frac{53}{60}

20x6

6x20

120

LHS = $\frac{53}{60}$

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

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

[LCM of 5 and 6 is 30]

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

[LCM of 4 and 30 is 120]

3x30

4x4

90+(16)

106

\frac{53}{60}

4x30

30x4

120

RHS = $\frac{53}{60}$

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 /)

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

RHS = Answer: $\frac{55}{84}$

SOLUTION 1 :

To verify,

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

LHS =

1	+	3	+	-3	=	1x4	+	3x3	+	-3
3	+	4	+	7	=	3x4	+	4x3	+	7

[ LCM of 3 and 4 is 12]

4	+	9	+	-3
12	+	12	+	7

4+9	+	-3	=	13	+	-3	=	13	-	3
12	+	7	=	12	+	7	=	12	-	7

[LCM of 12 ans 7 is 84]

13x7	-	3x12	=	91	-	36	=	91- 36	=	55	=	$\frac{55}{84}$
12x7		7x12		84		84		84		84

LHS = $\frac{55}{84}$

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

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

[LCM of 4 and 7 is 28]

1	+	21	-	12	=	1	+	21-12	=	1	+	9
3		28		28		3		28		3		28

[LCM of 3 and 28 is 84]

1x28

9x3

28+(27)

\frac{55}{84}

3x28

28x3

RHS = $\frac{55}{84}$

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 $\frac{-2}{7}$

RHS = Answer: $\frac{67}{84}$

SOLUTION 1 :

To verify,

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

LHS =

3	+	2	+	-2	=	3x6	+	2x4	+	-2
4	+	6	+	7	=	4x6	+	6x4	+	7

[ LCM of 4 and 6 is 24]

18	+	8	+	-2
24	+	24	+	7

18+8	+	-2	=	26	+	-2	=	26	-	2
24	+	7	=	24	+	7	=	24	-	7

[LCM of 24 ans 7 is 168]

26x7

2x24

182

182- 48

134

\frac{67}{84}

24x7

7x24

168

LHS = $\frac{67}{84}$

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

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

[LCM of 6 and 7 is 42]

3	+	14	-	12	=	3	+	14-12	=	3	+	2
4		42		42		4		42		4		42

[LCM of 4 and 42 is 168]

3x42

2x4

126

126+(8)

134

\frac{67}{84}

4x42

42x4

168

RHS = $\frac{67}{84}$

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 /)

$\frac{1}{4}$ , $\frac{4}{5}$ and $\frac{-3}{8}$

RHS = Answer: $\frac{27}{40}$

SOLUTION 1 :

To verify,

( $\frac{1}{4}$ + $\frac{4}{5}$ ) + ( $\frac{-3}{8}$ ) = $\frac{1}{4}$ + ( $\frac{4}{5}$ + ( $\frac{-3}{8}$ )

LHS =

1	+	4	+	-3	=	1x5	+	4x4	+	-3
4	+	5	+	8	=	4x5	+	5x4	+	8

[ LCM of 4 and 5 is 20]

5	+	16	+	-3
20	+	20	+	8

5+16	+	-3	=	21	+	-3	=	21	-	3
20	+	8	=	20	+	8	=	20	-	8

[LCM of 20 ans 8 is 160]

21x8

3x20

168

168- 60

108

\frac{27}{40}

20x8

8x20

160

LHS = $\frac{27}{40}$

RHS = $\frac{1}{4}$ + ( $\frac{4}{5}$ + ( $\frac{-3}{8}$ ) = $\frac{1}{4}$ + ( $\frac{4}{5}$ $\frac{-3}{8}$ )

1	+	4x8	-	3x5
4	+	5x8	-	8x5

[LCM of 5 and 8 is 40]

1	+	32	-	15	=	1	+	32-15	=	1	+	17
4		40		40		4		40		4		40

[LCM of 4 and 40 is 160]

1x40

17x4

40+(68)

108

\frac{27}{40}

4x40

40x4

160

RHS = $\frac{27}{40}$

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 /)

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

RHS = Answer: $\frac{25}{24}$

SOLUTION 1 :

To verify,

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

LHS =

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

[ LCM of 4 and 6 is 24]

18	+	16	+	-3
24	+	24	+	8

18+16	+	-3	=	34	+	-3	=	34	-	3
24	+	8	=	24	+	8	=	24	-	8

[LCM of 24 ans 8 is 192]

34x8

3x24

272

272- 72

200

\frac{25}{24}

24x8

8x24

192

LHS = $\frac{25}{24}$

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

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

[LCM of 6 and 8 is 48]

3	+	32	-	18	=	3	+	32-18	=	3	+	14
4		48		48		4		48		4		48

[LCM of 4 and 48 is 192]

3x48

14x4

144

144+(56)

200

\frac{25}{24}

4x48

48x4

192

RHS = $\frac{25}{24}$

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 $\frac{-4}{8}$

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

SOLUTION 1 :

To verify,

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

LHS =

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

[ LCM of 4 and 5 is 20]

10	+	12	+	-4
20	+	20	+	8

10+12	+	-4	=	22	+	-4	=	22	-	4
20	+	8	=	20	+	8	=	20	-	8

[LCM of 20 ans 8 is 160]

22x8

4x20

176

176- 80

\frac{3}{5}

20x8

8x20

160

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

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

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

[LCM of 5 and 8 is 40]

2	+	24	-	20	=	2	+	24-20	=	2	+	4
4		40		40		4		40		4		40

[LCM of 4 and 40 is 160]

2x40

4x4

80+(16)

\frac{3}{5}

4x40

40x4

160

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

LHS = RHS

Hence, associative property is true for addition.