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Question

Express each of the following ratios in its simplest form 
$$ 2 \dfrac{1}{3} : 3 \dfrac{1}{2} : 1 \dfrac{1}{4} $$ 


Solution

$$ 2 \dfrac{1}{3} : 3 \dfrac{1}{2} : 1 \dfrac{1}{4} $$ 
This can be written as 
$$ \dfrac{7}{3} : \dfrac{7}{2} : \dfrac{5}{4} $$ 
Now , taking L.C.M of $$ 3 , 2 $$ and $$ 4 $$ we get 
$$ \dfrac{7}{3} \times 12 : \dfrac{7}{2} \times 12 : \dfrac{5}{4} \times 12 $$ 
$$ = 28 : 42 : 15 $$ 
Hence , the simplest form of $$ 2 \dfrac{1}{3} : 3 \dfrac{1}{2} : 1 \dfrac{1}{4} $$ is $$ 28 : 42 : 15 $$

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