Fractions: Level 2 Challenges


A waiter's income consists of his salary and tips made. During one week his tips were 5/4 of his salary . What fraction of his income came from tips?

If \(\color{red}{a}\) and \(\color{blue}{b}\) are positive, what is the minimum possible value of \[\large \frac { \color{red}{a}}{ \color{blue}{b} } +\frac { \color{blue}{b} }{\color{red}{a} }?\]

Paul try to solve the value of \(\frac{x+y}{z}\) using a calculator.

He inputs \(x+y \div z\) and the result is \(12\).

For clarification, he inputs \(y+x \div z\) and the result is \(9\).

Lastly, Paul concludes that his input is wrong.

So, he input \((x+y) \div z\) and the result is \( 7\).

In the story, find the value of \(x+y+z\).

\[x=\dfrac{111110}{111111} , y = \dfrac{222221}{222223} , z = \dfrac{333331}{333334}\]

Compare \(x,y,z\).

Find the positive integer \(\color{blue}{X}\) that makes this equation true:

\[ \Large \frac { 2 }{ \color{blue}{X} } -\frac { \color{blue}{X}}{ 5 } =\frac { 1 }{ 15 }. \]


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