Evaluate
\frac{111}{8}=13.875
Factor
\frac{3 \cdot 37}{2 ^ {3}} = 13\frac{7}{8} = 13.875
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\begin{array}{l}\phantom{16)}\phantom{1}\\16\overline{)222}\\\end{array}
Use the 1^{st} digit 2 from dividend 222
\begin{array}{l}\phantom{16)}0\phantom{2}\\16\overline{)222}\\\end{array}
Since 2 is less than 16, use the next digit 2 from dividend 222 and add 0 to the quotient
\begin{array}{l}\phantom{16)}0\phantom{3}\\16\overline{)222}\\\end{array}
Use the 2^{nd} digit 2 from dividend 222
\begin{array}{l}\phantom{16)}01\phantom{4}\\16\overline{)222}\\\phantom{16)}\underline{\phantom{}16\phantom{9}}\\\phantom{16)9}6\\\end{array}
Find closest multiple of 16 to 22. We see that 1 \times 16 = 16 is the nearest. Now subtract 16 from 22 to get reminder 6. Add 1 to quotient.
\begin{array}{l}\phantom{16)}01\phantom{5}\\16\overline{)222}\\\phantom{16)}\underline{\phantom{}16\phantom{9}}\\\phantom{16)9}62\\\end{array}
Use the 3^{rd} digit 2 from dividend 222
\begin{array}{l}\phantom{16)}013\phantom{6}\\16\overline{)222}\\\phantom{16)}\underline{\phantom{}16\phantom{9}}\\\phantom{16)9}62\\\phantom{16)}\underline{\phantom{9}48\phantom{}}\\\phantom{16)9}14\\\end{array}
Find closest multiple of 16 to 62. We see that 3 \times 16 = 48 is the nearest. Now subtract 48 from 62 to get reminder 14. Add 3 to quotient.
\text{Quotient: }13 \text{Reminder: }14
Since 14 is less than 16, stop the division. The reminder is 14. The topmost line 013 is the quotient. Remove all zeros at the start of the quotient to get the actual quotient 13.
Examples
Quadratic equation
{ x } ^ { 2 } - 4 x - 5 = 0
Trigonometry
4 \sin \theta \cos \theta = 2 \sin \theta
Linear equation
y = 3x + 4
Arithmetic
699 * 533
Matrix
\left[ \begin{array} { l l } { 2 } & { 3 } \\ { 5 } & { 4 } \end{array} \right] \left[ \begin{array} { l l l } { 2 } & { 0 } & { 3 } \\ { -1 } & { 1 } & { 5 } \end{array} \right]
Simultaneous equation
\left. \begin{cases} { 8x+2y = 46 } \\ { 7x+3y = 47 } \end{cases} \right.
Differentiation
\frac { d } { d x } \frac { ( 3 x ^ { 2 } - 2 ) } { ( x - 5 ) }
Integration
\int _ { 0 } ^ { 1 } x e ^ { - x ^ { 2 } } d x
Limits
\lim _{x \rightarrow-3} \frac{x^{2}-9}{x^{2}+2 x-3}