document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1186575>Question 1186575</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I would be grateful for any help her.  I am confused and not sure how to explain.  Thank you in advance.\r<BR>\n" );
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document.write( "When 2 fractions have the same denominator, we add or subtract them by keeping the same denominator & adding or subtracting the numerators.  Example:<BR>\n" );
document.write( "Patti says: We should add the tops AND the bottoms.  She shows you this picture to explain why:<BR>\n" );
document.write( "S _ _ _ _   + S S S _ _ =S _ _ _ _    <these are blocks but there isn't a way to <BR>\n" );
document.write( "                        S S S _ _     make blocks in here.  The S's mean that is<BR>\n" );
document.write( " a block that is shaded.  So according to Patti: 1/5 + 3/5 = 1+3 =4/10<BR>\n" );
document.write( "                                                             5+5<BR>\n" );
document.write( "Explain what is wrong with Patti's reasoning.  In your explanation use our definition of fractions (our definition of fractions is from Common Core State Standards)<BR>\n" );
document.write( " How could Patti use benchmark fractions to realize her answer is wrong? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #817519 by </B><A HREF=/tutors/aboutme.mpl?userid=MathLover1><B>MathLover1(20850)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=MathLover1><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/cgi-bin/show-face.mpl?user=MathLover1><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=817519\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <BR>\n" );
document.write( "a. Petti’s method is not valid because she added both denominators (which changes total) instead of keeping it <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=same ALIGN=MIDDLE  ALT=\"same\"   DISABLED_style= \"max-width:90%; height:auto;\" >, and add only numerators like this:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F5 ALIGN=MIDDLE  ALT=\"1%2F5\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3%2F5+ ALIGN=MIDDLE  ALT=\"3%2F5+\"   DISABLED_style= \"max-width:90%; height:auto;\" > have <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=same ALIGN=MIDDLE  ALT=\"same\"   DISABLED_style= \"max-width:90%; height:auto;\" > denominator, so \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F5%2B+3%2F5=%281%2B3%29%2F5=4%2F5 ALIGN=MIDDLE  ALT=\"1%2F5%2B+3%2F5=%281%2B3%29%2F5=4%2F5\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "b. how could Patti use estimation and benchmark fractions to see if her answer is reasonable?\r<BR>\n" );
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document.write( "Benchmark fractions are easy to visualize and identify, and thus, help in estimating the parts.(she can also count all green squares, total is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4 ALIGN=MIDDLE  ALT=\"4\"   DISABLED_style= \"max-width:90%; height:auto;\" >)\r<BR>\n" );
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document.write( "Benchmark fractions are especially helpful on number lines. \r<BR>\n" );
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document.write( " draw a number line, divide the distance from <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0 ALIGN=MIDDLE  ALT=\"0\"   DISABLED_style= \"max-width:90%; height:auto;\" > to<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+1+ ALIGN=MIDDLE  ALT=\"+1+\"   DISABLED_style= \"max-width:90%; height:auto;\" >into <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5 ALIGN=MIDDLE  ALT=\"5\"   DISABLED_style= \"max-width:90%; height:auto;\" > equal pieces, each of them represents <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F5 ALIGN=MIDDLE  ALT=\"1%2F5\"   DISABLED_style= \"max-width:90%; height:auto;\" > \r<BR>\n" );
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document.write( "staring from <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0 ALIGN=MIDDLE  ALT=\"0\"   DISABLED_style= \"max-width:90%; height:auto;\" >, go one step to the right (draw a vertical line at<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+1%2F5 ALIGN=MIDDLE  ALT=\"+1%2F5\"   DISABLED_style= \"max-width:90%; height:auto;\" >) and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3 ALIGN=MIDDLE  ALT=\"3\"   DISABLED_style= \"max-width:90%; height:auto;\" > more steps to the right (draw  second vertical line at <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4%2F5 ALIGN=MIDDLE  ALT=\"4%2F5\"   DISABLED_style= \"max-width:90%; height:auto;\" >)<BR>\n" );
document.write( "so, it’s easy to see that you are <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4%2F5 ALIGN=MIDDLE  ALT=\"4%2F5\"   DISABLED_style= \"max-width:90%; height:auto;\" > of unit away from zero\r<BR>\n" );
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document.write( " <TR><TD  ALIGN=MIDDLE>Solved by <A  rel=nofollow HREF=http://wiki.algebra.com/index.php/Tutoring_-_pluggable_solvers>pluggable</A> solver: <A  rel=nofollow HREF=addition_on_number_line.solver>SHOWS addition on the number line, positive and negative numbers</A></TD></TR>\n" );
document.write( "<TR><TD  ALIGN=LEFT>3/5 is a positive number. When you add it, it shifts the number to the right by 3/5 units.<BR>\n" );
document.write( "  This s a cartoon:<BR><BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%0D%0A++cartoon%28+%0D%0A++++number_line%28+400%2C+-10%2C+10%2C+1%2F5+%29%2C%0D%0A++++number_line%28+400%2C+-10%2C+10%2C+1%2F5%2C+1%2F5%2B3%2F5+%29++%0D%0A++%29%0D%0A++ ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ></TD></TR>\n" );
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document.write( "c. only using proper way, we will get correct answer<BR>\n" );
document.write( "Patti’s answer <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4%2F10 ALIGN=MIDDLE  ALT=\"4%2F10\"   DISABLED_style= \"max-width:90%; height:auto;\" > is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=incorrect ALIGN=MIDDLE  ALT=\"incorrect\"   DISABLED_style= \"max-width:90%; height:auto;\" >, when we simplify it we get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%2F5 ALIGN=MIDDLE  ALT=\"2%2F5\"   DISABLED_style= \"max-width:90%; height:auto;\" > (which would be correct only if she have <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3%2F5-1%2F5 ALIGN=MIDDLE  ALT=\"3%2F5-1%2F5\"   DISABLED_style= \"max-width:90%; height:auto;\" >) \r<BR>\n" );
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document.write( " </SPAN>\n" );
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