Question

dividing fractions maze
beginning at \start\, find each quotient in simplest form to find your way through the maze. show all work!
start
\\(\frac{2}{3} \div \frac{3}{10}\\) \\(\frac{3}{8} \div \frac{3}{4}\\) \\(\frac{3}{10} \div \frac{2}{5}\\) \\(\frac{7}{12} \div \frac{3}{10}\\)
\\(2 \frac{2}{9}\\) \\(\frac{1}{3}\\) \\(\frac{3}{25}\\)
\\(\frac{1}{5}\\) \\(\frac{9}{32}\\) \\(\frac{3}{4}\\) \\(1 \frac{17}{18}\\)
\\(\frac{8}{9} \div \frac{5}{9}\\) \\(\frac{8}{15} \div \frac{3}{20}\\) \\(\frac{5}{16} \div \frac{30}{44}\\) \\(\frac{14}{15} \div \frac{49}{50}\\)
\\(\frac{40}{81}\\) \\(3 \frac{5}{9}\\) \\(\frac{27}{24}\\)
\\(\frac{4}{25}\\) \\(1 \frac{1}{6}\\) \\(\frac{20}{34}\\) \\(\frac{343}{375}\\)
\\(\frac{8}{12} \div \frac{2}{10}\\) \\(\frac{11}{12} \div \frac{33}{42}\\) \\(\frac{21}{27} \div \frac{7}{81}\\) the end
\\(3 \frac{1}{3}\\) \\(\frac{1}{4}\\) 9
name:
created by carrie wiederholz for flip 4 mat

Explanation:

Step1: Start with first fraction division

To divide fractions, multiply by the reciprocal:
$\frac{2}{3} \div \frac{3}{10} = \frac{2}{3} \times \frac{10}{3} = \frac{20}{9} = 2\frac{2}{9}$
Move to the box connected to $2\frac{2}{9}$: $\frac{8}{9} \div \frac{5}{9}$

Step2: Calculate second division

Multiply by reciprocal, simplify:
$\frac{8}{9} \div \frac{5}{9} = \frac{8}{9} \times \frac{9}{5} = \frac{8}{5} = 1\frac{3}{5}$
Move to the box connected to $1\frac{3}{5}$: $\frac{8}{12} \div \frac{2}{10}$

Step3: Calculate third division

Simplify fractions first, then multiply by reciprocal:
$\frac{8}{12} = \frac{2}{3}$, so $\frac{2}{3} \div \frac{2}{10} = \frac{2}{3} \times \frac{10}{2} = \frac{10}{3} = 3\frac{1}{3}$
Move to the box connected to $3\frac{1}{3}$: $\frac{11}{12} \div \frac{33}{42}$

Step4: Calculate fourth division

Simplify fractions, multiply by reciprocal:
$\frac{33}{42} = \frac{11}{14}$, so $\frac{11}{12} \div \frac{11}{14} = \frac{11}{12} \times \frac{14}{11} = \frac{14}{12} = \frac{7}{6} = 1\frac{1}{6}$
Move to the box connected to $1\frac{1}{6}$: $\frac{8}{15} \div \frac{3}{20}$

Step5: Calculate fifth division

Multiply by reciprocal, simplify:
$\frac{8}{15} \div \frac{3}{20} = \frac{8}{15} \times \frac{20}{3} = \frac{160}{45} = \frac{32}{9} = 3\frac{5}{9}$
Move to the box connected to $3\frac{5}{9}$: $\frac{5}{16} \div \frac{30}{44}$

Step6: Calculate sixth division

Simplify fractions, multiply by reciprocal:
$\frac{30}{44} = \frac{15}{22}$, so $\frac{5}{16} \div \frac{15}{22} = \frac{5}{16} \times \frac{22}{15} = \frac{110}{240} = \frac{11}{24}$
Move to the box connected to $\frac{11}{24}$: $\frac{7}{12} \div \frac{3}{10}$

Step7: Calculate seventh division

Multiply by reciprocal, simplify:
$\frac{7}{12} \div \frac{3}{10} = \frac{7}{12} \times \frac{10}{3} = \frac{70}{36} = \frac{35}{18} = 1\frac{17}{18}$
Move to the box connected to $1\frac{17}{18}$: $\frac{14}{15} \div \frac{49}{50}$

Step8: Calculate eighth division

Simplify fractions, multiply by reciprocal:
$\frac{14}{15} \div \frac{49}{50} = \frac{14}{15} \times \frac{50}{49} = \frac{700}{735} = \frac{20}{21}$
Move to the box connected to $\frac{20}{21}$: $\frac{21}{27} \div \frac{7}{81}$

Step9: Calculate final division

Simplify fractions, multiply by reciprocal:
$\frac{21}{27} = \frac{7}{9}$, so $\frac{7}{9} \div \frac{7}{81} = \frac{7}{9} \times \frac{81}{7} = 9$
Move to the box connected to 9: THE END

Answer:

The path through the maze is:

1. $\boldsymbol{\frac{2}{3} \div \frac{3}{10} = 2\frac{2}{9}}$
2. $\boldsymbol{\frac{8}{9} \div \frac{5}{9} = 1\frac{3}{5}}$
3. $\boldsymbol{\frac{8}{12} \div \frac{2}{10} = 3\frac{1}{3}}$
4. $\boldsymbol{\frac{11}{12} \div \frac{33}{42} = 1\frac{1}{6}}$
5. $\boldsymbol{\frac{8}{15} \div \frac{3}{20} = 3\frac{5}{9}}$
6. $\boldsymbol{\frac{5}{16} \div \frac{30}{44} = \frac{11}{24}}$
7. $\boldsymbol{\frac{7}{12} \div \frac{3}{10} = 1\frac{17}{18}}$
8. $\boldsymbol{\frac{14}{15} \div \frac{49}{50} = \frac{20}{21}}$
9. $\boldsymbol{\frac{21}{27} \div \frac{7}{81} = 9}$
10. THE END