$\displaystyle 18 \div \frac{1}{6} = \frac{18}{1} \div \frac{1}{6} = \frac{18}{1} \times \frac{6}{1} = 18 \times 6 = 108$

By order of operations, divide first. Since the divisor is a whole number, divide as is:

$\displaystyle 4.2 \div 14 = 0.3$

Add this quotient to 6.51.

$\displaystyle 6.51 + 4.2 \div 14 = 6.51 + 0.3$

Add vertically, aligning the decimal points (appending a zero to 0.3):

$\displaystyle 6.51$

$\displaystyle \underline{0.30}$

$\displaystyle 6.81$

By order of operations, divide first. Move the decimal point right two places in both dividend and divisor to make the divisor a whole number, and divide the resulting whole numbers:

$\displaystyle 6.4 \div 0.16 = 640 \div 16 = 40$

Add this quotient to 80.8: 

$\displaystyle 80.8 + 6.4 \div 0.16 = 80.8 + 40$

Append a decimal point and a zero to 40, align the decimal points, and add:

  $\displaystyle 80. 8$

  $\displaystyle \underline{40.0}$

$\displaystyle 120.8$

Rewrite this horizontally as a division expression, rewrite as a product, cross-cancel, and multply across:

$\displaystyle \dpi{150} \frac{\frac{3}{5}}{\frac{9}{20}}$ $\displaystyle = \frac{3}{5} \div \frac{9}{20} = \frac{3}{5} \cdot \frac{20}{9} = \frac{1}{1} \cdot \frac{4}{3} = \frac{4}{3}$

Rewrite this horizontally as a division expression, rewrite as a product, cross-cancel, and multply across:

$\displaystyle \frac{7\frac{1}{2}}{5 } = 7\frac{1}{2} \div 5 = \frac{15} {2} \div \frac{5}{1} = \frac{15} {2} \cdot \frac{1} {5}=\frac{3} {2} \cdot \frac{1} {1} =\frac{3} {2}$

Since $\displaystyle 3 \div 2 = 1 \textrm{ R }1$,

$\displaystyle \frac{3} {2} = 1 \frac{1} {2}$

Rewrite this horizontally as a division expression, rewrite as a product, cross-cancel, and finally multiply across:

$\displaystyle \frac{6}{4 \frac{1}{2}} = 6 \div 4 \frac{1}{2} = \frac{6}{1}\div \frac{9}{2}= \frac{6}{1}\cdot \frac{2}{9} = \frac{2}{1}\cdot \frac{2}{3} = \frac{2\cdot 2}{1\cdot 3} = \frac{4}{3}$

Since $\displaystyle 4 \div 3 = 1 \textrm{ R }3$,

$\displaystyle \frac{4}{3} = 1 \frac{1}{3}$,

which is the correct answer.

When dividing by a fraction between 0 and 1, the answer will always get larger. In this case it is larger than simply adding the two fractions together.

Simply use the long division process. The quotient will be: 

$\displaystyle 12 \div 64 = 0.01875$

Rewrite as a division and evaluate:

$\displaystyle \frac{4\frac{1}{2} }{\frac{3}{10}}$

$\displaystyle = 4\frac{1 }{2} \div \frac{3}{10}$

$\displaystyle = \frac{1 + 4 \times 2}{2} \div \frac{3}{10}$

$\displaystyle = \frac{9}{2} \div \frac{3}{10}= \frac{9}{2} \times \frac{10}{3}= \frac{3}{1} \times \frac{5}{1}= \frac{15}{1} = 15$

Rewrite as a division, then solve:

$\displaystyle \frac{5 \frac{1}{4}}{1 \frac{5}{9}}$

$\displaystyle = 5 \frac{1}{4} \div 1 \frac{5}{9}$

$\displaystyle = \frac{1 + 5 \times 4}{4} \div \frac{5 + 1 \times 9}{9}$

$\displaystyle = \frac{21}{4} \div \frac{14}{9}$

$\displaystyle = \frac{21}{4} \times \frac{9}{14}$

$\displaystyle = \frac{3}{4} \times \frac{9}{2}$

$\displaystyle = \frac{3 \times 9}{4 \times 2} = \frac{27}{8} = 3 \frac{3}{8}$