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 /)

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

RHS =

Answer:_______________

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

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

RHS =

Answer:_______________

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

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

RHS =

Answer:_______________

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

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

RHS =

Answer:_______________

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

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

RHS =

Answer:_______________

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

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

RHS =

Answer:_______________

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

$\frac{1}{2}$ , $\frac{2}{6}$ and $\frac{-2}{7}$

RHS =

Answer:_______________

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

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

RHS =

Answer:_______________

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

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

RHS =

Answer:_______________

10)

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

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

RHS =

Answer:_______________

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

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

RHS = Answer: $\frac{17}{14}$

SOLUTION 1 :

To verify,

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

LHS =

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

[ LCM of 2 and 4 is 8]

4	+	8	+	-2
8	+	8	+	7

4+8	+	-2	=	12	+	-2	=	12	-	2
8	+	7	=	8	+	7	=	8	-	7

[LCM of 8 ans 7 is 56]

12x7	-	2x8	=	84	-	16	=	84- 16	=	68	=	$\frac{17}{14}$
8x7		7x8		56		56		56		56

LHS = $\frac{17}{14}$

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

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

[LCM of 4 and 7 is 28]

1	+	28	-	8	=	1	+	28-8	=	1	+	20
2		28		28		2		28		2		28

[LCM of 2 and 28 is 56]

1x28

20x2

28+(40)

\frac{17}{14}

2x28

28x2

RHS = $\frac{17}{14}$

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 /)

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

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

SOLUTION 1 :

To verify,

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

LHS =

1	+	4	+	-2	=	1x4	+	4x2	+	-2
2	+	4	+	5	=	2x4	+	4x2	+	5

[ LCM of 2 and 4 is 8]

4	+	8	+	-2
8	+	8	+	5

4+8	+	-2	=	12	+	-2	=	12	-	2
8	+	5	=	8	+	5	=	8	-	5

[LCM of 8 ans 5 is 40]

12x5	-	2x8	=	60	-	16	=	60- 16	=	44	=	$\frac{11}{10}$
8x5		5x8		40		40		40		40

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

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

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

[LCM of 4 and 5 is 20]

1	+	20	-	8	=	1	+	20-8	=	1	+	12
2		20		20		2		20		2		20

[LCM of 2 and 20 is 40]

1x20

12x2

20+(24)

\frac{11}{10}

2x20

20x2

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 /)

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

RHS = Answer: $\frac{17}{60}$

SOLUTION 1 :

To verify,

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

LHS =

3	+	2	+	-4	=	3x6	+	2x4	+	-4
4	+	6	+	5	=	4x6	+	6x4	+	5

[ LCM of 4 and 6 is 24]

18	+	8	+	-4
24	+	24	+	5

18+8	+	-4	=	26	+	-4	=	26	-	4
24	+	5	=	24	+	5	=	24	-	5

[LCM of 24 ans 5 is 120]

26x5

4x24

130

130- 96

\frac{17}{60}

24x5

5x24

120

LHS = $\frac{17}{60}$

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

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

[LCM of 6 and 5 is 30]

3	+	10	-	24	=	3	+	10-24	=	3	+	-14
4		30		30		4		30		4		30

[LCM of 4 and 30 is 120]

3x30

-14x4

-56

90+(-56)

\frac{17}{60}

4x30

30x4

120

RHS = $\frac{17}{60}$

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 /)

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

RHS = Answer: $\frac{23}{30}$

SOLUTION 1 :

To verify,

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

LHS =

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

[ LCM of 3 and 6 is 18]

12	+	9	+	-2
18	+	18	+	5

12+9	+	-2	=	21	+	-2	=	21	-	2
18	+	5	=	18	+	5	=	18	-	5

[LCM of 18 ans 5 is 90]

21x5	-	2x18	=	105	-	36	=	105- 36	=	69	=	$\frac{23}{30}$
18x5		5x18		90		90		90		90

LHS = $\frac{23}{30}$

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

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

[LCM of 6 and 5 is 30]

2	+	15	-	12	=	2	+	15-12	=	2	+	3
3		30		30		3		30		3		30

[LCM of 3 and 30 is 90]

2x30

3x3

60+(9)

\frac{23}{30}

3x30

30x3

RHS = $\frac{23}{30}$

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 /)

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

RHS = Answer: $\frac{59}{60}$

SOLUTION 1 :

To verify,

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

LHS =

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

[ LCM of 4 and 6 is 24]

18	+	20	+	-3
24	+	24	+	5

18+20	+	-3	=	38	+	-3	=	38	-	3
24	+	5	=	24	+	5	=	24	-	5

[LCM of 24 ans 5 is 120]

38x5

3x24

190

190- 72

118

\frac{59}{60}

24x5

5x24

120

LHS = $\frac{59}{60}$

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

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

[LCM of 6 and 5 is 30]

3	+	25	-	18	=	3	+	25-18	=	3	+	7
4		30		30		4		30		4		30

[LCM of 4 and 30 is 120]

3x30

7x4

90+(28)

118

\frac{59}{60}

4x30

30x4

120

RHS = $\frac{59}{60}$

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 /)

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

RHS = Answer: $\frac{29}{14}$

SOLUTION 1 :

To verify,

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

LHS =

3	+	5	+	-3	=	3x5	+	5x2	+	-3
2	+	5	+	7	=	2x5	+	5x2	+	7

[ LCM of 2 and 5 is 10]

15	+	10	+	-3
10	+	10	+	7

15+10	+	-3	=	25	+	-3	=	25	-	3
10	+	7	=	10	+	7	=	10	-	7

[LCM of 10 ans 7 is 70]

25x7

3x10

175

175- 30

145

\frac{29}{14}

10x7

7x10

LHS = $\frac{29}{14}$

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

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

[LCM of 5 and 7 is 35]

3	+	35	-	15	=	3	+	35-15	=	3	+	20
2		35		35		2		35		2		35

[LCM of 2 and 35 is 70]

3x35

20x2

105

105+(40)

145

\frac{29}{14}

2x35

35x2

RHS = $\frac{29}{14}$

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 /)

$\frac{1}{2}$ , $\frac{2}{6}$ and $\frac{-2}{7}$

RHS = Answer: $\frac{23}{42}$

SOLUTION 1 :

To verify,

( $\frac{1}{2}$ + $\frac{2}{6}$ ) + ( $\frac{-2}{7}$ ) = $\frac{1}{2}$ + ( $\frac{2}{6}$ + ( $\frac{-2}{7}$ )

LHS =

1	+	2	+	-2	=	1x6	+	2x2	+	-2
2	+	6	+	7	=	2x6	+	6x2	+	7

[ LCM of 2 and 6 is 12]

6	+	4	+	-2
12	+	12	+	7

6+4	+	-2	=	10	+	-2	=	10	-	2
12	+	7	=	12	+	7	=	12	-	7

[LCM of 12 ans 7 is 84]

10x7	-	2x12	=	70	-	24	=	70- 24	=	46	=	$\frac{23}{42}$
12x7		7x12		84		84		84		84

LHS = $\frac{23}{42}$

RHS = $\frac{1}{2}$ + ( $\frac{2}{6}$ + ( $\frac{-2}{7}$ ) = $\frac{1}{2}$ + ( $\frac{2}{6}$ $\frac{-2}{7}$ )

1	+	2x7	-	2x6
2	+	6x7	-	7x6

[LCM of 6 and 7 is 42]

1	+	14	-	12	=	1	+	14-12	=	1	+	2
2		42		42		2		42		2		42

[LCM of 2 and 42 is 84]

1x42

2x2

42+(4)

\frac{23}{42}

2x42

42x2

RHS = $\frac{23}{42}$

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 /)

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

RHS = Answer: $\frac{22}{15}$

SOLUTION 1 :

To verify,

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

LHS =

3	+	4	+	-2	=	3x5	+	4x3	+	-2
3	+	5	+	6	=	3x5	+	5x3	+	6

[ LCM of 3 and 5 is 15]

15	+	12	+	-2
15	+	15	+	6

15+12	+	-2	=	27	+	-2	=	27	-	2
15	+	6	=	15	+	6	=	15	-	6

[LCM of 15 ans 6 is 90]

27x6

2x15

162

162- 30

132

\frac{22}{15}

15x6

6x15

LHS = $\frac{22}{15}$

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

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

[LCM of 5 and 6 is 30]

3	+	24	-	10	=	3	+	24-10	=	3	+	14
3		30		30		3		30		3		30

[LCM of 3 and 30 is 90]

3x30

14x3

90+(42)

132

\frac{22}{15}

3x30

30x3

RHS = $\frac{22}{15}$

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 /)

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

RHS = Answer: $\frac{13}{30}$

SOLUTION 1 :

To verify,

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

LHS =

2	+	2	+	-2	=	2x6	+	2x4	+	-2
4	+	6	+	5	=	4x6	+	6x4	+	5

[ LCM of 4 and 6 is 24]

12	+	8	+	-2
24	+	24	+	5

12+8	+	-2	=	20	+	-2	=	20	-	2
24	+	5	=	24	+	5	=	24	-	5

[LCM of 24 ans 5 is 120]

20x5

2x24

100

100- 48

\frac{13}{30}

24x5

5x24

120

LHS = $\frac{13}{30}$

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

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

[LCM of 6 and 5 is 30]

2	+	10	-	12	=	2	+	10-12	=	2	+	-2
4		30		30		4		30		4		30

[LCM of 4 and 30 is 120]

2x30

-2x4

-8

60+(-8)

\frac{13}{30}

4x30

30x4

120

RHS = $\frac{13}{30}$

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 /)

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

RHS = Answer: $\frac{41}{28}$

SOLUTION 1 :

To verify,

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

LHS =

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

[ LCM of 4 and 4 is 16]

8	+	20	+	-2
16	+	16	+	7

8+20	+	-2	=	28	+	-2	=	28	-	2
16	+	7	=	16	+	7	=	16	-	7

[LCM of 16 ans 7 is 112]

28x7

2x16

196

196- 32

164

\frac{41}{28}

16x7

7x16

112

LHS = $\frac{41}{28}$

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

2	+	5x7	-	2x4
4	+	4x7	-	7x4

[LCM of 4 and 7 is 28]

2	+	35	-	8	=	2	+	35-8	=	2	+	27
4		28		28		4		28		4		28

[LCM of 4 and 28 is 112]

2x28

27x4

108

56+(108)

164

\frac{41}{28}

4x28

28x4

112

RHS = $\frac{41}{28}$

LHS = RHS

Hence, associative property is true for addition.