Evaluate
\frac{110}{7}\approx 15.714285714
Factor
\frac{2 \cdot 5 \cdot 11}{7} = 15\frac{5}{7} = 15.714285714285714
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\begin{array}{l}\phantom{14)}\phantom{1}\\14\overline{)220}\\\end{array}
Use the 1^{st} digit 2 from dividend 220
\begin{array}{l}\phantom{14)}0\phantom{2}\\14\overline{)220}\\\end{array}
Since 2 is less than 14, use the next digit 2 from dividend 220 and add 0 to the quotient
\begin{array}{l}\phantom{14)}0\phantom{3}\\14\overline{)220}\\\end{array}
Use the 2^{nd} digit 2 from dividend 220
\begin{array}{l}\phantom{14)}01\phantom{4}\\14\overline{)220}\\\phantom{14)}\underline{\phantom{}14\phantom{9}}\\\phantom{14)9}8\\\end{array}
Find closest multiple of 14 to 22. We see that 1 \times 14 = 14 is the nearest. Now subtract 14 from 22 to get reminder 8. Add 1 to quotient.
\begin{array}{l}\phantom{14)}01\phantom{5}\\14\overline{)220}\\\phantom{14)}\underline{\phantom{}14\phantom{9}}\\\phantom{14)9}80\\\end{array}
Use the 3^{rd} digit 0 from dividend 220
\begin{array}{l}\phantom{14)}015\phantom{6}\\14\overline{)220}\\\phantom{14)}\underline{\phantom{}14\phantom{9}}\\\phantom{14)9}80\\\phantom{14)}\underline{\phantom{9}70\phantom{}}\\\phantom{14)9}10\\\end{array}
Find closest multiple of 14 to 80. We see that 5 \times 14 = 70 is the nearest. Now subtract 70 from 80 to get reminder 10. Add 5 to quotient.
\text{Quotient: }15 \text{Reminder: }10
Since 10 is less than 14, stop the division. The reminder is 10. The topmost line 015 is the quotient. Remove all zeros at the start of the quotient to get the actual quotient 15.
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}