Basic Mathematics

# 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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