Question

Match the following if it is known that $a,b,c$ and $d$ are in proportion.

• A. Invertendo property
• B. Alternando Property
• C. Componendo Property
• D. Dividendo Property

Answer 1

If $a,b,c$ and $d$ are in proportion, then we write it as $a:b::c:d$.
$⟹\frac{a}{b}=\frac{c}{d}$
$⟹\frac{b}{a}=\frac{d}{c}$
$⟹b:a::d:c$, and this property is known as Invertendo.
Now, if $a:b::c:d$, then by the rule of proportion $b\times c=a\times d$
$⟹c\times b=a\times d$
$⟹a:c::b:d$, and this property is known as Alternando.
Now, if $a:b::c:d$, then $\frac{a}{b}=\frac{c}{d}$
$⟹\frac{a}{b}+1=\frac{c}{d}+1$
$⟹\frac{a+b}{b}=\frac{c+d}{d}$, and this property is known as Componendo.
Also, if $a:b::c:d$, then $\frac{a}{b}=\frac{c}{d}$
$⟹\frac{a}{b}-1=\frac{c}{d}-1$
$⟹\frac{a-b}{b}=\frac{c-d}{d}$, and this property is known as Dividendo.