 # \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 ?

• Questions are typically answered in as fast as 30 minutes

### Plainmath recommends

• Get a detailed answer even on the hardest topics.
• Ask an expert for a step-by-step guidance to learn to do it yourself. Obiajulu
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 $$\displaystyle{\frac{{{8}}}{{{6}}}}$$.
$$\displaystyle\because{x}\times{\frac{{{10}}}{{{20}}}}+{\frac{{{1}}}{{{15}}}}={\frac{{{8}}}{{{6}}}}$$
$$\displaystyle\Rightarrow{\frac{{{x}}}{{{2}}}}+{\frac{{{1}}}{{{15}}}}={\frac{{{8}}}{{{6}}}}$$
$$\displaystyle\Rightarrow{\frac{{{x}}}{{{2}}}}={\frac{{{8}}}{{{6}}}}-{\frac{{{1}}}{{{15}}}}$$
$$\displaystyle\Rightarrow{\frac{{{x}}}{{{2}}}}={\frac{{{8}\times{5}-{1}\times{2}}}{{{30}}}}$$
$$\displaystyle\Rightarrow{\frac{{{x}}}{{{2}}}}={\frac{{{40}-{2}}}{{{30}}}}$$
$$\displaystyle\Rightarrow{x}={2}\times{\frac{{{38}}}{{{30}}}}$$
$$\displaystyle\Rightarrow{x}={\frac{{{38}}}{{{15}}}}$$