document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1132092>Question 1132092</A>: <I><SPAN STYLE=\"word-break: break-all;\"> a)My maths teacher is dividing my class into groups. She makes two groups, each with a quarter of the class and three groups each with one-sixth of the class. How many are there in the class?<BR>\n" );
document.write( "b) My English teacher wants to divide our class into one half, one third and one ninth but the division will not go exactly. He borrows a boy from the class next door, does the division (which works out exactly, with a whole number of us in each group) and then sends him back. How many are there in the class?\r<BR>\n" );
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document.write( "Regards </SPAN>\n" );
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document.write( "(a) 2(1/4)+3(1/6) = 1, so all the students are in groups.  The number of students can be any number for which 1/4 of the students and 1/3 of the students are whole numbers.<br><BR>\n" );
document.write( "Since the least common multiple of 3 and 4 is 12, the number of students can be any multiple of 12.<BR>\n" );
document.write( "12 students = 2 groups of 3 and 3 groups of 2<BR>\n" );
document.write( "24 students = 2 groups of 6 and 3 groups of 4<BR>\n" );
document.write( "36 students = 2 groups of 9 and 3 groups of 6<BR>\n" );
document.write( "etc., etc....<br><BR>\n" );
document.write( "(b) 1/2 + 1/3 + 1/9 = 17/18.<br><BR>\n" );
document.write( "So the teacher borrows one boy from the other class to make 18.   Then 1/2 of 18 = 9; 1/3 of 18 = 6; and 1/9 of 18 = 2; 9+6+2 = 17.  Then the borrowed boy is sent back to his class.<br><BR>\n" );
document.write( "Since exactly 1 boy was borrowed; there is only one answer to this problem: your class has 17 students. </SPAN>\n" );
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