Problem:
what is the explanation of 2 1/4 ÷ 1/6
Solution:
[tex] \red{2 \: \frac{1}{4} \div \frac{1}{6} = \frac{9}{4} \div \frac{1}{6} = \frac{9}{4} \times \frac{6}{1} = \frac{9}{2} \times \frac{3}{1} = \frac{27}{2} = } \green{ \boxed{13 \: \frac{1}{2} }}[/tex]
Checking:
1.
[tex] \green{13 \: \frac{1}{2} \times \frac{1}{6} = \frac{27}{2} \times \frac{1}{6} = \frac{9}{2} \times \frac{1}{2} = \frac{9}{4} = } \red{2 \: \frac{1}{4} }[/tex]
2.
[tex] \green{2 \: \frac{1}{4} \div 13 \: \frac{1}{2} = \frac{9}{4} \div \frac{27}{2} = \frac{9}{4} \times \frac{2}{27} = \frac{1}{2} \times \frac{1}{3} = } \red{ \frac{1}{6} }[/tex]
Final Answer:
[tex] \blue{ \boxed{ \boxed{13 \: \frac{1}{2} }}}[/tex]
Additional Knowledge:
To divide a mixed fraction by a proper fraction:
- Convert the mixed fraction into an improper fraction
- Find the reciprocal of the proper fraction
- Multiply the improper fraction by the reciprocal of the proper fraction
- Simplify the answer if the the answer wasn't in lowest term
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