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Question
Evaluate:
\(\left (\dfrac{5}{-27} \right )\times \left ( \dfrac{-9}{10} \right )\)
\(\left (\dfrac{5}{-27} \right )\times \left ( \dfrac{-9}{10} \right )\)
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Solution
Step:Multiplying the given rational numbers
Given:\(\left (\dfrac{5}{-27} \right )\times \left ( \dfrac{-9}{10} \right )\)
\(\because product ~of ~two~ rational ~numbers=\frac{product ~of ~the ~numerators}{product~ of~ the ~denominators}\)
\(\therefore \left ( \dfrac{5}{-27} \right )\times \left ( \dfrac{-9}{10} \right )=\dfrac{5\times (-9)}{-27\times 20}\)
\(=\dfrac{5\times 9}{27\times 20}\)
\(=\dfrac{5\times 9}{9\times 3\times 5\times 4}\)
\(=\dfrac{1}{3\times 4}\)
\(=\dfrac{1}{12}\)
Hence, the required product is \(\dfrac{1}{12}\).
Given:\(\left (\dfrac{5}{-27} \right )\times \left ( \dfrac{-9}{10} \right )\)
\(\because product ~of ~two~ rational ~numbers=\frac{product ~of ~the ~numerators}{product~ of~ the ~denominators}\)
\(\therefore \left ( \dfrac{5}{-27} \right )\times \left ( \dfrac{-9}{10} \right )=\dfrac{5\times (-9)}{-27\times 20}\)
\(=\dfrac{5\times 9}{27\times 20}\)
\(=\dfrac{5\times 9}{9\times 3\times 5\times 4}\)
\(=\dfrac{1}{3\times 4}\)
\(=\dfrac{1}{12}\)
Hence, the required product is \(\dfrac{1}{12}\).
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