How many times does 12{\displaystyle {\frac {1}{2}}} go into 8{\displaystyle 8}?  Since the problem is asking how many groups of 12{\displaystyle {\frac {1}{2}}} are in 8, the problem is one of division. Turn 8 into a fraction by placing it over 1: 8=81{\displaystyle 8={\frac {8}{1}}}. Find the reciprocal of the fraction by reversing the numerator and denominator: 12{\displaystyle {\frac {1}{2}}} becomes 21{\displaystyle {\frac {2}{1}}}. Multiply the two fractions together: 81×21=161{\displaystyle {\frac {8}{1}}\times {\frac {2}{1}}={\frac {16}{1}}}. Simplify, if necessary: 161=16{\displaystyle {\frac {16}{1}}=16}. 16÷58{\displaystyle 16\div {\frac {5}{8}}}.  Convert 16 into a fraction by placing it over 1: 16=161{\displaystyle 16={\frac {16}{1}}}. Take the fraction’s reciprocal by reversing the numerator and denominator: 58{\displaystyle {\frac {5}{8}}} becomes 85{\displaystyle {\frac {8}{5}}}. Multiply the two fractions together: 161×85=1285{\displaystyle {\frac {16}{1}}\times {\frac {8}{5}}={\frac {128}{5}}}. Simplify, if necessary: 1285=2535{\displaystyle {\frac {128}{5}}=25{\frac {3}{5}}}. Rufus has 9 cans of food. She eats 23{\displaystyle {\frac {2}{3}}} of a can every day. How many days will her food last?  Draw 9 circles representing the 9 cans. Since she eats 23{\displaystyle {\frac {2}{3}}} at a time, divide each circle into thirds. Color groups of 23{\displaystyle {\frac {2}{3}}}. Count the number of complete groups. There should be 13. Interpret the leftover pieces. There is 1 piece leftover, which is 13{\displaystyle {\frac {1}{3}}}. Since a whole group is 23{\displaystyle {\frac {2}{3}}}, you have half a group left over. So, your fraction is 12{\displaystyle {\frac {1}{2}}}. Combine the number of whole groups and fractional groups to find your final answer: 9÷23=1312{\displaystyle 9\div {\frac {2}{3}}=13{\frac {1}{2}}}.
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