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 /)

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

RHS =

Answer:_______________

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

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

RHS =

Answer:_______________

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

$\frac{1}{4}$ , $\frac{2}{6}$ and $\frac{-4}{5}$

RHS =

Answer:_______________

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

$\frac{1}{2}$ , $\frac{5}{6}$ and $\frac{-4}{8}$

RHS =

Answer:_______________

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

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

RHS =

Answer:_______________

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

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

RHS =

Answer:_______________

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

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

RHS =

Answer:_______________

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

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

RHS =

Answer:_______________

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

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

RHS =

Answer:_______________

10)

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

$\frac{2}{3}$ , $\frac{2}{6}$ and $\frac{-2}{7}$

RHS =

Answer:_______________

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

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

RHS = Answer: $\frac{93}{70}$

SOLUTION 1 :

To verify,

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

LHS =

3	+	2	+	-4	=	3x5	+	2x2	+	-4
2	+	5	+	7	=	2x5	+	5x2	+	7

[ LCM of 2 and 5 is 10]

15	+	4	+	-4
10	+	10	+	7

15+4	+	-4	=	19	+	-4	=	19	-	4
10	+	7	=	10	+	7	=	10	-	7

[LCM of 10 ans 7 is 70]

19x7	-	4x10	=	133	-	40	=	133- 40	=	93	=	$\frac{93}{70}$
10x7		7x10		70		70		70		70

LHS = $\frac{93}{70}$

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

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

[LCM of 5 and 7 is 35]

3	+	14	-	20	=	3	+	14-20	=	3	+	-6
2		35		35		2		35		2		35

[LCM of 2 and 35 is 70]

3x35

-6x2

105

-12

105+(-12)

\frac{93}{70}

2x35

35x2

RHS = $\frac{93}{70}$

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 /)

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

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

SOLUTION 1 :

To verify,

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

LHS =

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

[ LCM of 4 and 6 is 24]

12	+	20	+	-2
24	+	24	+	6

12+20	+	-2	=	32	+	-2	=	32	-	2
24	+	6	=	24	+	6	=	24	-	6

[LCM of 24 ans 6 is 144]

32x6

2x24

192

192- 48

144

\frac{1}{1}

24x6

6x24

144

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

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

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

[LCM of 6 and 6 is 36]

2	+	30	-	12	=	2	+	30-12	=	2	+	18
4		36		36		4		36		4		36

[LCM of 4 and 36 is 144]

2x36

18x4

72+(72)

144

\frac{1}{1}

4x36

36x4

144

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 /)

$\frac{1}{4}$ , $\frac{2}{6}$ and $\frac{-4}{5}$

RHS = Answer: $\frac{-13}{60}$

SOLUTION 1 :

To verify,

( $\frac{1}{4}$ + $\frac{2}{6}$ ) + ( $\frac{-4}{5}$ ) = $\frac{1}{4}$ + ( $\frac{2}{6}$ + ( $\frac{-4}{5}$ )

LHS =

1	+	2	+	-4	=	1x6	+	2x4	+	-4
4	+	6	+	5	=	4x6	+	6x4	+	5

[ LCM of 4 and 6 is 24]

6	+	8	+	-4
24	+	24	+	5

6+8	+	-4	=	14	+	-4	=	14	-	4
24	+	5	=	24	+	5	=	24	-	5

[LCM of 24 ans 5 is 120]

14x5

4x24

70- 96

-26

\frac{-13}{60}

24x5

5x24

120

LHS = $\frac{-13}{60}$

RHS = $\frac{1}{4}$ + ( $\frac{2}{6}$ + ( $\frac{-4}{5}$ ) = $\frac{1}{4}$ + ( $\frac{2}{6}$ $\frac{-4}{5}$ )

1	+	2x5	-	4x6
4	+	6x5	-	5x6

[LCM of 6 and 5 is 30]

1	+	10	-	24	=	1	+	10-24	=	1	+	-14
4		30		30		4		30		4		30

[LCM of 4 and 30 is 120]

1x30

-14x4

-56

30+(-56)

-26

\frac{-13}{60}

4x30

30x4

120

RHS = $\frac{-13}{60}$

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 /)

$\frac{1}{2}$ , $\frac{5}{6}$ and $\frac{-4}{8}$

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

SOLUTION 1 :

To verify,

( $\frac{1}{2}$ + $\frac{5}{6}$ ) + ( $\frac{-4}{8}$ ) = $\frac{1}{2}$ + ( $\frac{5}{6}$ + ( $\frac{-4}{8}$ )

LHS =

1	+	5	+	-4	=	1x6	+	5x2	+	-4
2	+	6	+	8	=	2x6	+	6x2	+	8

[ LCM of 2 and 6 is 12]

6	+	10	+	-4
12	+	12	+	8

6+10	+	-4	=	16	+	-4	=	16	-	4
12	+	8	=	12	+	8	=	12	-	8

[LCM of 12 ans 8 is 96]

16x8	-	4x12	=	128	-	48	=	128- 48	=	80	=	$\frac{5}{6}$
12x8		8x12		96		96		96		96

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

RHS = $\frac{1}{2}$ + ( $\frac{5}{6}$ + ( $\frac{-4}{8}$ ) = $\frac{1}{2}$ + ( $\frac{5}{6}$ $\frac{-4}{8}$ )

1	+	5x8	-	4x6
2	+	6x8	-	8x6

[LCM of 6 and 8 is 48]

1	+	40	-	24	=	1	+	40-24	=	1	+	16
2		48		48		2		48		2		48

[LCM of 2 and 48 is 96]

1x48

16x2

48+(32)

\frac{5}{6}

2x48

48x2

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 /)

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

RHS = Answer: $\frac{17}{20}$

SOLUTION 1 :

To verify,

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

LHS =

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

[ LCM of 4 and 5 is 20]

15	+	12	+	-3
20	+	20	+	6

15+12	+	-3	=	27	+	-3	=	27	-	3
20	+	6	=	20	+	6	=	20	-	6

[LCM of 20 ans 6 is 120]

27x6

3x20

162

162- 60

102

\frac{17}{20}

20x6

6x20

120

LHS = $\frac{17}{20}$

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

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

[LCM of 5 and 6 is 30]

3	+	18	-	15	=	3	+	18-15	=	3	+	3
4		30		30		4		30		4		30

[LCM of 4 and 30 is 120]

3x30

3x4

90+(12)

102

\frac{17}{20}

4x30

30x4

120

RHS = $\frac{17}{20}$

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 /)

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

RHS = Answer: $\frac{13}{14}$

SOLUTION 1 :

To verify,

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

LHS =

3	+	2	+	-4	=	3x4	+	2x3	+	-4
3	+	4	+	7	=	3x4	+	4x3	+	7

[ LCM of 3 and 4 is 12]

12	+	6	+	-4
12	+	12	+	7

12+6	+	-4	=	18	+	-4	=	18	-	4
12	+	7	=	12	+	7	=	12	-	7

[LCM of 12 ans 7 is 84]

18x7	-	4x12	=	126	-	48	=	126- 48	=	78	=	$\frac{13}{14}$
12x7		7x12		84		84		84		84

LHS = $\frac{13}{14}$

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

3	+	2x7	-	4x4
3	+	4x7	-	7x4

[LCM of 4 and 7 is 28]

3	+	14	-	16	=	3	+	14-16	=	3	+	-2
3		28		28		3		28		3		28

[LCM of 3 and 28 is 84]

3x28

-2x3

-6

84+(-6)

\frac{13}{14}

3x28

28x3

RHS = $\frac{13}{14}$

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 /)

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

RHS = Answer: $\frac{61}{70}$

SOLUTION 1 :

To verify,

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

LHS =

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

[ LCM of 4 and 5 is 20]

10	+	16	+	-3
20	+	20	+	7

10+16	+	-3	=	26	+	-3	=	26	-	3
20	+	7	=	20	+	7	=	20	-	7

[LCM of 20 ans 7 is 140]

26x7

3x20

182

182- 60

122

\frac{61}{70}

20x7

7x20

140

LHS = $\frac{61}{70}$

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

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

[LCM of 5 and 7 is 35]

2	+	28	-	15	=	2	+	28-15	=	2	+	13
4		35		35		4		35		4		35

[LCM of 4 and 35 is 140]

2x35

13x4

70+(52)

122

\frac{61}{70}

4x35

35x4

140

RHS = $\frac{61}{70}$

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 /)

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

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

SOLUTION 1 :

To verify,

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

LHS =

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

[ LCM of 2 and 6 is 12]

12	+	4	+	-4
12	+	12	+	6

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

[LCM of 12 ans 6 is 72]

16x6	-	4x12	=	96	-	48	=	96- 48	=	48	=	$\frac{2}{3}$
12x6		6x12		72		72		72		72

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

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

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

[LCM of 6 and 6 is 36]

2	+	12	-	24	=	2	+	12-24	=	2	+	-12
2		36		36		2		36		2		36

[LCM of 2 and 36 is 72]

2x36

-12x2

-24

72+(-24)

\frac{2}{3}

2x36

36x2

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 /)

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

RHS = Answer: $\frac{3}{10}$

SOLUTION 1 :

To verify,

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

LHS =

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

[ LCM of 4 and 5 is 20]

10	+	12	+	-4
20	+	20	+	5

10+12	+	-4	=	22	+	-4	=	22	-	4
20	+	5	=	20	+	5	=	20	-	5

[LCM of 20 ans 5 is 100]

22x5

4x20

110

110- 80

\frac{3}{10}

20x5

5x20

100

LHS = $\frac{3}{10}$

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

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

[LCM of 5 and 5 is 25]

2	+	15	-	20	=	2	+	15-20	=	2	+	-5
4		25		25		4		25		4		25

[LCM of 4 and 25 is 100]

2x25

-5x4

-20

50+(-20)

\frac{3}{10}

4x25

25x4

100

RHS = $\frac{3}{10}$

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 /)

$\frac{2}{3}$ , $\frac{2}{6}$ and $\frac{-2}{7}$

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

SOLUTION 1 :

To verify,

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

LHS =

2	+	2	+	-2	=	2x6	+	2x3	+	-2
3	+	6	+	7	=	3x6	+	6x3	+	7

[ LCM of 3 and 6 is 18]

12	+	6	+	-2
18	+	18	+	7

12+6	+	-2	=	18	+	-2	=	18	-	2
18	+	7	=	18	+	7	=	18	-	7

[LCM of 18 ans 7 is 126]

18x7

2x18

126

126- 36

\frac{5}{7}

18x7

7x18

126

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

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

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

[LCM of 6 and 7 is 42]

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

[LCM of 3 and 42 is 126]

2x42

2x3

84+(6)

\frac{5}{7}

3x42

42x3

126

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

LHS = RHS

Hence, associative property is true for addition.