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Question

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

A
Invertendo property
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B
Alternando Property
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C
Componendo Property
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D
Dividendo Property
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Solution

## If a,b,c and d are in proportion, then we write it as a:b::c:d. ⟹ab=cd ⟹ba=dc ⟹b:a::d:c, and this property is known as Invertendo. Now, if a:b::c:d, then by the rule of proportion b×c=a×d ⟹c×b=a×d ⟹a:c::b:d, and this property is known as Alternando. Now, if a:b::c:d, then ab=cd ⟹ab+1=cd+1 ⟹a+bb=c+dd, and this property is known as Componendo. Also, if a:b::c:d, then ab=cd ⟹ab−1=cd−1 ⟹a−bb=c−dd, and this property is known as Dividendo.

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