For example, if you are calculating 7÷34{\displaystyle 7\div {\frac {3}{4}}}, you would first change 7{\displaystyle 7} to 71{\displaystyle {\frac {7}{1}}}.
For example, the inverse of 34{\displaystyle {\frac {3}{4}}} is 43{\displaystyle {\frac {4}{3}}}.
For example, 71×43=283{\displaystyle {\frac {7}{1}}\times {\frac {4}{3}}={\frac {28}{3}}}
For example, 283{\displaystyle {\frac {28}{3}}} simplifies to the mixed number 913{\displaystyle 9{\frac {1}{3}}}.
For example, if you are calculating 5÷34{\displaystyle 5\div {\frac {3}{4}}}, you would draw 5 circles.
For example, if you are dividing by 34{\displaystyle {\frac {3}{4}}}, the 4 in the denominator tells you to divide each whole shape into fourths.
For example, if you are dividing 5 by 34{\displaystyle {\frac {3}{4}}}, you would color 3 quarters a different color for each group. Note that many groups will contain 2 quarters in one whole, and 1 quarter in another whole.
For example, you should have created 6 groups of 34{\displaystyle {\frac {3}{4}}} among your 5 circles.
For example, after dividing the 5 shapes into groups of 34{\displaystyle {\frac {3}{4}}}, you have 2 quarters, or 24{\displaystyle {\frac {2}{4}}} left. Since a whole group is 3 pieces, and you have 2 pieces, your fraction is 23{\displaystyle {\frac {2}{3}}}.
For example, 5÷34=623{\displaystyle 5\div {\frac {3}{4}}=6{\frac {2}{3}}}.
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}.
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}}}.
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}}}.
