Question

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★HERE IS YOURS QUESTION★

◆ Define Componando & Dividendo Rule ? Explain this with reference to an example.

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Answer 1

hello@

here is u r answer ##
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1) if a:b::c:d then
then a/b=c/d
now adding 1 both side
a/b +1= c/d +1
a+b/b=c+d/d it is componendo..........(I)
2) if a:b::c:d
then a/b=c/d
now subtracting 1 both side
a/b -1=c/d -1
a-b/b=c-d/d it is dividendo.................(ii)
3) now divide eq(ii) from (i)
(a+b)b/(a-b)b = (c+d)d/(c-d)d
a+b/a-b = c+d/c-d it is componendo and dividendo...............
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I hope dear it is helpful for u :)

Answer 2

⭐ʜᴇʏ ᴍᴀᴛᴇ!!⭐

ʜᴇʀᴇ's ᴜʀ ᴀɴsᴡᴇʀ ᴅᴇᴀʀ:-)
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◆ᴛʜᴀɴᴋ ᴜ ғᴏʀ ᴛʜᴇ ǫᴜᴇsᴛɪᴏɴ ◆

COMPONENDO AND DIVIDENDO are the theorems of proportions that helps us to perform calculations in a quick way. It reduces the amount of expansions needed.

✔The rules based on componendo and dividendo are as follows:-

If a,b,c, and d are the numbers and b,d are non-zero and also, a/b= c/d , then the following data would be taken out:-

⚫ Componendo :- (a+b)/b = (c+d)/d.

⚪ Dividendo :- (a-b)/b = (c-d)/d

⚫ For k not equal to (a/b), (a+kb)/(a-kb)=. (c+kd)/(c-kd).

⚪ And also for k not equal to (-b/d), (a/b) = (a+kc)/(b+kd).

⏩Now, Let us take two examples:-

Example 1 --

$\frac{a}{b} = 16/3 \: \: \: then \: \: \frac{a + b}{a - b} = what$
By using equation 3 that is
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For k not equal to (a/b), (a+kb)/(a-kb)=. (c+kd)/(c-kd).
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with k= 1 we know that if a/b = c/d , then

$\frac{a +b }{a - b} = \frac{c + d}{c -d} \\ \\ thus \\ \frac{a +b}{a - b} = \frac{16 + 3}{16 - 3} = \frac{19}{13}$

So, with the help of Componendo and Dividendo we can perform various calculations in a quick way and also can reduce expansions.

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