\frac{10}{20} and \frac{1}{15} are fractions. let x be the another f

vazelinahS 2021-10-04 Answered
\(\displaystyle{\frac{{{10}}}{{{20}}}}\) and \(\displaystyle{\frac{{{1}}}{{{15}}}}\) are fractions. let x be the another fraction.when the fraction x is multiplied by \(\displaystyle{\frac{{{10}}}{{{20}}}}\) and then added with \(\displaystyle{\frac{{{1}}}{{{15}}}}\) the resultant fraction is \(\displaystyle{\frac{{{8}}}{{{6}}}}\). Find the value of the fraction x ?

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Expert Answer

Obiajulu
Answered 2021-10-05 Author has 15637 answers
Step 1
we need to write all the steps according to the question.
we need to write all the operations as question says.
Step 2
x is a fraction.
x=?
According to the question, when x is multiplied by \(\displaystyle{\frac{{{10}}}{{{20}}}}\) and then added with \(\displaystyle{\frac{{{1}}}{{{15}}}}\) the result is \(\displaystyle{\frac{{{8}}}{{{6}}}}\).
\(\displaystyle\because{x}\times{\frac{{{10}}}{{{20}}}}+{\frac{{{1}}}{{{15}}}}={\frac{{{8}}}{{{6}}}}\)
\(\displaystyle\Rightarrow{\frac{{{x}}}{{{2}}}}+{\frac{{{1}}}{{{15}}}}={\frac{{{8}}}{{{6}}}}\)
\(\displaystyle\Rightarrow{\frac{{{x}}}{{{2}}}}={\frac{{{8}}}{{{6}}}}-{\frac{{{1}}}{{{15}}}}\)
\(\displaystyle\Rightarrow{\frac{{{x}}}{{{2}}}}={\frac{{{8}\times{5}-{1}\times{2}}}{{{30}}}}\)
\(\displaystyle\Rightarrow{\frac{{{x}}}{{{2}}}}={\frac{{{40}-{2}}}{{{30}}}}\)
\(\displaystyle\Rightarrow{x}={2}\times{\frac{{{38}}}{{{30}}}}\)
\(\displaystyle\Rightarrow{x}={\frac{{{38}}}{{{15}}}}\)
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