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 a\color{#D61F06}{a} and b\color{#3D99F6}{b} are positive, what is the minimum possible value of ab+ba?\large \frac { \color{#D61F06}{a}}{ \color{#3D99F6}{b} } +\frac { \color{#3D99F6}{b} }{\color{#D61F06}{a} }?

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

He inputs x+y÷zx+y \div z and the result is 1212.

For clarification, he inputs y+x÷zy+x \div z and the result is 99.

Lastly, Paul concludes that his input is wrong.

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

In the story, find the value of x+y+zx+y+z.

x=111110111111,y=222221222223,z=333331333334x=\dfrac{111110}{111111} , y = \dfrac{222221}{222223} , z = \dfrac{333331}{333334}

Compare x,y,zx,y,z.

Find the positive integer X\color{#3D99F6}{X} that makes this equation true:

2XX5=115. \Large \frac { 2 }{ \color{#3D99F6}{X} } -\frac { \color{#3D99F6}{X}}{ 5 } =\frac { 1 }{ 15 }.

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