document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1209050>Question 1209050</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Frank spent 1/7 of his money on shoes and 2/5 of the remaining amount on a shirt. How much money does he have left in terms of a fraction of the original amount? </SPAN>\n" );
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document.write( "Answer: <font color=red>18/35</font>\r<BR>\n" );
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document.write( "Explanation\r<BR>\n" );
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document.write( "Draw a grid of rectangles that are 7 units tall and 5 units across.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%0D%0Adrawing%28400%2C400%2C-4%2C3%2C-5%2C4%2C%0D%0Aline%28-3%2C+3%2C+2%2C+3%29%2Cline%28-3%2C+2%2C+2%2C+2%29%2Cline%28-3%2C+1%2C+2%2C+1%29%2Cline%28-3%2C+0%2C+2%2C+0%29%2Cline%28-3%2C+-1%2C+2%2C+-1%29%2Cline%28-3%2C+-2%2C+2%2C+-2%29%2Cline%28-3%2C+-3%2C+2%2C+-3%29%2Cline%28-3%2C+-4%2C+2%2C+-4%29%2Cline%28-3%2C+3%2C+-3%2C+-4%29%2Cline%28-2%2C+3%2C+-2%2C+-4%29%2Cline%28-1%2C+3%2C+-1%2C+-4%29%2Cline%280%2C+3%2C+0%2C+-4%29%2Cline%281%2C+3%2C+1%2C+-4%29%2Cline%282%2C+3%2C+2%2C+-4%29%2Clocate%28-3.5%2C2.75%2C1%29%2Clocate%28-3.5%2C1.75%2C2%29%2Clocate%28-3.5%2C0.75%2C3%29%2Clocate%28-3.5%2C-0.25%2C4%29%2Clocate%28-3.5%2C-1.25%2C5%29%2Clocate%28-3.5%2C-2.25%2C6%29%2Clocate%28-3.5%2C-3.25%2C7%29%2Clocate%28-2.55%2C3.5%2C1%29%2Clocate%28-1.55%2C3.5%2C2%29%2Clocate%28-0.55%2C3.5%2C3%29%2Clocate%280.45%2C3.5%2C4%29%2Clocate%281.45%2C3.5%2C5%29%0D%0A%29%0D%0A ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "You can use graph paper or make your own grid. <BR>\n" );
document.write( "Another approach is to take a screenshot of a blank excel spreadsheet so you can use it in something like MS Paint.\r<BR>\n" );
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document.write( "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.\r<BR>\n" );
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document.write( "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.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%0D%0Adrawing%28400%2C400%2C-4%2C3%2C-5%2C4%2C%0D%0Aline%28-3%2C+3%2C+2%2C+3%29%2Cline%28-3%2C+2%2C+2%2C+2%29%2Cline%28-3%2C+1%2C+2%2C+1%29%2Cline%28-3%2C+0%2C+2%2C+0%29%2Cline%28-3%2C+-1%2C+2%2C+-1%29%2Cline%28-3%2C+-2%2C+2%2C+-2%29%2Cline%28-3%2C+-3%2C+2%2C+-3%29%2Cline%28-3%2C+-4%2C+2%2C+-4%29%2Cline%28-3%2C+3%2C+-3%2C+-4%29%2Cline%28-2%2C+3%2C+-2%2C+-4%29%2Cline%28-1%2C+3%2C+-1%2C+-4%29%2Cline%280%2C+3%2C+0%2C+-4%29%2Cline%281%2C+3%2C+1%2C+-4%29%2Cline%282%2C+3%2C+2%2C+-4%29%2Clocate%28-3.5%2C2.75%2C1%29%2Clocate%28-3.5%2C1.75%2C2%29%2Clocate%28-3.5%2C0.75%2C3%29%2Clocate%28-3.5%2C-0.25%2C4%29%2Clocate%28-3.5%2C-1.25%2C5%29%2Clocate%28-3.5%2C-2.25%2C6%29%2Clocate%28-3.5%2C-3.25%2C7%29%2Clocate%28-2.55%2C3.5%2C1%29%2Clocate%28-1.55%2C3.5%2C2%29%2Clocate%28-0.55%2C3.5%2C3%29%2Clocate%280.45%2C3.5%2C4%29%2Clocate%281.45%2C3.5%2C5%29%2C%0D%0Ared%28+line%28-3%2C3%2C2%2C2%29%2Cline%28-3%2C2%2C2%2C3%29+%29%2C%0D%0Ablue%28+line%28-3%2C2%2C-1%2C-4%29%2Cline%28-3%2C-4%2C-1%2C2%29+%29%0D%0A%29%0D%0A ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "The final unshaded region is 6 units tall and 3 units across. <BR>\n" );
document.write( "There are 6*3 = 18 small rectangles in this unshaded region. <BR>\n" );
document.write( "This is out of 7*5 = 35 original small rectangles.<BR>\n" );
document.write( "<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.\r<BR>\n" );
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document.write( "A non-visual method.\r<BR>\n" );
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document.write( "Frank spends 1/7 his money on shoes. <BR>\n" );
document.write( "He has 1 - (1/7) = 6/7 of it remaining after buying the shoes.<BR>\n" );
document.write( "Since he spends 2/5 of that on a shirt, he keeps 3/5 of that leftover portion.<BR>\n" );
document.write( "(6/7)*(3/5) = (6*3)/(7*5) = <font color=red>18/35</font>\r<BR>\n" );
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document.write( "An example\r<BR>\n" );
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document.write( "Let's say Frank starts with $350.<BR>\n" );
document.write( "He spends (1/7)*350 = 50 dollars on shoes.<BR>\n" );
document.write( "After buying the shoes, he would have 350-50 = 300 dollars.<BR>\n" );
document.write( "(2/5)*300 = 120 dollars is spent on the shirt and his final leftover amount is 300-120 = 180 dollars.\r<BR>\n" );
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document.write( "Then 180/350 = (18*10)/(35*10) = <font color=red>18/35</font> is the fractional amount he has compared to the starting $350.\r<BR>\n" );
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document.write( "18/35 = 0.51429 = 51.429% approximately<BR>\n" );
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