Sasi Math (Revised for 1024)

Scroll:Real Number System >> Rational Numbers ( Exercise 1.1) >> saq (4376)

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 division of the following pairs of rational numbers.(ples use /)

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

RHS =

Answer:_______________

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

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

RHS =

Answer:_______________

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

$\frac{1}{2}$ , $\frac{5}{6}$ and $\frac{-4}{7}$

RHS =

Answer:_______________

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

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

RHS =

Answer:_______________

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

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

RHS =

Answer:_______________

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

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

RHS =

Answer:_______________

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

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

RHS =

Answer:_______________

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

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

RHS =

Answer:_______________

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

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

RHS =

Answer:_______________

10)

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

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

RHS =

Answer:_______________

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

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

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

SOLUTION 1 :

To verify,

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

LHS =

2	÷	5	÷	-4	=	2	÷	5	x	5	=	2	÷	-25	=	2	x	20	=	40	=	$\frac{-8}{15}$
3		5		5		3		5		-4		3		20		3		25		-75

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

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

2	÷	5	÷	-4	=	2	x	5	÷	5	=	10	÷	-4	=	10	x	- 5	=	50	=	- $\frac{5}{6}$
3		5		5		3		5		-4		15		5		15		4		-60

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

LHS ≠ RHS

Hence, associative property is not true for division.

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

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

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

SOLUTION 1 :

To verify,

$\frac{1}{4}$ ÷ ( $\frac{4}{4}$ ÷ ( $\frac{-2}{8}$ )) = ( $\frac{1}{4}$ ÷ $\frac{4}{4}$ ) ÷ ( $\frac{-2}{8}$ )

LHS =

1	÷	4	÷	-2	=	1	÷	4	x	8	=	1	÷	-32	=	1	x	8	=	8	=	- $\frac{1}{1}$ 6
4		4		8		4		4		-2		4		8		4		32		-128

LHS = - $\frac{1}{1}$ 6

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

1	÷	4	÷	-2	=	1	x	4	÷	8	=	4	÷	-2	=	4	x	- 8	=	32	=	- $\frac{1}{1}$
4		4		8		4		4		-2		16		8		16		2		-32

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

LHS ≠ RHS

Hence, associative property is not true for division.

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

$\frac{1}{2}$ , $\frac{5}{6}$ and $\frac{-4}{7}$

RHS = Answer: 2 $\frac{1}{2}$ 0

SOLUTION 1 :

To verify,

$\frac{1}{2}$ ÷ ( $\frac{5}{6}$ ÷ ( $\frac{-4}{7}$ )) = ( $\frac{1}{2}$ ÷ $\frac{5}{6}$ ) ÷ ( $\frac{-4}{7}$ )

LHS =

1	÷	5	÷	-4	=	1	÷	5	x	7	=	1	÷	-35	=	1	x	24	=	24	=	$\frac{-12}{35}$
2		6		7		2		6		-4		2		24		2		35		-70

LHS = $\frac{-12}{35}$

RHS = $\frac{1}{2}$ + ( $\frac{5}{6}$ + ( $\frac{-4}{7}$ ) = $\frac{1}{2}$ + ( $\frac{5}{6}$ $\frac{-4}{7}$ )

1	÷	5	÷	-4	=	1	x	6	÷	7	=	6	÷	-4	=	6	x	- 7	=	42	=	-2 $\frac{1}{2}$ 0
2		6		7		2		5		-4		10		7		10		4		-40

RHS = -2 $\frac{1}{2}$ 0

LHS ≠ RHS

Hence, associative property is not true for division.

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

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

RHS = Answer: $\frac{3}{8}$

SOLUTION 1 :

To verify,

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

LHS =

1	÷	4	÷	-4	=	1	÷	4	x	6	=	1	÷	-24	=	1	x	16	=	16	=	$\frac{-1}{6}$
4		4		6		4		4		-4		4		16		4		24		-96

LHS = $\frac{-1}{6}$

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

1	÷	4	÷	-4	=	1	x	4	÷	6	=	4	÷	-4	=	4	x	- 6	=	24	=	- $\frac{3}{8}$
4		4		6		4		4		-4		16		6		16		4		-64

RHS = - $\frac{3}{8}$

LHS ≠ RHS

Hence, associative property is not true for division.

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

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

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

SOLUTION 1 :

To verify,

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

LHS =

1	÷	2	÷	-4	=	1	÷	2	x	6	=	1	÷	-12	=	1	x	20	=	20	=	$\frac{-5}{6}$
2		5		6		2		5		-4		2		20		2		12		-24

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

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

1	÷	2	÷	-4	=	1	x	5	÷	6	=	5	÷	-4	=	5	x	- 6	=	30	=	- $\frac{15}{8}$
2		5		6		2		2		-4		4		6		4		4		-16

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

LHS ≠ RHS

Hence, associative property is not true for division.

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

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

RHS = Answer: $\frac{8}{1}$

SOLUTION 1 :

To verify,

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

LHS =

3	÷	2	÷	-3	=	3	÷	2	x	8	=	3	÷	-16	=	3	x	12	=	36	=	$\frac{-9}{8}$
2		4		8		2		4		-3		2		12		2		16		-32

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

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

3	÷	2	÷	-3	=	3	x	4	÷	8	=	12	÷	-3	=	12	x	- 8	=	96	=	- $\frac{8}{1}$
2		4		8		2		2		-3		4		8		4		3		-12

RHS = - $\frac{8}{1}$

LHS ≠ RHS

Hence, associative property is not true for division.

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

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

RHS = Answer: $\frac{15}{2}$

SOLUTION 1 :

To verify,

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

LHS =

2	÷	2	÷	-2	=	2	÷	2	x	6	=	2	÷	-12	=	2	x	10	=	20	=	$\frac{-5}{6}$
2		5		6		2		5		-2		2		10		2		12		-24

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

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

2	÷	2	÷	-2	=	2	x	5	÷	6	=	10	÷	-2	=	10	x	- 6	=	60	=	- $\frac{15}{2}$
2		5		6		2		2		-2		4		6		4		2		-8

RHS = - $\frac{15}{2}$

LHS ≠ RHS

Hence, associative property is not true for division.

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

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

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

SOLUTION 1 :

To verify,

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

LHS =

2	÷	3	÷	-2	=	2	÷	3	x	5	=	2	÷	-15	=	2	x	8	=	16	=	$\frac{-8}{15}$
2		4		5		2		4		-2		2		8		2		15		-30

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

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

2	÷	3	÷	-2	=	2	x	4	÷	5	=	8	÷	-2	=	8	x	- 5	=	40	=	- $\frac{10}{3}$
2		4		5		2		3		-2		6		5		6		2		-12

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

LHS ≠ RHS

Hence, associative property is not true for division.

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

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

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

SOLUTION 1 :

To verify,

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

LHS =

2	÷	5	÷	-3	=	2	÷	5	x	5	=	2	÷	-25	=	2	x	12	=	24	=	$\frac{-8}{25}$
3		4		5		3		4		-3		3		12		3		25		-75

LHS = $\frac{-8}{25}$

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

2	÷	5	÷	-3	=	2	x	4	÷	5	=	8	÷	-3	=	8	x	- 5	=	40	=	- $\frac{8}{9}$
3		4		5		3		5		-3		15		5		15		3		-45

RHS = - $\frac{8}{9}$

LHS ≠ RHS

Hence, associative property is not true for division.

10)

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

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

RHS = Answer: $\frac{12}{5}$

SOLUTION 1 :

To verify,

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

LHS =

1	÷	5	÷	-2	=	1	÷	5	x	8	=	1	÷	-40	=	1	x	12	=	12	=	$\frac{-3}{20}$
2		6		8		2		6		-2		2		12		2		40		-80

LHS = $\frac{-3}{20}$

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

1	÷	5	÷	-2	=	1	x	6	÷	8	=	6	÷	-2	=	6	x	- 8	=	48	=	- $\frac{12}{5}$
2		6		8		2		5		-2		10		8		10		2		-20

RHS = - $\frac{12}{5}$

LHS ≠ RHS

Hence, associative property is not true for division.