Math, asked by aahaman77, 1 year ago

prove componendo dividendo​

Answers

Answered by pallavi4191
0

Answer:

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Answered by skpoetess
1

Answer:

Proof

a

,

b

,

c

and

d

are four literals but

b

and

d

are non-zero literal numbers. Assume, the ratio of

a

to

b

is equal to the ratio of

c

to

d

.

a

b

=

c

d

Step: 1

Add one both sides of the left and right hand side fractions.

a

b

+

1

=

c

d

+

1

a

+

b

b

=

c

+

d

d

Step: 2

Subtract one both sides of the left and right hand side fractions.

a

b

1

=

c

d

1

a

b

b

=

c

d

d

Step: 3

Divide the equation obtained in step 1 by the equation obtained in step 2.

[

a

+

b

b

]

[

a

b

b

]

=

[

c

+

d

d

]

[

c

d

d

]

[

a

+

b

b

]

×

[

b

a

b

]

=

[

c

+

d

d

]

×

[

d

c

d

]

[

a

+

b

a

b

]

×

[

b

b

]

=

[

c

+

d

c

d

]

×

[

d

d

]

[

a

+

b

a

b

]

×

[

b

b

]

=

[

c

+

d

c

d

]

×

[

d

d

]

[

a

+

b

a

b

]

×

1

=

[

c

+

d

c

d

]

×

1

a

+

b

a

b

=

c

+

d

c

d

Therefore, it is proved that if ratio of

a

to

b

is equal to the ratio of

c

to

d

, then the ratio of

a

+

b

to

a

b

is equal to the ratio of

c

+

d

to

c

d

. This property is called the componendo and dividendo rule.

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