Evaluate
\frac{111}{14}\approx 7.928571429
Factor
\frac{3 \cdot 37}{2 \cdot 7} = 7\frac{13}{14} = 7.928571428571429
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\begin{array}{l}\phantom{14)}\phantom{1}\\14\overline{)111}\\\end{array}
Use the 1^{st} digit 1 from dividend 111
\begin{array}{l}\phantom{14)}0\phantom{2}\\14\overline{)111}\\\end{array}
Since 1 is less than 14, use the next digit 1 from dividend 111 and add 0 to the quotient
\begin{array}{l}\phantom{14)}0\phantom{3}\\14\overline{)111}\\\end{array}
Use the 2^{nd} digit 1 from dividend 111
\begin{array}{l}\phantom{14)}00\phantom{4}\\14\overline{)111}\\\end{array}
Since 11 is less than 14, use the next digit 1 from dividend 111 and add 0 to the quotient
\begin{array}{l}\phantom{14)}00\phantom{5}\\14\overline{)111}\\\end{array}
Use the 3^{rd} digit 1 from dividend 111
\begin{array}{l}\phantom{14)}007\phantom{6}\\14\overline{)111}\\\phantom{14)}\underline{\phantom{9}98\phantom{}}\\\phantom{14)9}13\\\end{array}
Find closest multiple of 14 to 111. We see that 7 \times 14 = 98 is the nearest. Now subtract 98 from 111 to get reminder 13. Add 7 to quotient.
\text{Quotient: }7 \text{Reminder: }13
Since 13 is less than 14, stop the division. The reminder is 13. The topmost line 007 is the quotient. Remove all zeros at the start of the quotient to get the actual quotient 7.
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}