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If a/b = c/d, implies (a b)/(a–b) = (c d)/(c–d), the process is called
- a)Componendo
- b)Dividendo
- c)Componendo and Dividendo
- d)none of these
Correct answer is option 'C'. Can you explain this answer?
Most Upvoted Answer
If a/b = c/d, implies (a b)/(a–b) = (c d)/(c–d), the process is called...
Componendo and Dividendo
Componendo and Dividendo is a mathematical rule used to manipulate equations involving fractions. It allows us to prove that two ratios are equal by adding or subtracting the numerator and denominator of each ratio. This process is also known as the method of alternation.
The rule states that if a/b = c/d, then (a+b)/(a-b) = (c+d)/(c-d). We can also reverse the process and say that if (a+b)/(a-b) = (c+d)/(c-d), then a/b = c/d.
Explanation
In this question, we are given that a/b = c/d. We need to prove that (a b)/(a–b) = (c d)/(c–d). We can use the Componendo and Dividendo rule to prove this statement.
Let's start by adding and subtracting the numerator and denominator of each ratio:
(a+b)/(a-b) = [(a+b)/(a+b)]*(a/b) / [(a+b)/(a+b)]*(a-b)
(c+d)/(c-d) = [(c+d)/(c+d)]*(c/d) / [(c+d)/(c+d)]*(c-d)
Simplifying these expressions, we get:
(a+b)/(a-b) = (a+b)/(a+b-a+b) * a/b / (a+b-a-b) = 2a/b
(c+d)/(c-d) = (c+d)/(c+d-c-d) * c/d / (c+d-c-d) = 2c/d
Now we can substitute these expressions back into our original statement:
(a b)/(a–b) = (a/b)*(b/(a-b)) = (a/b)*(1/(1-a/b)) = (a/b)*(1/(b-a)/b) = a/(b-a)
(c d)/(c–d) = (c/d)*(d/(c-d)) = (c/d)*(1/(1-c/d)) = (c/d)*(1/(d-c)/d) = c/(d-c)
We can see that a/(b-a) = c/(d-c), which proves the statement (a b)/(a–b) = (c d)/(c–d) using the Componendo and Dividendo rule.
Componendo and Dividendo is a mathematical rule used to manipulate equations involving fractions. It allows us to prove that two ratios are equal by adding or subtracting the numerator and denominator of each ratio. This process is also known as the method of alternation.
The rule states that if a/b = c/d, then (a+b)/(a-b) = (c+d)/(c-d). We can also reverse the process and say that if (a+b)/(a-b) = (c+d)/(c-d), then a/b = c/d.
Explanation
In this question, we are given that a/b = c/d. We need to prove that (a b)/(a–b) = (c d)/(c–d). We can use the Componendo and Dividendo rule to prove this statement.
Let's start by adding and subtracting the numerator and denominator of each ratio:
(a+b)/(a-b) = [(a+b)/(a+b)]*(a/b) / [(a+b)/(a+b)]*(a-b)
(c+d)/(c-d) = [(c+d)/(c+d)]*(c/d) / [(c+d)/(c+d)]*(c-d)
Simplifying these expressions, we get:
(a+b)/(a-b) = (a+b)/(a+b-a+b) * a/b / (a+b-a-b) = 2a/b
(c+d)/(c-d) = (c+d)/(c+d-c-d) * c/d / (c+d-c-d) = 2c/d
Now we can substitute these expressions back into our original statement:
(a b)/(a–b) = (a/b)*(b/(a-b)) = (a/b)*(1/(1-a/b)) = (a/b)*(1/(b-a)/b) = a/(b-a)
(c d)/(c–d) = (c/d)*(d/(c-d)) = (c/d)*(1/(1-c/d)) = (c/d)*(1/(d-c)/d) = c/(d-c)
We can see that a/(b-a) = c/(d-c), which proves the statement (a b)/(a–b) = (c d)/(c–d) using the Componendo and Dividendo rule.
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If a/b = c/d, implies (a b)/(a–b) = (c d)/(c–d), the process is called...
Boss...you forgot to put + in numerator on both Sides...
That is formula there is nothing to explain..You have to learn it...
That is formula there is nothing to explain..You have to learn it...
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