document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=6167>Question 6167</A>: <I><SPAN STYLE=\"word-break: break-all;\"> how to write algebraic expression?  ex;<BR>\n" );
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document.write( "    7 less than 4 times a number<BR>\n" );
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document.write( "    11 more than half a number\r<BR>\n" );
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document.write( "     5 mmore than the product of a number and 3\r<BR>\n" );
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document.write( "     1/2 the difference of a number and 15\r<BR>\n" );
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document.write( "    I had this in my algebra test last month but I can't remember how to do it nor can I find it in my algebra book. Im a mom helping a child tonight but we are stumped. also im stuck on (reciprocals) 9/8, -3y/5, -2.45 and last but not least (solve) -t/12=2/3, 9a-7a=4 ???? thank you in advance for any help you provide<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #3279 by </B><A HREF=/tutors/aboutme.mpl?userid=glabow><B>glabow(165)</B></A><img src=\"/images/stars/stars-09.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=glabow><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=3279\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> You have three questions here. Here goes ---<BR>\n" );
document.write( "Sometimes it helps to rephrase the word problem in the opposite order.<BR>\n" );
document.write( "7 less than 4 times a number is the same as: a number times 4, less 7.<BR>\n" );
document.write( "This is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4x-7 ALIGN=MIDDLE  ALT=\"4x-7\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "11 more than half a number is the same as: half a number and 11 more.<BR>\n" );
document.write( "This is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2F2%2B11 ALIGN=MIDDLE  ALT=\"x%2F2%2B11\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Can you now write 5 more than the product of a number and 3, which is the same as the product of a number and 3 and 5 more?\r<BR>\n" );
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document.write( "A reciprocal of a number is a second number such that when the two numbers are multiplied the answer is 1. The reciprocal of 7 is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F7 ALIGN=MIDDLE  ALT=\"1%2F7\"   DISABLED_style= \"max-width:90%; height:auto;\" >. The reciprocal of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F7 ALIGN=MIDDLE  ALT=\"1%2F7\"   DISABLED_style= \"max-width:90%; height:auto;\" > is 7. Why? Because <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+%281%29%281%2F7%29=1 ALIGN=MIDDLE  ALT=\"+%281%29%281%2F7%29=1\"   DISABLED_style= \"max-width:90%; height:auto;\" > In fact, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%29%281%2Fx%29=1 ALIGN=MIDDLE  ALT=\"%28x%29%281%2Fx%29=1\"   DISABLED_style= \"max-width:90%; height:auto;\" >. So most people just say, the reciprocal of a number is 1 divided by the number. Dividing by a fraction is the same as multiplying by the reciprocal of the fraction. The general rule is reverse the numerator and the denominator and multiply. So 1 divided by a fraction is the same as 1 multiplied by the fraction \"turned upside down.\" In general, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F%28x%2Fy%29=%281%29%28y%2Fx%29 ALIGN=MIDDLE  ALT=\"1%2F%28x%2Fy%29=%281%29%28y%2Fx%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "But be careful! 0 has no reciprocal! So watch out for things like <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+1%2F%280%2F9%29 ALIGN=MIDDLE  ALT=\"+1%2F%280%2F9%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "There is no such thing as division by zero.<BR>\n" );
document.write( "To answer your question, the first number 9/8 has the reciprocal 8/9. And so on.\r<BR>\n" );
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document.write( "Your third question asks to find t when <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-t%2F12=2%2F3 ALIGN=MIDDLE  ALT=\"-t%2F12=2%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "You multiply both sides by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-12 ALIGN=MIDDLE  ALT=\"-12\"   DISABLED_style= \"max-width:90%; height:auto;\" > which is<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28-12%29%28-t%2F12%29=%28-12%29%282%2F3%29 ALIGN=MIDDLE  ALT=\"%28-12%29%28-t%2F12%29=%28-12%29%282%2F3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=12t%2F12=-24%2F3 ALIGN=MIDDLE  ALT=\"12t%2F12=-24%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t=-8 ALIGN=MIDDLE  ALT=\"t=-8\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Look closely at that first part <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28-12%29%28-t%2F12%29 ALIGN=MIDDLE  ALT=\"%28-12%29%28-t%2F12%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "That's <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28-12%29%28-1%2F12%29t ALIGN=MIDDLE  ALT=\"%28-12%29%28-1%2F12%29t\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "See the reciprocals? </SPAN>\n" );
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