If a /b = p/q, then (a + b)/b = b/(a+d) exists FALSE.
Let a, b, c, d be the four numbers, then
if a : b = c : d then (a + b) : b :: (c + d) : d.
If a : b :: c : d then (a - b) : b :: (c - d) : d.
Given equation,
[tex]$\Rightarrow \frac{a}{b}=\frac{p}{q}$[/tex]
Adding 1 on both sides of the equation, we get
[tex]${data-answer}amp;\Rightarrow \frac{a}{b}+1=\frac{p}{q}+1 \\[/tex]
[tex]${data-answer}amp;\Rightarrow \frac{a+b}{b}=\frac{p+q}{q}[/tex]
This rule exists also comprehended as the Componendo property of fractions.
Therefore, [tex]$\frac{a+b}{b}=\frac{p+q}{q}$[/tex] then a = pb + q but the hypothesis says that
a = (p+b) / q.
If a /b = p/q, then (a + b)/b = b/(a+d) exists FALSE.
To learn more about the Componendo property of fractions refer to:
https://brainly.com/question/2933117
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