Question

a rational no 6/7 is subtracted from 9/11. the result is then added to the additive inverse of -5/8. what is the reciprocal of the final sum? ​

Answer 1

$\displaystyle\huge\red{\underline{\underline{Solution}}}$

GIVEN

• A rational no 6/7 is subtracted from 9/11

• The result is then added to the additive inverse of -5/8

TO DETERMINE

The reciprocal of the final sum

FORMULA TO BE IMPLEMENTED

1. The additive inverse of a

real number x is - x

$2. \: \: \sf{If \: \: x \ne 0}$

$\displaystyle \sf{Then \: the \: reciprocal \: of \: x \: is \: \: \: \frac{1}{x} }$

CALCULATION

$\displaystyle \sf{A \: rational \: no \: \: \frac{6}{7} \: \: is \: substracted \: from \: \frac{9}{11} \: }$

So the resulting rational number

$= \displaystyle \sf{ \frac{9}{11} \: - \frac{6}{7} }$

$= \displaystyle \sf{ \frac{63 - 66}{77} \: }$

$= \displaystyle \sf{ - \frac{3}{77} \: }$

$\displaystyle \sf{ \: }Now \: the \: Additive \: inverse \: of \: \: - \frac{5}{8} \: \: is \: \: \frac{5}{8}$

So the next resulting rational number is

$\displaystyle \sf{ \: } = \frac{5}{8} - \frac{3}{77}$

$\displaystyle \sf{ \: } = \frac{385 - 24}{616}$

$\displaystyle \sf{ \: } = \frac{361}{616}$

Now the required reciprocal of the last obtained rational number is

$= \displaystyle \sf{ \: } \frac{1}{ \frac{361}{616} }$

$= \displaystyle \sf{ \: } \frac{616}{361}$

RESULT

$\boxed{ \displaystyle \sf{ \: The \: required \: rational \: number = \: }{ \frac{616}{361} \: \: } }$

━━━━━━━━━━━━━━━━

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Answer 2

Step-by-step explanation:

A rational no 6/7 is subtracted from 9/11

The result is then added to the additive inverse of -5/8

TO DETERMINE

The reciprocal of the final sum

FORMULA TO BE IMPLEMENTED

1. The additive inverse of a

real number x is - x

2.

�

�

�

≠

0

2.Ifx



=0

�

ℎ

�

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ℎ

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�

�

1

�

Thenthereciprocalofxis

x

1

CALCULATION

�

�

�

�

�

�

�

�

�

�

�

6

7

�

�

�

�

�

�

�

�

�

�

�

�

�

�

�

�

�

9

11

Arationalno

7

6

issubstractedfrom

11

9

So the resulting rational number

=

9

11

−

6

7

=

11

9

−

7

6

=

63

−

66

77

=

77

63−66

=

−

3

77

=−

77

3

�

�

�

�

ℎ

�

�

�

�

�

�

�

�

�

�

�

�

�

�

�

�

�

�

−

5

8

�

�

5

8

NowtheAdditiveinverseof−

8

5

is

8

5

So the next resulting rational number is

=

5

8

−

3

77

=

8

5

−

77

3

=

385

−

24

616

=

616

385−24

=

361

616

=

616

361

Now the required reciprocal of the last obtained rational number is

=

1

361

616

=

616

361

1

=

616

361

=

361

616A rational no 6/7 is subtracted from 9/11

The result is then added to the additive inverse of -5/8

TO DETERMINE

The reciprocal of the final sum

FORMULA TO BE IMPLEMENTED

1. The additive inverse of a

real number x is - x

2.

�

�

�

≠

0

2.Ifx



=0

�

ℎ

�

�

�

ℎ

�

�

�

�

�

�

�

�

�

�

�

�

�

�

�

�

1

�

Thenthereciprocalofxis

x

1

CALCULATION

�

�

�

�

�

�

�

�

�

�

�

6

7

�

�

�

�

�

�

�

�

�

�

�

�

�

�

�

�

�

9

11

Arationalno

7

6

issubstractedfrom

11

9

So the resulting rational number

=

9

11

−

6

7

=

11

9

−

7

6

=

63

−

66

77

=

77

63−66

=

−

3

77

=−

77

3

�

�

�

�

ℎ

�

�

�

�

�

�

�

�

�

�

�

�

�

�

�

�

�

�

−

5

8

�

�

5

8

NowtheAdditiveinverseof−

8

5

is

8

5

So the next resulting rational number is

=

5

8

−

3

77

=

8

5

−

77

3

=

385

−

24

616

=

616

385−24

=

361

616

=

616

361

Now the required reciprocal of the last obtained rational number is

=

1

361

616

=

616

361

1

=

616

361

=

361

616

A rational no 6/7 is subtracted from 9/11

The result is then added to the additive inverse of -5/8

TO DETERMINE

The reciprocal of the final sum

FORMULA TO BE IMPLEMENTED

1. The additive inverse of a

real number x is - x

2.

�

�

�

≠

0

2.Ifx



=0

�

ℎ

�

�

�

ℎ

�

�

�

�

�

�

�

�

�

�

�

�

�

�

�

�

1

�

Thenthereciprocalofxis

x

1

CALCULATION

�

�

�

�

�

�

�

�

�

�

�

6

7

�

�

�

�

�

�

�

�

�

�

�

�

�

�

�

�

�

9

11

Arationalno

7

6

issubstractedfrom

11

9

So the resulting rational number

=

9

11

−

6

7

=

11

9

−

7

6

=

63

−

66

77

=

77

63−66

=

−

3

77

=−

77

3

�

�

�

�

ℎ

�

�

�

�

�

�

�

�

�

�

�

�

�

�

�

�

�

�

−

5

8

�

�

5

8

NowtheAdditiveinverseof−

8

5

is

8

5

So the next resulting rational number is

=

5

8

−

3

77

=

8

5

−

77

3

=

385

−

24

616

=

616

385−24

=

361

616

=

616

361

Now the required reciprocal of the last obtained rational number is

=

1

361

616

=

616

361

1

=

616

361

=

361

616

A rational no 6/7 is subtracted from 9/11

The result is then added to the additive inverse of -5/8

TO DETERMINE

The reciprocal of the final sum

FORMULA TO BE IMPLEMENTED

1. The additive inverse of a

real number x is - x

2.

�

�

�

≠

0

2.Ifx



=0

�

ℎ

�

�

�

ℎ

�

�

�

�

�

�

�

�

�

�

�

�

�

�

�

�

1

�

Thenthereciprocalofxis

x

1

CALCULATION

�

�

�

�

�

�

�

�

�

�

�

6

7

�

�

�

�

�

�

�

�

�

�

�

�

�

�

�

�

�

9

11

Arationalno

7

6

issubstractedfrom

11

9

So the resulting rational number

=

9

11

−

6

7

=

11

9

−

7

6

=

63

−

66

77

=

77

63−66

=

−

3

77

=−

77

3

�

�

�

�

ℎ

�

�

�

�

�

�

�

�

�

�

�

�

�

�

�

�

�

�

−

5

8

�

�

5

8

NowtheAdditiveinverseof−

8

5

is

8

5

So the next resulting rational number is

=

5

8

−

3

77

=

8

5

−

77

3

=

385

−

24

616

=

616

385−24

=

361

616

=

616

361

Now the required reciprocal of the last obtained rational number is

=

1

361

616

=

616

361

1

=

616

361

=

361

616