Question 1209050
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Answer: <font color=red>18/35</font>


Explanation


Draw a grid of rectangles that are 7 units tall and 5 units across.
{{{
drawing(400,400,-4,3,-5,4,
line(-3, 3, 2, 3),line(-3, 2, 2, 2),line(-3, 1, 2, 1),line(-3, 0, 2, 0),line(-3, -1, 2, -1),line(-3, -2, 2, -2),line(-3, -3, 2, -3),line(-3, -4, 2, -4),line(-3, 3, -3, -4),line(-2, 3, -2, -4),line(-1, 3, -1, -4),line(0, 3, 0, -4),line(1, 3, 1, -4),line(2, 3, 2, -4),locate(-3.5,2.75,1),locate(-3.5,1.75,2),locate(-3.5,0.75,3),locate(-3.5,-0.25,4),locate(-3.5,-1.25,5),locate(-3.5,-2.25,6),locate(-3.5,-3.25,7),locate(-2.55,3.5,1),locate(-1.55,3.5,2),locate(-0.55,3.5,3),locate(0.45,3.5,4),locate(1.45,3.5,5)
)
}}}
You can use graph paper or make your own grid. 
Another approach is to take a screenshot of a blank excel spreadsheet so you can use it in something like MS Paint.


Shade the entire top row to represent Frank spending 1/7 of his starting money. You have shaded 1 row out of 7 rows total. The unshaded stuff is what he has left after buying the shoes (but he hasn't bought the shirt just yet). I'll represent this shading with a red X.


Then shade two entire columns (out of the 5 total columns) so we can depict Frank spending 2/5 of his remaining money. I'll represent this additional shading with a blue X. The unshaded blocks represent his remaining amount of money after buying the shoes and shirt.
{{{
drawing(400,400,-4,3,-5,4,
line(-3, 3, 2, 3),line(-3, 2, 2, 2),line(-3, 1, 2, 1),line(-3, 0, 2, 0),line(-3, -1, 2, -1),line(-3, -2, 2, -2),line(-3, -3, 2, -3),line(-3, -4, 2, -4),line(-3, 3, -3, -4),line(-2, 3, -2, -4),line(-1, 3, -1, -4),line(0, 3, 0, -4),line(1, 3, 1, -4),line(2, 3, 2, -4),locate(-3.5,2.75,1),locate(-3.5,1.75,2),locate(-3.5,0.75,3),locate(-3.5,-0.25,4),locate(-3.5,-1.25,5),locate(-3.5,-2.25,6),locate(-3.5,-3.25,7),locate(-2.55,3.5,1),locate(-1.55,3.5,2),locate(-0.55,3.5,3),locate(0.45,3.5,4),locate(1.45,3.5,5),
red( line(-3,3,2,2),line(-3,2,2,3) ),
blue( line(-3,2,-1,-4),line(-3,-4,-1,2) )
)
}}}
The final unshaded region is 6 units tall and 3 units across. 
There are 6*3 = 18 small rectangles in this unshaded region. 
This is out of 7*5 = 35 original small rectangles.
<font color=red>18/35</font> is the final answer. The fraction cannot be reduced since 18 and 35 do not have any common factors other than 1.


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A non-visual method.


Frank spends 1/7 his money on shoes. 
He has 1 - (1/7) = 6/7 of it remaining after buying the shoes.
Since he spends 2/5 of that on a shirt, he keeps 3/5 of that leftover portion.
(6/7)*(3/5) = (6*3)/(7*5) = <font color=red>18/35</font>


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An example


Let's say Frank starts with $350.
He spends (1/7)*350 = 50 dollars on shoes.
After buying the shoes, he would have 350-50 = 300 dollars.
(2/5)*300 = 120 dollars is spent on the shirt and his final leftover amount is 300-120 = 180 dollars.


Then 180/350 = (18*10)/(35*10) = <font color=red>18/35</font> is the fractional amount he has compared to the starting $350.


18/35 = 0.51429 = 51.429% approximately
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